Editor-in-Chief : V.K. Rastogi
ASIAN JOURNAL OF PHYSICS
An International Peer Reviewed Research Journal
Frequency : Monthly,
ISSN : 0971 – 3093
Editor-In-Chief (Hon.) :
Dr. V.K. Rastogi
e-mail:[email protected]
[email protected]
AJP | ISSN : 0971 – 3093 Vol 25, No 9, September, 2016 |
25th Anniversary Year of AJP-2016
Special issue
on
Advances in High Precision Spectroscopy and Tests of Fundamental Physics, Part-1
Edited by
Bijaya Kumar Sahoo
Asian Journal of Physics
(A Publication Not for Profit)
Vol. 25, No 9 (2016)
CONTENTS
Guest Editorial
About the Guest Editor
Prospect of molecular clocks
Masatoshi Kajita
1051
Oscillation frequencies for simultaneous trapping of heteronuclear alkali atoms
Kiranpreet Kaur, B K Sahoo and Bindiya Arora
1061
Singly charged ions for optical clocks
N Batra, A Roy, S Majhi, S Panja and S De
1069
Permanent EDM measurement in Cs using nonlinear magneto-optic rotation
Harish Ravi, Mangesh Bhattarai, Abhilash Y D, Ummal Momeen* and Vasant Natarajan
1093
Precise many-electron calculations of isotope shift for alkali like atoms or ions
Sourav Roy, Anal Bhowmik and Sonjoy Majumder
1103
Energy level crossing of highly charged ions for optical clocks
Yan-mei Yu and Bing-bing Suo
1119
The magnetic moment of the bound electron
G Werth and S Sturm
1143
Computational methods for high-precision spectroscopy of three-electron atomic systems
Liming Wang, Chun Li, and Zong-Chao Yan
1161
Precision measurements based on 40Ca+ ion optical frequency standards
Hua Guan, Yao Huang, Cheng-bin Li, Li-yan Tang, and Ke-lin Gao
1207
Precision physics with molecules
Amar C Vutha
1233
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1051-1059 |
Prospect of molecular clocks
Masatoshi Kajita
National Institute of Information and Communications Technology
Koganei, Tokyo 184-8795, JAPAN
While uncertainties of some of the atomic transition frequencies have been reduced to the level of 10–8, the molecular transition frequencies are currently diffcult to be measured with the uncertainty below 10–15. This is mainly because of the complicated energy levels of the molecules having the vibrational-rotational states. This paper lists some molecular transition frequencies, which can be measured with the uncertainties lower than 10–16. © Anita Publications. All rights reserved.
Keywords: Precise measurement, Cold molecules, Molecular ion
Total Refs : 45
1. Hasegawa A, Fukuda K, Kajita M, Ito H, Kumagai M, Hosokawa M, Morikawa T, Metrologia, 41(2004)257-263.
2. Heavner T P, Donley E A, Levi F, Costanzo G, Parker T E, Shirley J H, Ashby N, Barlow S, Jefferts S R, Metrologia, 51 (2005)174-182.
3. Diddams S, Jones D, Ye J, Cundiff S T, Hall J L, Ranka J, Windeler R, Holzwarth R, Udem T, Hänsch T, Phys Rev Lett, 84(2000)5102-5105.
4. Dehmelt H, IEEE Trans Instrum Meas, 31(1982)83-87.
5. Chou C W, Hume D B, Koelemeij J C J, Wineland D J, Rosenband T, Phys Rev Lett, 104(2010) 070802-070806.
6. Huntemann N, Sanner C, Lipphardt B, Tamm Chr, Peik E, Phys Rev Lett, 116(2016)063001-063006.
7. Ushijima I, Takamoto M, Das M, Ohkubo T, Katori H, Nature Photo, 9(2015)185-189.
8. Nicholson T, Cambell S, Hutson R, Marti G, Bloom B, McNally R, Zhang W, Barrett M, Saonova M, Strouse G, Tew W, Ye J, Nature Communications, 6(2015)6896; doi:10.1038/ncomms7896.
9. Rosenband T, Hume D B, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A , Swan W C, Newbery N R, Itano W M , Wineland D J, Bergquist J C, Science,319(2008)1808-1812.
10. Godun R M, Nisbet-Jones P B R, Jones J M, King S A, Johnson L A M, Margolis H S, Szymaniec K, SLea S N, Bongs K, Gill P,Phys Rev Lett, 113(2014)210801; doi.org/10.1103/PhysRevLett.113.210801
11. Huntemann N, Lipphardt B, Tamm Chr, Gerginov V, Weyers S, Peik E, Phys Rev Lett, 113(2014)210802; doi.org/10.1103/PhysRevLett.113.210802
12. Hong F.-L, Onae A, Jiang J, Guo R, Inaba H, Minoshima K, Schibli T R, Matsumoto H, Nakagawa K, Opt Lett, 28(2003)2324-2326.
13. Shelkovnikov A, Butcher R J, Chardonnet C, Amy-Klein A, Phys Rev Lett, 100(2008)150801; http://dx.doi. org/10.1103/PhysRevLett.100.150801.
14. Weinstein J D, deCarvalho R, Guillet T, Friedrich B, Doyle J M, Nature (London), 395(1998)148-150.
15. Bethlem H L, Berden G, Crompvoets F M H, Jongma R T, van Roij A J A, Meijer G, Nature, 406(2000)491-494.
16. Crompvoets F M H, Bethlem H L, Jongma R T, Meijer G, Nature, 411(2001)174-176.
17. Norrgard E B, McCarron D J, Steinecker M H, Tarbutt M R, DeMille D, Phys Rev Lett, 116(2016)063004, 1-6; doi: 10.1103/PhysRevLett.116.063004.
18. Prehn A, Ibruegger M, Gloeckner R, Rempe G, Zeppenfeld M, Phys Rev Lett, 116(2016)063005, 1-6. doi: 10.1103/ PhysRevLett.116.063005
19. Fioretti A, Amiot C, Dion C M, Dulieu O, Mazzoni M, Smirne G, Gabbanini C, Euro Phys J D, 15(20001)189-198.
20. Ulmanis J, Deiglmayr J, Repp M, Wwester R, Weidemueller M, Chem Rev, 112(2012)4890-4927.
21. Donley E A, Claussen N R, Thomson S T, Wieman C E , Nature (London), 417(2002)529-533.
22. Aikawa K, Akamatsu D, Hayashi M, Oasa K, Kobayashi J, Naidon P, Kishimoto T, Ueda M, Inouye S, Phys Rev Lett, 105(2010)203001, 1-4;
doi: 10.1103/PhysRevLett.105.203001
23. Ni K.–K, Ospelkaus S, de Miranda M H G, Pèer A, Neyenhuis B, Zierbel J J, Kotochigova S, Julienne P S, Jin D S, Ye J, Science, 322(2008)231-235.
24. Koelemeij J C J, Roth B, Wicht A, Ernsting I, Schiller S, Phys Rev Lett, 98(2007)173002, 1-4; doi:10.1103/ PhysRevLett.98.173002.
25. Kajita M, Moriwaki Y, J Phys B: At Mol Opt Phys, 42(2009)154022, 1-6; doi:10.1088/0953-4075/42/15/154022
26. Kajita M, Abe M, Hada M, Moriwaki Y, J Phys B: At Mol Opt Phys, 44(2011)02540, 1-7; doi: 10.1088/0953-4075/44/2/025402
27. Schneider T, Roth B, Dunker H, Ersting I, Schiller S, Nature Phys, 6(2010)275-278.
28. Schmidt P O, Rosenband T, Langer C, Itano W M, Bergquist J C, Wineland D J, Science, 309(2005)749-752.
29. Yudin V I, Taichenachev A V, Oates C W, Barber Z W, Lemke N D, Ludlow A D, Sterr U, Lisdat Ch, Riehle F, Phys Rev A, 82 (2010) 011804 (R) 1-4;
doi: 10.1103/PhysRevA.82.011804.
30. Hobson R, Bowden W, King S A, Baird P E, Hill I R, Gill P, Phys Rev A, 93(2016)010501 (R) 1-5; doi: 10.1103/ PhysRevA.93.010501
31. Kajita M, Abe M, J Phys B: At Mol Opt Phys, 45(2012)185401, 1-5; doi:10.1088/0953-4075/45/18/185401.
32. Khanyile N B, Shu G, Brown K, Nature Communications, 6(2015)7825; doi:10.1038/ncomms8825.
33. Kajita M, Gopakumar G, Abe M, Keller M, Phys Rev A , 89(2014)032509,1-6; doi: 10.1103/ PhysRevA.89.032509
34. Mur-Petit J, Garcia-Ripoll J J, Perez-Rios J, Compos-Martinez J, Hernandez M I, Willitsch S, Phys Rev A, 85 (2012)022308,
1-8; doi:10.1103/PhysRevA.85.022308
35. Germann M, Tong X, Willitsch S, Nature Phys, 10(2014)820-824.
36. Kajita M, Phys Rev A, 92(2015)043423, 1-6; doi: 10.1103/PhysRevA.92.043423
37. Zelevinsky T, Kotochigova S, Ye J, Phys Rev Lett, 100(2008)043201, 1-4; doi: 10.1103/PhysRevLett.100.043201
38. Kotochigova S, Zelevinsky T, Ye J, Phys Rev A, 79(2009)012504, 1-7; doi: 10.1103/PhysRevA.79.012504
39. Kajita M, Gopakumar G, Abe M, Hada M, Phys Rev A, 84(2011022507, 1-6; doi: 10.1103/PhysRevA.84.022507
40. Kajita M, Gopakumar G, Abe M, Hada M, J Phys B: At Mol Opt Phys, 46(2013)025001, 1-5; doi: 10.1088/0953- 4075/46/2/025001
41. Ivanova M, Stein A, Pashov A, Stolyarov A V, Knoeckel H, Tiemann E, J Chem. Phys, 135(2011)174303, 1-10; doi:10.1063/1.3652755.
42. Krois G, Pototshinig J V, Lackner F, Ernst W, J Phys Chem A, 117(2013)13719-13731; doi: 10.1021/jp407818k
43. Hara H, Takasu Y, Yamaoka Y, Doyle J M, Takahashi Y, Phys Re Lett, 106(2011)205304, 1-4; doi: 10.1103/ PhysRevLett.106.205304
44. Kajita M, Gopakumar G, Abe M, Hada M, J Mol Spectrosc, 300 (2014)99-107.
45. Biesheuvel J, Karr J -Ph, Hilico L, Eikema K S E, Ubachs W, Koelemeij J C J, Nature Com, 7(2016)10385, 1-7; doi:10.1038/ncomms10385
Prospect of molecular clocks.pdf
Masatoshi Kajita
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1061-1068 |
Oscillation frequencies for simultaneous trapping of heteronuclear alkali atoms
Kiranpreet Kaura, B K Sahoob and Bindiya Aroraa*
aDepartment of Physics, Guru Nanak Dev University, Amritsar, Punjab-143 005, India
bTheoretical Physics Division, Physical Research Laboratory, Navrangpura, Ahemadabad-380 009, India
We investigate oscillation frequencies for simultaneous trapping of more than one type of alkali atoms in a common optical lattice. For this purpose, we present numerical results for “magic” trapping conditions, where the oscillation frequencies for two different kinds of alkali atoms using laser lights in the wavelength range 500-1200 nm are same. These wavelengths will be of immense interest for studying static and dynamic properties of boson-boson, boson-fermion, fermion-fermion, and boson-boson-boson mixtures involving different isotopes of Li, Na, K, Rb, Cs and Fr alkali atoms. In addition to this, we were also able to locate a magic wavelength around 808.1 nm where all the three Li, K, and Rb atoms are found to be suitable for oscillating at the same frequency in a common optical trap.
Total Refs: 53
1. Annual Review of Cold Atoms and Molecules, (eds) K. WMadison, Y. Wang, A. M. Rey, K. Bongs, Vol. 1. (World Scientific Publication), 2013.
2. BlochI , Nature Phys, 1, (2005) 23.
3. Inouye S, J. Goldwin J, Olsen M L, Ticknor C, Bohn J L, Jin D S, Phys. Rev. Lett, 93(2004), 183201.
4. P. P. Orth, D. L. Bergman, and K. L. Hur, Phys. Rev. A 80, 023624 (2009).
5. F. Schreck, L. Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, and C. Salomon, Phys. Rev. Lett. 87, 080403 (2001).
6. Z. Hadzibabic, C. A. Stan, K. Dieckmann, S. Gupta, M. W. Zwierlein, A. Gorlitz, and W. Ketterle, Phys. Rev. Lett. 88, 160401 (2002).
7. G. Modugno, G. Roati, F. Riboli, F. Ferlaino, R. J. Brecha, and M. Inguscio, Science 297, 2240 (2002).
8. C. A. Stan, M. W. Zwierlein, C. H. Schunck, S. M. F. Raupach, and W. Ketterle, Phys. Rev. Lett. 93, 143001 (2004).
9. C. Ebner and D. Edwards, Phys. Rep. 2C, 77 (1970).
10. K. Mølmer, Phys. Rev. Lett. 80, 1804 (1998).
11. E.Timmermans and R.Cˆot´e, Phys. Rev. Lett. 80, 3419 (1998).
12. R. Ejnisman, P. Rudy, N. P. Bigelow, P. S. P. Cardona, A. M. Tuboy, D. M. B. P. Milori, V. S. Bagnato, and I. D. Goldman, Braz. J. Phys. 27, 247 (1997).
13. M. S. Safronova, B. Arora, and C. W. Clark, Phys. Rev. A 73, 022505 (2006).
14. B. K. Sahoo and B. Arora, Phys. Rev. A 87, 023402 (2013).
15. B. Arora and B. K. Sahoo, Phys. Rev. A 86, 033416 (2012).
16. U. Dammalapati, K. Harada, and Y. SakemiPhys. Rev. A 93, 043407 (2016).
17. U. Schloder, H. Engler, U. Schunemann, R. Grimm, and M. Weidmuller, Eur. Phys. J. D 7, 331-340 (1999).
18. M.S. Santos, P. Nussenzveig, L.G. Marcassa, K. Helmerson, J. Fleming, S.C. Zilio, and V.S. Bagnato, Phys. Rev. A 52, R4340 (1995).
19. J.P. Shaffer, W. Chapulpczak, and N.P. Bigelow, Phys. Rev. Lett. 82, 1124 (1999).
20. B. K. Sahoo, D. K. Nandy, B. P. Das and Y. Sakemi, Phys. Rev. A 91, 042507 (2015).
21. B. K. Sahoo, Phys. Rev. A 92, 052506 (2015).
22. B. K. Sahoo and B. P. Das, Phys. Rev. A 92, 052511 (2015).
23. Y. Sakemi, K. Harada, T. Hayamizu, M. Itoh, H. Kawamura, S.Liu, H. S. Nataraj, A. Oikawa, M. Saito, T. Sato, H. P. Yoshida,T. Aoki, A. Hatakeyama, T. Murakami, K. Imai, K. Hatanaka,T.Wakasa, Y. Shimizu, and M. Uchida, J. Phys.: Conf. Ser. 302,012051 (2011).
24. E. Gomez, S. Aubin, G. D. Sprouse, L. A. Orozco and D. P. DeMille, Phys. Rev. A 75, 033418 (2007).
25. C. Ekstr¨om, L. Robertsson, and A. Ros´en, PhysicaScripta34, 624 (1986).
26. J. E. Simsarian, W. Z. Zhao, L. A. Orozco, and G. D. Sprouse, Phys. Rev. A 59, 195 (1999).
27. J. E. Simsarian, L. A. Orozco, G. D. Sprouse, and W. Z. Zhao, Phys. Rev. A 57, 2448 (1998).
28. S. Aubin, E. Gomez, L. A. Orozco, and G. D. Sprouse, Phys. Rev. A 70, 042504 (2004).
29. E. Gomez, L. A. Orozco, A. P. Galvan, and G. D. Sprouse, Phys. Rev. A 71, 062504 (2005).
30. R. Collister, G. Gwinner, M. Tandecki, J. A. Behr, M. R. Pearson, J. Zhang, L. A. Orozco, S. Aubin, E. Gomez, Fr PNC Collaboration, et al., Phys. Rev. A 90, 052502 (2014).
31. S. Sanguinetti et al., Opt. Lett. 34, 893 (2009).
32. B. K. Sahoo, T. Aoki, B. P. Das and Y. Sakemi, Phys. Rev. A 93, 032520 (2016).
33. Sahoo B K, J Phys B, 43(2010)085005.
34. Dzuba V A, FlambaumV V, Sushkov O P, Phys Rev A, 51, 3454 (1995).
35. M. Marinescu, D. Vrinceanu, and H. R. Sadeghpour, Phys Rev A, 58, R4259 (1998).
36. M. S. Safronova, W. R. Johnson, and A. Derevianko, Phys Rev A , 60, 4476 (1999).
37. M. S. Safronova and W. R. Johnson, Phys Rev A , 62, 022112 (2000).
38. Mukherjee D, Sahoo B K, Nataraj H S, Das B P, J Phys Chem A, 113(2009)12549.
39. M. Taglieber, A. –C. Voigt, T. Aoki, and K. Dieckmann, Phys Rev Lett, 100, 010401 (2008).
40. B. Arora, D. K. Nandy, and B. K. Sahoo, Phys. Rev. A 85, 012506 (2012).
41. U. Volz and H. Schmoranzer, Phys. Scr. T 65, 48 (1996).
42. R. J. Rafac, C. E. Tanner, A. E. Livingston and H. G. Berry, Phys. Rev. A 60, 3648 (1999).
43. J. Kaur, D. K. Nandy, B. Arora and B. K. Sahoo, Phys. Rev. A 91, 012705 (2015).
44. L.-Y. Tang, Z.-C. Yan, T.-Y. Shi, and J. Mitroy, Phys. Rev. A 81, 042521 (2010).
45. A. J. Thakkar and C. Lupinetti, Chem. Phys. Lett 402, 270 (2005).
46. U. I. Safronova, W. R. Johnson, and M. S. Safronova, Phys. Rev. A 76, 042504 (2007).
47. J. Mitroy and M. W. J. Bromley,Phys. Rev. A 68, 052714 (2003).
48. A. Borschevsky, V. Pershina, E. Eliav, and U. Kaldor, J. Chem. Phys. 138, 124302 (2013).
49. A. Derevianko, W. R. Johnson, M. S. Safronova, and J. F. Babb, Phys. Rev. Lett. 82, 3589 (1999).
50. A. Miffre, M. Jacquey, M. B¨uchner, G. Trenec, and J. Vigue, Eur. Phys. J. D 38, 353 (2006).
51. C. R. Ekstrom, J. Schmiedmayer, M. S. Chapman, T. D. Hammond, and D. E. Pritchard, Phys. Rev. A 51, 3883 (1995).
52. W. F. Holmgren, M. C. Revelle, V. P. A. Lonij, and A. D. Cronin,Phys. Rev. A 81, 053607 (2010).
53. Amini J M, Gould H, Phys Rev Lett, 91(2003), 153001
Oscillation frequencies for simultaneous trapping of heteronuclear alkali atoms.pdf
Kiranpreet Kaur, B K Sahoo and Bindiya Arora
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1069-1092 |
Singly charged ions for optical clocks
N Batra1,2, A Roy2, S Majhi2, S Panja1,2 and S De1,2
1Academy of Scientic and Innovative Research (AcSIR),
CSIR- National Physical Laboratory (CSIR-NPL) Campus, New Delhi, India
2CSIR-National Physical Laboratory, Dr. K. S. Krishnan Marg, New Delhi-110012, India.
In modern era atomic clocks are the most accurate instruments given by the scientific community which use State-of-the-Art cooling and trapping technologies. Atomic clocks at the optical frequencies are new addition in the last one decade which provide 1s accuracy over the age of the universe. Neutral atoms in optical lattices and single ion in a Paul trap are the two well established techniques for optical frequency standards. In this article we focus on the atomic ions optical frequency standards. Recent worldwide developments, different choice of the species and associated dominant systematics have been discussed in this review. © Anita Publications. All rights reserved.
Keywords: Atomic clocks, Frequency standards, Optical frequency standards, Optical lattice, Ion trap, Systematic shifts, Precision measurement.
Total Refs: 150
1. Taylor B N, The International System of Units (SI) (U.S. Government Printing Oce, Gaithersburg, Maryland), 2001.
2. Heavner T P, Donley E A, Levi F, Costanzo G, Parker T E, Shirley J H, Ashby N, Barlow S, Jeerts S R, Metrologia, 51(2014)174-182.
3. Turyshev S G, From Quantum to Cosmos: Fundamental Physics Research in Space, (World Scientic, Singapore), 2009.
4. Morhr P J, Newell D B, Taylor B N, CODATA Recommended Values of the Fundamental Physical Constants: 2014, doi: org/10.5281/zenodo.22826 (2015).
5. Morhr P J, Taylor B N, Rev Mod Phys, 72(2000)351; doi:org/10.1103/RevModPhys.72.351
6. Wense L V, Seiferle B, Laatiaoui M, Neumayr J B, Maier H J, Wirth H F, Mokry C, Runke J, Eberhardt K, Düllmann C E, Trautmann N G, Thirolf P G, Nature, 533(2016)47; doi:10.1038/nature17669
7. Katori H, Ido T, Gonokami M K, J Phys Soc Jpn, 68(1999)2479-2482.
8. McKeever J, Buck J R, Boozer A D, Kuzmich A, Nagerl H C, Kurn D M S, Kimble H J, Phys Rev Lett, 90(2003)133602; doi.org/10.1103/PhysRevLett.90.133602.
9. A D Ludlow, Boyd M M, Ye J, Peik E, Schmidt P O, Rev Mod Phys, 87(2015)637; doi:org/10.1103/RevModPhys.87.637
10. Katori H, Takamoto M, Palchikov V G, OvsiannikovV D, Phys Rev Lett, 91(2003)s173005; doi:org/10.1103/PhysRevLett.91.173005.
11. Dehmelt H G, IEEE Trans Instrum Meas, 31(1982)83-87.
12. Takamoto M, Katori H, Phys Rev Lett, 91(2003)223001; doi:org/10.1103/PhysRevLett.91.223001.
13. Ludlow A D, Boyd M M, Zelevinsky T, Foreman S M, Blatt S, Notcutt M, Ido T, Ye J, Phys Rev Lett, 96, (2006)033003; doi: 10.1103/PhysRevLett.96.033003.
14. Baillard X, Fouche M, Targat R Le, Westergaard P G, Lecallier A, Coq Y Le, Rovera G D, Bize S, Lemonde P, Opt Lett, 32(2007)1812; doi:org/10.1364/OL.32.001812.
15. Akatsuka T, Takamoto M, Katori H, Nat Phys, 4(2008)954; doi:10.1038/nphys1108
16. Ludlow A D, Zelevinsky T, Campbell G K, Blatt S, Boyd M M, de Miranda M H G, Martin M J, Thomsen J W, Foreman S M, Ye J, Fortier T M, Stalnaker J E, Diddams S A, Le Coq Y, Barber Z W, Poli N, Lemke N D, Beck K M, Oates C W, Science, 319(2008)1805; doi: 10.1126/science.1153341
17. Yamaguchi A, Fujieda M, Kumagai M, Hachisu H, Nagano S, Li Y, Ido T, Takano T, Takamoto M, Katori H, Appl Phys Express, 4(2011)082203; doi:org/10.1143/APEX.4.082203
18. Falke S, Schnatz H, Winfred J S R V, Middelmann T, Vogt S, Weyers S, Lipphardt B, Grosche G, Riehle F, Sterr U, Lisdat C, Metrologia, 48(2011)399; doi:org/10.1088/0026-1394/48/5/022
19. Hong F-L, Musha M, Takamoto M, Inaba H, Yanagimachi S, Takamizawa A, Watabe K, Ikegami T, Imae M, Fujii Y, Amemiya M, Nakagawa K, Ueda K, Katori H, Opt Lett, 34(2009)692; doi:org/10.1364/OL.34.000692.
20. Ushijima I, Takamoto M, Das M, Ohkubo T, Katori H, Nature Photonics, 9(2015)185; doi:10.1038/nphoton.2015.5
21. Porsev S G, Derevianko A, Fortson E N, Phys Rev A, 69(2004)021403(R); doi:org/10.1103/PhysRevA.69.021403.
22. Park C Y, Yoon T H, Phys Re A, 68(2003)055401; doi:org/10.1103/PhysRevA.68.055401.
23. Maruyama R, Wynar R H, Romalis M V, Andalkar A, Swallow M D, Pearson C E, Fortson E N, Phys Rev A, 68(2003)011403; doi:org/10.1103/PhysRevA.68.011403 .
24. Hoyt C W, Barber Z W, Oates C W, Fortier T M, Diddams S A, Hollberg L, Phys Rev Lett, 95(2005)083003; doi: 10.1103/PhysRevLett.95.083003.
25. Kohno T, Yasuda M, Hosaka K, Inaba H, Nakajima Y, Hong F L, Appl Phys Express, 2(2009)072501; doi:org/10.1143/APEX.2.072501.
26. Nevsky A Y, Bressel U, Ernsting I, Eisele C, Okhapkin M, Schiller S, Gubenko A, Livshits D, Mikhrin S, Krestnikov I, Kovsh A, Appl Phys B, 92(2008)501; doi:10.1007/s00340-008-3113-4.
27. Pizzocaro M, Costanzo G, Godone A, Levi F, Mura A, Zoppi M, Calonico D, IEEE Trans Ultrason Ferroelectr.Freq Control, 59(2012)426; doi:10.1109/TUFFC.2012.2211
28. Beloy K P, Hinkley N M, Phillips N B, Sherman J A, Schioppo M, Lehman J H, Feldman A D, Hanssen L M, Oates C W, Ludlow A D, Phys Rev Lett,113 (2014)260801; doi:org/10.1103/PhysRevLett.113.260801
29. Hachisu H, Miyagishi K, Porsev S, Derevianko A, Ovsiannikov V, Palćhikov V, Takamotoand M, Katori H, Phys Rev Lett, 100(2008)053001; doi: org/10.1103/PhysRevLett.100.053001
30. Yi L, Mejri S, McFerran J J, Coq Y Le, Bize S, Phys Rev Lett, 106(2011)073005; doi:org/10.1103/PhysRevLett.106.073005.
31. Yamanaka K, Ohmae N, Ushijima I, Takamoto M, Katori H, Phys Rev Lett, 114(2015)230801; doi: 10.1103/PhysRevLett.114.230801.
32. De S, Batra N, Chakraborty S, Panja S, Sen Gupta A, Curr Sci, 106(2014)1348-1352.
33. Wineland D J, Dehmelt H, Bull Am Phys Soc, 20(1975)637.
34. Hänsch T W, Schawlow A L, Opt Comm, 13(1975)68-69.
35. Wineland D, Drullinger R E, Walls F L, Phys Rev Lett, 40(1978)1639; doi:org/10.1103/PhysRevLett.40.1639
36. Neuhauser W, Hohenstatt M, Toschek P, Dehmelt H, Phys Rev Lett, 41(1978)233; doi:org/10.1103/PhysRevLett.41.233
37. Neuhauser W, Hohenstatt M, ToschekP E, Dehmelt H, Phys Rev A, 22(1980)1137; doi:org/10.1103/PhysRevA.22.1137
38. Wineland D J, Itano W M, Phys Lett A, 82(1981)75-78.
39. Stenholm S, Rev Mod Phys, 58(1986)699; doi:org/10.1103/RevModPhys.58.699
40. Paul W, Raether M, Z Physik 140(1955)262; doi:10.1007/BF01328923.
41. Raizen M G, Gilligan J M, Bergquist J C, Itano W M, Wineland D J, Phys Rev A, 45(1992)6493; doi:org/10.1103/PhysRevA.45.6493.
42. Rastogi A, Batra N, Roy A, Thangjam J, Kalsi V P S, Panja S, De S, Mapan, 30(2015)169-174; doi:10.1007/
s12647-015-0140-6
43. Schrama C A, Peik E, Smith W W, Walther H, Opt Comm, 101(1993)32-36.
44. Dehmelt H G, Toschek P, Bull Am Phys Soc [2],, 20(1975)61; https://arxiv.org/pdf/1407.3493.pdf.
45. Dehmelt H G, Walther H, Bull Am Phys Soc, 20(1975)61; https://arxiv.org/pdf/1407.3493.pdf.
46. Chou C W, Hume D B, Koelemeij J C J, Wineland D J, Rosenband T, Phys Rev Lett, 104(2010)070802; doi: org/10.1103/PhysRevLett.104.070802.
47. Rosenband T, Hume D B, Schmidt P O, Chou C W, Brusch A, Lorini L, Oskay W H, Drullinger R E, Fortier T M, Stalnaker J E, Diddams S A, Swann W C, Newbury N R, Itano W M, Wineland D J, Bergquist J C, Science, 319(2008)1808-1812.
48. Larson D J, Bergquist J C, Bollinger J J, Itano W M, Wineland D J, Phys Rev Lett, 57(1986)70; doi:org/10.1103/PhysRevLett.57.70.
49. Wubbena J B, Amairi S, Mandel O, Schmidt P O, Phys Rev A, 85(2012)043412; doi:org/10.1103/PhysRevA.85.043412.
50. Cirac J I, Zoller P, Phys Rev Lett, 74 (1995)4091; doi:org/10.1103/PhysRevLett.74.4091.
51. Barton P A, Donald C J S, Lucas D M, Stevens D A, Steane A M, Stacey D N, Phys Rev A, 62(2000)032503; doi: org/10.1103/PhysRevA.62.032503
52. Chwalla M, Benhelm J, Kim K, Kirchmair G, Monz T, Riebe M, Schindler P, Villar A S, Hänsel W, Roos C F, Blatt R, Abgrall M, Santarelli G, Rovera G D, Laurent Ph, Phys Rev Lett, 102(2009)023002; doi:org/10.1103/PhysRevLett.102.023002.
53. Guan H, Huang Y, Liu Pei-Liang, Bian W, Shao H, Gao Ke-Lin, Chinese Physics B, 24(2015)0542131-05421314.
54. KeLin G, Chinese Sci Bull, 58(2013)853; doi:10.1007/s11434-012-5646-5
55. Huang Y, Cao J, Liu P, Liang K, Ou B, Guan H, Huang X, Li T, Gao K, Phys Rev A, 85(2012)030503; doi: org/10.1103/PhysRevA.85.030503
56. Matsubara K, Hachisu H, Li Y, Nagano S, Locke C, Nogami A, Kajita M, Hayasaka K, Ido T, Hosokawa M, Opt Express, 20(2012)22034; doi: 10.1364/OE.20.022034.
57. Matsubara K, Hayasaka K, Li Y, Ito H, Nagano S, Kajita M, Hosokawa M, Appl Phys Express, 1 (2008)067011; doi: org/10.1143/APEX.1.067011.
58. Benhelm J, Kirchmair G, Rapol U, Korber T, Roos C F, Blatt R, Phys Rev A, 75(2007)032506; doi:org/10.1103/PhysRevA.75.032506
59. Kajita M, Li Y, Matsubara K, Hayasaka K, Hosokawa M , Phys Rev A, 72(2005)043404; doi.org/10.1103/PhysRevA.72.043404
60. Champenois C, Houssin M, Lisowski C, Knoop M, G. Hagel G, M. Vedel, Vedel F, Phys Lett A, 331(2004)298; doi:org/10.1016/j.physleta.2004.09.008.
61. Boshier M G, Barwood G P, Huang G, Klein H A, Appl Phys B, 71(2000)51-56.
62. Margolis H S, Barwood G P, Huang G, Klein H A, Lea S N, Szymaniec K, Gill P, Science, 306(2004)1355;doi: 10.1126/science.1105497
63. Dube P, Madej A A, Bernard J E, Marmet L, Boulanger J S, Cundy S , Phys Rev Lett, 95(2005)033001; doi: org/10.1103/PhysRevLett.95.033001
64. Dube P, Madej A A, Zhou Z, Bernard J E, Phys. Rev. A, 87(2013)023806; doi:org/10.1103/PhysRevA.87.023806
65. Becker T, Zanthier J, Nevsky A, Schwedes C, Skvortsov M, Walther H, Peik E, Phys Rev A, 63(2001)051802(R); doi:org/10.1103/PhysRevA.63.051802
66. Zanthier J V, Eichenseer M, Nevsky A Yu, Okhapkin M, Schwedes Ch, Walther H, Laser Phys, 15(2005)1021-1027.
67. Peik E, Hollemann G, Walther H, Phys Rev A, 49(1994)402; doi.org/10.1103/PhysRevA.49.402.
68. Peik E, Hollemann G, Walther H, Phys Scr, T59, 403 (1995).; doi.org/10.1088/0031-8949/1995/T59/055
69. Sherman J, Trimble W, Metz S, Nagourney W, Fortson N, in 2005 Digest of the LEOS Summer Topical Meetings, (IEEE), New York, 2005, p. 99; doi: 10.1109/LEOSST.2005.1528012
70. Pyka K, Herschbach N, Keller J, Mehlstaübler T E, Appl Phys B, 114(2014)231; doi: 10.1007/s00340-013-5580-5.
71. Li Y, Ohtsubo N, Matsubara K, Nagano S, Hayasaka K, in Conference on Precision Electromagnetic Measurements (CPEM 2014), Rio de Janeiro, 2014, p 60.
72. Liu T, Wang Y H, Elman V, Stejskal A, Zhao Y N, Zhang J, Lu Z H, Wang L J, Dumke R, Becker Th, Walther H,Frequency Control Symposium, (2007) Joint with the 21st European Frequency and Time Forum. IEEE International; doi: 10.1109/FREQ.2007.4319107.
73. Ramsey N F, Molecular Beams, (Oxford Univ. Press, London), 1956.
74. Appasamy B, Siemers I, Stalgies Y, Eschner J, Blatt R , Neuhauser W, Toschek P E, Appl Phys B, 60(1995)473; doi:10.1007/BF01081329
75. Nagourney W, Yu N, Dehmelt H, Opt Comm, 793(1990)176; doi:org/10.1016/0030-4018(90)90031-N
76. Yu N, Zhao X, Dehmelt H, Nagourney W, Phys Rev A, 50(1994)2738; doi:org/10.1103/PhysRevA.50.2738.
77. Kleczewski A, Homan M R, Sherman J A, Magnuson E, Blinov B B, Fortson E N, Phys Rev A, 85(2012)043418; doi:org/10.1103/PhysRevA.85.043418
78. Koerber T W, Schacht M H, Hendrickson K R G, Nagourney W, Fortson E N, Phys Rev Lett, 88(2002)143002; org/10.1103/PhysRevLett.88.143002
79. Sherman J A, Koerber T W, Markhotok A, Nagourney W, Fortson E N, Phys Rev Lett, 94(2005)243001; org/10.1103/PhysRevLett.94.243001
80. Fortson N, Phys Rev Lett, 70(1993)2383; doi:org/10.1103/PhysRevLett.70.2383
81. Koerber T W, Schacht M, Nagourney W, Fortson E N, J Phys B: Mol Opt Phys, 36(2003)637; doi.org/10.1088/0953-4075/36/3/320
82. Sahoo B K, Chaudhuri R, Das B P, Mukherjee D, Phys Rev Lett, 96(2006)163003; doi:org/10.1103/PhysRevLett.96.163003
83. Whitford B G, Siemsen K J, Madej A, Sankey J D, Opt Lett, 19(1994)356-358.
84. Tamm C, Huntemann N, Lipphardt B, Gerginov V, Nemitz N, Kazda M, Weyers S, Peik E, Phys Rev A, 89(2014)023820; doi:org/10.1103/PhysRevA.89.023820.
85. King S A, Godun R M, Webster S A, Margolis H S, Johnson L A M, Szymaniec K, Baird P E G, Gill P, New J Phys, 14(2012)013045; doi:org/10.1088/1367-2630/14/1/013045.
86. Huntemann N, Okhapkin M, Lipphardt B, Weyers S, Tamm Chr, Peik E, Phys Rev Lett, 108(2012)090801; doi: org/10.1103/PhysRevLett.108.090801.
87. Huntemann N, Sanner B, Lipphardt B, Tamm Chr, Peik E, Phys Rev Lett, 116(2016)063011;doi: 10.1103/PhysRevLett.116.063001.
88. Hinkley N, Sherman J A, Phillips N B, Schioppo M, Lemke N D, Beloy K, Pizzocaro M, Oates C W, Ludlow A D, Science, 341(2013)1215-1218.
89. Barrett M D, New J Phys, 17(2015)053024; doi:org/10.1088/1367-2630/17/5/053024
90. Arnold K, Hajiyev E, Paez E, Lee C H, Barret M D, Bollinger J, Phys Rev A, 92(2015)032108; doi: 10.1103/PhysRevA.92.032108.
91. Paez E, Arnold K J, Hajiyez E, Barrett M D, Phys Rev A, 93(2016)042112; doi: 10.1103/PhysRevA.93.042112.
92. Arin B S, Lutetium Ion Spectroscopy, Thesis, National University of Singapore, (2014).
93. Barrett M D (private communication).
94. Kozlov A, Dzuba V A, Flambaum V V, Phys Rev A, 90(2014)042505; doi:org/10.1103/PhysRevA.90.042505
95. Oskay W, Itano W, Bergquist J, Phys Rev Lett, 94(2005)163001; doi:org/10.1103/PhysRevLett.94.163001
96. Oskay W H, Diddams S A, Donley E A, Fortier T M, Heavner T P, Hollberg L, Itano W M, Jefferts S R, Delaney M J, Kim K, Levi F, Parker T E, Bergquist J C, Phys Rev Lett, 97(2006)020801; doi:org/10.1103/PhysRevLett.97.020801
97. Itano W M, J Res Natl Inst Stand Technol, 105(2000)829-837.
98. Berkeland D J, Miller J D, Bergquist J C, Itano W M, Wineland D J, J Appl Phys, 83(1998)10; doi:org/10.1063/1.367318.
99. Stalnaker J E, Diddams S A, Fortier T M, Kim K, Hollberg L, Bergquist J C, Itano W M, Delany M J, Lorini L, Oskay W H, Heavner T P, Jeerts S R, Levi F, Parker T E, Shirley J, Appl Phys B, 167(2007)89; doi:10.1007/s00340-007-2762-z.
100. Versolato O O, Wansbeek L W, Jungmann K, Timmermans R G E, Willmann L, Wilschut H W, Phys Rev A, 83(2011)043829; doi: org/10.1103/PhysRevA.83.043829
101. Versolato O O, Giri G S, van den Berg J E, Böll O, Dammalapati U, van der Hoek D J, Hoekstra S, Jungmann K, Kruithof W L, Müller S, Nuñez Portela M, Onderwater C J G, Santra B, Timmermans R G E, Wansbeek L W, Willmann L, Wilschut H W, Phys Lett A, 375(2011)3130-3134.
102. Versolato O O, Giri G S, Wansbeek L W, van den Berg J E, van der Hoek D J, Jungmann K, Kruithof W L, Onderwater C J G, Sahoo B K, Santra B, Shidling P D, Timmermans R G E, Willmann L, Wilschut H W, Phys Rev A, 82(R) (2010)010501(R); doi.org/10.1103/PhysRevA.82.010501.
103. Giri G S, Versolato O O, van den Berg J E, Böll O, Dammalapati U, van der Hoek D J, Jungmann K, Kruithof W L, Müller S, Portela M Nuñez, Onderwater C J G, Santra B, Timmermans R G E, Wansbeek L W, Willmann L, Wilschut H W, Phys Rev A, 84(2011)020503(R); doi:org/10.1103/PhysRevB.84.020503
104. Dzuba V A, Flambaum V V, Phys Rev A, 61(2000)034502; doi:org/10.1103/PhysRevA.61.034502.
105. Versolato O O, Wansbeek L W, Giri G S et al, Berg J E van den, Hoek D J van der, Jungmann K, Kruithof W L, Onderwater L C J G, Sahoo, B K, Santra B, Shidling P D, Timmermans R G E, Willmann L, Wilschut H W, Hyperfine Interact, 9(2011)199; doi:10.1007/s10751-011-0296-6.
106. Wansbeek L W, Sahoo B K , Timmermans R G E, Jungmann K, Das B P, Mukherjee D, Phys Rev A, 78(2008)050501R; doi.org/10.1103/PhysRevA.78.050501
107. Portela M N, Dijck E A, Mohanty A, Bekker H, van den Berg J E, Giri G S, S. Hoekstra S, Onderwater C J G, Schlesser S, Timmermans R G E, Versolato O O, Willmann L, Wilschut H W, Jungmann K, Appl Phys B, 114(2014)173-182; doi: 10.1007/s00340-013-5603-2.
108. Dicke R H, Phys Rev, 89(1953)472; doi.org/10.1103/PhysRev.89.472
109. Riehle F, Frequency Standards: Basics and Applications, (Wiley-VCH Verlag GmbH Co. KGaA), 2004.
110. Gill P, Metrologia, 42(2005)S125; doi:org/10.1088/0026-1394/42/3/S13
111. Sobelman I I , Atomic Spectra and Radiative Transitions, (Springer-Verlag, Berlin), 1979.
112. Edmonds A R, Angular Momentum in Quantum Mechanics, (Princeton Univ. Press, New Jersey), 1974.
113. Batra N, Sahoo B K, De S, Chinese Phys B, 25(2016)113703; doi:org/10.1088/1674-1056/25/11/113703.
114. Schneider T, Peik E, Tamm C, Phys Rev Lett, 94(2005)230801;doi:org/10.1103/PhysRevLett.94.230801
115. Gabrielse G, Hanneke D, Kinoshita T, Nio M, Odom B, Phys Rev Lett, 97(2006)030802;doi: org/10.1103/PhysRevLett.97.030802
116. Farajollahi H, Salehi A, JCAP02(2012)041; doi:org/10.1088/1475-7516/2012/02/041
117. Chou C W, Hume D B, Rosenband T, Wineland D J, Science, 329(2010)1630-1633.
118. Vutha A C, New J Phys, 17(2015)6; doi.org/10.1088/1367-2630/17/6/063030
119. Blatt S, Ludlow A D, Campbell G K, Thomsen J W, Zelevinsky T, Boyd M M, Ye J, Baillard X, Fouché M, Targat R Le, Brusch A, Lemonde P, Takamoto M, Hong F.-L, Katori H, Flambaum V V, Phys Rev Lett, 100(2008)140801; doi: org/10.1103/PhysRevLett.100.140801.
120. Wolf P, Bordé Ch J, Clairon A, Duchayne L, Landragin A, Lemonde P, Santarelli G, Ertmer W, Rasel E, Cataliotti F S, Inguscio M, Tino G M, Gill P, Klein H, Reynaud S, Salomon C, Peik E, Bertolami O, Gil P, Páramos J, Jentsch C, Johann U, Rathke A, Bouyer P, Cacciapuoti L, Izzo D, Natale P De, Christophe B, Touboul P, Turyshev S G, Anderson J, Tobar M E, Schmidt-Kaler F, Vigué J, Madej A A, Marmet L, Angonin M.-C, Delva P, Tourrenc P, Metris G, Müller H, Walsworth R, Lu Z H, Wang L J, Bongs K, Toncelli A, Tonelli M, Dittus H, Lämmerzahl C, Galzerano G, Laporta P, Laskar J, Fienga A, Roques F, Sengstock K, Exp Astron, 23(2009)551-687.
121. Dzuba V A, Flambaum V V, Safronova M S, Porsev S G, Pruttivarasin T, M A, Häffner H, Nature Phys, 12 (2016) 465-468; doi: 10.1038/nphys3610
122. Margolis H S, Contemporary Phys, 51(2010)37; doi:10.1080/00107510903257616
123.Friebe J, Riedmann M, Wübbena T, Pape A, Kelkar H, Ertmer W, Terra O, Sterr U, Weyers S, Grosche G, Schnatz H, Rasel E M, New J Phys, 13(2011)125010; doi:10.1088/1367-2630/13/12/125010
124. Kulosa A P, Fim D, Zipfel K H, Rühmann S, Sauer S, Jha N, Gibble K, Ertmer W, Rasel E M, Safronova M S, Safronova U I, Porsev S G, Phys Rev Lett, 115(2015)240801; doi: org/10.1103/PhysRevLett.115.240801
125. Degenhardt C, Stoehr H, Lisdat C, Wilpers G, Schnatz H, Lipphardt B, Phy Rev A, 72(2005)062111; doi.org/10.1103/PhysRevA.72.062111
126. Wilpers G, Oates C W, Diddams S A, Bartels A, Fortier T M, Oskay W H, Bergquist J C, Jefferts S R, Heavner T P, Parker T E, Hollberg L, Metrologia, 44(2007)146; doi:10.1088/0026-1394/44/2/005
127. Campbell G K, Ludlow A D, Blatt S, Thomsen J W, Martin M J, de Miranda M H G, Zelevinsky T, Boyd M M, Ye J, Diddams S A, Heavner T P, Parker T E, Jefferts S R, Metrologia, 45(2008)539; doi:org/10.1088/0026-1394/45/5/008
128. Nicholson T L, Campbell S L, Hutson R B, Marti G E, Bloom B J, McNally R L, Zhang W, Barrett M D, Safronova M S, Strouse G F, Tew W L, Ye J, Nat Comm, 6(2015)6896; doi: 10.1038/ncomms/7896.
129. Targat R Le, Lorini L, Coq Y Le, Zawada M, Guéna J, Abgrall M, Gurov M, Rosenbusch P, Rovera D G, Nagórny B, Gartman R, Westergaard P G, Tobar M E, Lours M, Santarelli G, Clairon A, Bize S, Laurent P, Lemonde P, J. Lodewyck J, Nat Comm, 4(2013)2109; doi: 10.1038/ncomms3109
130. Falke S, Lemke N, Grebing C, Lipphardt B, Weyers S, Gerginov V, Huntemann N, Hagemann C, Al-Masoudi A, Häfner S, Vogt S, Sterr U, Lisdat C, New J Phys, 16(2014)073023; doi.org/10.1088/1367-2630/16/1/013015;
131. Hachisu H, Fujieda M, Nagano S, Gotoh T, Nogami A, Ido T, Falke St, Huntemann N, Grebing C, Lipphardt B, Lisdat Ch, Piester D, Opt Lett, 39(2014)4072-4075.
132. Akamatsu D, Inaba H, Hosaka K, Yasuda M, Onae T, Suzuyama T, Amemiya M, Hong F, Appl Phys Express, 7 (2014)012401; doi.org/10.7567/APEX.7.012401.
133. Katori H in OSA Technical Digest (online) of Conference on Lasers and Electro-Optics, (CLEO 2015), San Jose, 2015, Optical Society of America, paper SF1L.1.
134. Lemke N D, Ludlow A D, Barber Z W, Fortier T M, Diddams S A, Jiang Y, Jefferts S R, Heavner T P, Parker T E, Oates C W, Phys Rev Lett, 103(2009)063001; doi:org/10.1103/PhysRevLett.103.063001
135. Akamatsu D, Yasuda M, Inaba H, Hosaka K, Tanabe T, Onae A, Hong F, Opt Express, 22(2014)7898-7905.
136. Park C Y, Yu Dai-Hyuk, Lee Won-Kyu, Park Sang Eon, Kim Eok Bong, Lee Sun Kyung, Cho Jun Woo, Yoon Tai Hyun, Mun Jongchul,
Park Sung Jong, Kwon Taeg Yong, Lee Sang-Bum, Metrologia, 50(2013)119; doi: org/10.1088/0026-1394/50/2/119
137. Yu D H, Lee S, Lee W K, Park C Y, Park S E, Heo M S, Mun J, Lee S B, Kwon T Y, in Proceedings of Conference on Precision Electromagnetic Measurements (CPEM 2014), Rio de Janeiro, 2014, p. 668.
138. McFerran J J, Yi L, Mejri S, Di Manno S, Zhang W, Guena J, Le Coq Y, Bize S, Phys Rev Lett, 108(2012)
183004;doi: org/10.1103/PhysRevLett.108.183004
139. Barwood G P, Huang G, Klein H A, Johnson L A M, King S A, Margolis S, Szymaniec K, Gill P , Phys Rev A, 89(2014)050501(R); doi: doi.org/10.1103/PhysRevA.89.050501
140. Wang Y H, Liu T, Dumke R, Stejskal A, Zhao Y N, Zhang J, Lu Z H, Wang L J, Becker Th, Walther H, Laser Phys, 17(2007)1017-1024.
141. Godun R, Nisbet-Jones P, Jones J, King S, Johnson L, Margolis H, Szymaniec K, Lea S, Bongs K, Gill P, Phys Rev Lett, 113(2014)210801; doi: org/10.1103/PhysRevLett.113.210801
142. Tommaseo G, Pfeil T, Revalde G, Werth G, Indelicato P, Desclaux J P, Eur Phys Journal: D, 25(2003)113-121.
143. Roos C F, Chwalla M, Kim K, Riebe M, Blatt R, Nature, 443(2006)316-319.
144. Barwood G P, Gill P, Huang G, Klein H A, in Conference on Precision Electromagnetic Measurements (CPEM 2012), Washington DC, 2012, p. 270.
145. Jiang D, Arora B, Safronova M S, Clark C W, J Phys B, 42(2009)154020; doi: org/10.1088/0953-4075/42/15/154020.
146. Barwood G P, Margolis H S, Huang G, Gill P, Klein H, Phys Rev Lett, 93(2004)133001; doi:org/10.1103/PhysRevLett.93.133001
147. Meggers W F, Res J Natl Bur Stand, 71A(1967)396-544.
148. Rosenband T, Schmidt P O, Hume D B, Itano W M, Fortier T M, Stalnaker J E, Kim K, Diddams S A,Koelemeij J C J, Bergquist J C, Wineland D J, Phys Rev Lett, 98(2007)220801; doi:org/10.1103/PhysRevLett.98.220801
149. Safronova M S, M. G. Kozlov, C.W. Clark, Phys Rev Lett, 107(2011)143006; /doi.org/10.1103/PhysRevLett.107.143006
150. Dube P, Madej A A, Tibbo M, Bernard J E, Phys Rev Lett, 112(2014)173002; doi: org/10.1103/PhysRevLett.112.173002
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1093-1101 |
Permanent EDM measurement in Cs using nonlinear magneto-optic rotation
Harish Ravi, Mangesh Bhattarai, Abhilash Y D, Ummal Momeen* and Vasant Natarajan
Department of Physics, Indian Institute of Science, Bangalore-560 012, India
*School of Advanced Sciences, VIT University, Vellore 632 014, India
We use the technique of chopped nonlinear magneto-optic rotation (NMOR) at room temperature in 133Cs vapor cell to measure the permanent electric dipole moment (EDM) in the atom. The cell has paraffin coating on the walls to increase the relaxation time. The signature of the EDM is a shift in the Larmor precession frequency which is correlated with the application of an E field. We analyze errors in the technique, and show that the main source of systematic error is the appearance of a longitudinal B field when the E field is applied. This error can be eliminated by doing measurements on the two ground hyperfine levels. Using an E field of 2.6 kV/cm, we place an upper limit on the electron EDM of 2.9´10–22 e-cm (95% condence). This limit can be increased by 7 orders-of-magnitude|and brought below the current best experimental value|with easily implementable improvements to the technique. © Anita Publications. All rights reserved.
Keywords: NMOR; EDM; Paraffin coating.
Total Refs: 14
Permanent EDM measurement in Cs using nonlinear magneto-optic rotation.pdf
Harish Ravi, Mangesh Bhattarai, Abhilash Y D, Ummal Momeen and Vasant Natarajan
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1103-1117 |
Precise many-electron calculations of isotope shift for alkali like atoms or ions
Sourav Roy1, Anal Bhowmik2 and Sonjoy Majumder2
1 Department of Chemistry, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
2 Department of Physics, Indian Institute of Technology-Kharagpur, Kharagpur-721 302, India
In this paper, we review the precise many-body calculations isotope shift for alkali and singly ionized alkaline earth atoms. Relativistic coupled cluster method is employed here to have correlation exhaustive results. We showed that the preciseness of the results not only depends on the proper consideration of excitation cluster amplitudes, but also important on exact description of Dirac-Hartree-Fock orbitals wavefunctions over the radial extent. Our results for the mass constants are also compared with the values extracted from the experimental measurements. Distinct and interesting relativistic correction of IS, magic nucleon number and even-odd staggering phenomena of nucleus are studied in terms of different isotopes. © Anita Publications. All rights reserved
Total Refs: 62
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1119-1141 |
Energy level crossing of highly charged ions for optical clocks
Yan-mei Yu1 and Bing-bing Suo2
1Beijing National Laboratory for Condensed Matter Physics,
Institute of Physics, Chinese Academy of Sciences, Beijing 100190,China and
2Institute of Modern Physics, Northwest University, Xi’an, Shaanxi 710069, China
New clock scheme based on the highly charged ions (HCIs) has been proposed for the accuracy at 10–19 recently. The key advantage of HCIs comes from their high ionic charge. The E1 transitions in HCIs are in x-ray range usually. However, near the level crossings, configuration crossing keeps frequencies of transitions in the optical range and also provides wealthy chances for looking for the relatively strong transition line for cooling. Preliminary knowledge of energy level crossings in HCIs is very useful to select suitable ions for better atomic clocks.. In this paper, a large quantity of energy level data of the HCIs are summarized in order to illustrate 3d − 4s, 4d−5s, 5d−6s, 4f −5d, 4f − 6s, 4f − 5p, and 4f − 5s crossings in isoelectronic sequences with the increasing number of electrons. The tendency of the energy level crossings that occur at the first six rows of the periodic table is reviewed. Some new HCIs near the energy level crossings are suggested that have transitions within the wavelength range accessible to modern lasers and have enriched sensitivity to potential time variation of fine structure constant. © Anita Publications. All rights reserved
Keywords: Energy level crossing; Highly charged ions; Optical clocks, E1 transition
PACS numbers: 31.15.ap, 31.15.aj, 32.10.Dk
Total Refs:21
1. Chou C W, D B Hume, Koelemeij J C J, Wineland D J, and Rosenband T, Phys. Rev. Lett. 104(2010) 070802.
2. Hinkley N, Sherman J A, Phillips N B, Schioppo M, Lemke N D, Beloy K, Pizzocaro M, Oates C W, Lud-low A D, Science 341(2013) 1215.
3. Bloom B J, Nicholson T L, Williams J R, Campbell S L, Bishof M, Zhang X, Zhang W, Bromley S L, Ye J, Nature (London) 506(2014) 71.
4. Ushijima I, Takamoto M, Das M, Ohkubo T, and Katori H, Nature Photonics 9(2015) 185.
5. Campbell C J, Radnaev A G, Kuzmich A, Dzuba V A, Flambaum V V, and Derevianko A, Phys. Rev. Lett. 108(2012) 120802.
6. Derevianko A, Dzuba V A, Flambaum V V, Phys. Rev. Lett. 109(2012) 180801.
7. Yudin V I, Taichenachev A V, and Derevianko A, Phys. Rev. Lett. 113(2014) 233003.
8. Berengut J C, Dzuba V A, Flambaum V V, and Ong A, Phys. Rev. A 86(2012) 022517.
9. Berengut J C, Dzuba V A, and Flambaum V V, Phys. Rev. Lett. 105(2010) 120801.
10. Berengut J C, Dzuba V A, Flambaum V V, and Ong A, Phys. Rev. Lett. 106(2011) 210802.
11. Berengut J C, Dzuba V A, and Flambaum V V, Phys. Rev. A 84(2011) 054501.
12. Berengut J C, Dzuba V A, Flambaum V V, and Ong A, Phys. Rev. Lett. 109(2012) 070802.
13. Berengut J C, Dzuba V A, and Flambaum V V, Phys. Rev. A 86(2012) 054501.
14. Dzuba V A, Flambaum V V, and Katori H, Phys. Rev. A 91(2015) 022119.
15. Dzuba V A , Derevianko A, and Flambaum V V, Phys. Rev. A 86(2012) 054501.
16. Safronova M S, Dzuba V A, Flambaum V V, Safronova U I, Porsev S G, and Kozlov M G, Phys. Rev. Lett. 113(2014) 030801.
17. Safronova M S, Dzuba V A, Flambaum V V, Safronova U I, Porsev S G, and Kozlov M G, Phys. Rev. A 90(2014) 042513.
18. Safronova M S, Dzuba V A, Flambaum V V, Safronova U I, Porsev S G, and Kozlov M G, Phys. Rev. A 90(2014) 052509.
19. Windberger A, Crespo L´opez-Urrutia J R, Bekker H, Oreshkina N S, Berengut J C, Bock V, Borschevsky A, Dzuba V A, Eliav E, Harman Z, Kaldor U, Kaul S, Safronova U I, Flambaum V V, Keitel C H, Schmidt P O, Ullrich J, and Versolato O O, Phys. Rev. Lett. 114(2015) 150801.
20. DIRAC, a relativistic ab initio electronic structure pro-gram, Release DIRAC14 (2014), written by Visscher L, Jensen H J Aa, Bast R, Saue T, with contributions from Bakken V, Dyall K G, Dubillard S, Ekstr¨om U, Eliav E, Enevoldsen T, Faßhauer E, Fleig T, Fossgaard O, Gomes A S P, Helgaker T, Lærdahl J K, Lee Y S, Henriksson J, Iliaˇs M, Jacob Ch R, Knecht S, Ko-morovsk´y S, Kullie O, Larsen C V, H. Nataraj S, Nor-man P, Olejniczak G, Olsen J, Park Y C, Pedersen J K, Pernpointner M, Ruud K, Salek P, Schimmelpfennig B, Sikkema J, Thorvaldsen A J, Thyssen J, Van Stralen J, Villaume S, Visser O, Winther T, and Yamamoto S (see http://www.diracprogram.org).
21. Dyall K G, J. Phys. Chem. A 113(2009) 12638; Theor. Chem. Acc. 117(2007) 483; Theor. Chem. Acc. 112(2004) 403; Theor. Chem. Acc. 125(2009) 97; Theor. Chem. Acc. 129(2011) 603; Gomes A S P, Dyall K G and Visscher L, Theor. Chem. Acc. 127(2010) 369. Available from the Dirac web site, http://dirac.chem.sdu.dk.
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1143-1159 |
The magnetic moment of the bound electron
G Werth1 and S Sturm2
1Johannes Gutenberg University, Institutfuer Physik, 55099 Mainz, Germany
2Max-Planck Institute for Nuclear Physics, Saupfercheckweg, 169117 Heidelberg, Germany
The magnetic moments of electrons, generally expressed by the dimensionless g-factorg = ΔE/μB BΔm as scaling factor for the energy difference ΔE between Zeeman levels of quantum number m in a magnetic field B is an important quantity for our understanding of atomic structure. Penning traps are the instruments of choice to measure values of g for charged particles. We review results of measurements performed in recent years onmulti-electron ions which serve as test of atomic structure calculations. Very precise results have been obtained on hydrogen- andlithium-like ions which represent to date the most stringent test of Quantum Electrodynamic calculations in bound systems. From a combination of experimental and theoretical results we derived a new value for the electron’s atomic mass, improving the number listed in the tables of fundamental constants by more than one order of magnitude.© Anita Publications. All rights reserved.
Keywords: Magnetic moment, Spin, Zeeman levels
Total Refs: 33
1. Kusch P and Foley H M, Phys Rev, 72 (1947) 1256.
2. Brown L S, Gabrielse G, Phys Rev A, 25(1982)2423; doi.org/10.1103/PhysRevA.25.2423
3. Werth G, Gheorghe V, Major F G,Charged particle traps II, Springer, Heidelberg (2009)
4. Flambaum V et al.,Zh. Eksp.Teor.Fiz. (Sov. Phys. JETP) 75 (1978) 75
5. Marx G et al., Eur Phys J D, 4 (1998) 1279
6. Dicke R H, Phys Rev, 89(1953)472; http://dx.doi.org/10.1103/PhysRev.89.472
7. Lichtenberg C et al. Eur. Phys. J. D, 2(1998)29;
8. Lindroth E, Ynnerman A, Phys Rev A, 47(1993)961; doi.org/10.1103/PhysRevA.47.961
9. Kallay M, Nataraj H S, Sahoo B K, Das B P, Visscher L, Phys Rev A, 83(2011)030503; doi.org/10.1103/ PhysRevA.83.030503
10. Indelicato P, A.-M MÅrtensson-Pendrill A.-M, Quint W, Desclaux J.-P, Hyperfine Interactions, 146/147(2003)127-131.
11. Kinoshita T, Int. J. of Mod. Phys. A 29(2014) 1430003
12. Hanneke D et al., Phys Rev Lett, 100(2008)111807-
13. Breit G, Nature, 133 (1928)649
14. Karshenboim S G in: The Hydrogen Atom (S.G. Karshenboimed.). ( Springer, Berlin) 2001, p. 651
15. Yerokhin V A, and Jentschura U D, Phys Rev A, 81 (2010) 012502
16. Yerokhin V A, Harman Z, PR A88(2013)042502
17. Eides M I, Martin T J, Phys Rev Lett, 105(2010)100402
18. GlazovD A, Shabaev V M, Phys. Lett. A 297(2002) 408
19. Shabaev V M et al., arXiv:1508.00392vI
20. Glazov D A et al. Springer Tracts Mod.Phys, 256(2014) 137
21. Sturm S, Blaum K, Werth G, Ann Phys, 525(2013)620.
22. Diederich M et al., Hyperfine Interactions, 115(1998)185.
23. Sturm S et al., Phys Rev Lett, 107(2011)143003; doi.org/10.1103/PhysRevLett.107.143003
24. Sturm S et al., Phys Rev A, 87(2013) 030501
25. HäffnerH et al., Phys Rev Lett, 85 (2000) 5308
26. Verdu J, Djekić S, Stahl S, Valenzuela T, Vogel M, Werth, Beier T, Kluge H.-J, Quint W, Phys Rev Lett, 92 (2004) 093002;doi.org/10.1103/PhysRevLett.92.093002
27. Sturm S, Wagner A, Kretzschmar M, Quint W, Werth G, Blaum K. , Phys Rev A, 87(2013)030501;doi. org/10.1103/PhysRevA.87.030501
28. Shabaev V M, Glazov D A, Shabaeva M B, Yerokhin V A, Plunien G, Soff G, Phys Rev A, 65(2002) 062104;
http://dx.doi.org/10.1103/PhysRevA.65.062104.
29. Glazov D A, Shabaev V M, Tupitsyn I I, Volotka A V, Yerokhin V A, Plunien G, Soff G, Phys Rev A, 70(2004)062104;doi.org/10.1103/PhysRevA.70.062104
30. Wagner A et al., Phys Rev Lett, 110(2013) 033003
31. Köhler F et al., Nature Comm, 7 (2016)10246
32. Sturm S, Köhler F, Zatorski J, Wagner A, Harman Z, Werth G, Quint W, C H Keitel, Blaum K, Nature, 506 (2014) 467-470.
33. Köhler F, S Sturm S, Kracke A, Werth G, Quint W, Blaum K., J Phys B: At Mol Opt Phys, 48(2015)144032;
doi.org/10.1088/0953-4075/48/14/144032 [email protected]
The magnetic moment of the bound electron.pdf
The magnetic moment of the bound electron by G Werth and S Sturm
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1161-1206 |
Computational methods for high-precision spectroscopy of three-electron atomic systems
Liming Wang1, Chun Li2, and Zong-Chao Yan3
1Department of Physics, Henan Normal University, Xinxiang, Henan, P. R. China 453007
2Department of Mathematics, Nanjing University, Nanjing, Jiangsu, P. R. China 210093
3 Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
4Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences, Wuhan, Hubei, P. R. China 430071
Recent progress on computational methods for high precision calculations of three-electron atomic systems are reviewed. We first introduce two important methods for solving the time independent Schrödinger equation, the Rayleigh-Ritz variational method and Rayleigh-Schrödinger perturbation method. We then show how to construct a nonrelativistic wave function variationally in Hylleraas coordinates and how to solve the eigenvalue problems of the Hamiltonian for a three-electron atomic system. We then focus on computational aspects of relativistic and quantum electrodynamic corrections to atomic energy levels. Some theoretical results for nonrelativistic energy eigenvalues, ionization energies, fine structure splittings, and isotope shifts are reviewed. Finally, we include two special sections that describe, respectively, basic mathematical properties of Schrödinger operators and mathematical theory of the Fromm-Hill integral. © Anita Publications. All rights reserved.
Keywords: Schrödinger equation; Rayleigh-Ritz variational method; Rayleigh-Schrödinger perturbation method; Hamiltonian
Total Refs:165
1. Lamb W E and Retherford R C, Phys Rev, 72(1947)241.
2. Grant I P, in Handbook of Atomic, Molecular, and Optical Physics, edited by Drake G W (Springer Science+Business Media, Inc.) 2006, p325.
3. Salpeter E and Bethe H A, Phys Rev, 84(1951)1232;doi
4. King F W, J Mole Struct (Theochem), 400(1997)7-56.
5. (a) Hylleraas E A, Z. Phys. 48(1928)469;
(b) Hylleraas E A, Z. Phys. 54 (1929) 347.
6. Drake G W F, Cassar M M, and Nistor R A, Phys Rev A, 65 (2002) 054501.
7. Korobov V I, Phys Rev A, 66 (2002) 024501.
8. Schwartz C, Int. J. Mod. Phys. E 15 (2006) 877; arXiv: math-ph/0605018.
9. Puchalski M, Kedziera D, Pachucki K, Phys Rev A, 82(2010)062509; doi.org/10.1103/PhysRevA.82.062509; [email protected]
10. Wang L M, Yan Z-C, Qiao H X, Drake G W F, Phys Rev A, 85(2012)052513;doi.org/10.1103/PhysRevA.85.052513 [email protected]
11. James H M, Coolidge A S, Phys Rev, 49 (1936) 688; doi.org/10.1103/PhysRev.49.688
12. Perkins J F, J Chem Phys, 48 (1968) 1985.
13. King F W, Phys Rev A, 40 (1989) 1735.
14. King F W, Phys Rev A, 43 (1991) 3285; 58 (1998) 3597.
15. Drake G W F, Yan Z-C, Phys Rev A, 52 (1995) 3681.
16. Yan Z-C, Drake G W F, Phys Rev A, 52 (1995) 3711.
17. Yan Z-C and Drake G W F, J. Phys. B 30 (1997) 4723; 33 (2000) 2437.
18. Pachucki K, Puchalski M, Remiddi E, Phys Rev A, 70(2004)032502; doi.org/10.1103/PhysRevA.70.032502 [email protected] [email protected]; [email protected]
19. Puchalski M, Pachucki K, Phys Rev A, 73(2006)022503; doi.org/10.1103/PhysRevA.73.022503 [email protected] : [email protected]
20. Sims J S, Hagstrom S A, Phys Rev A, 80(2009)052507; doi.org/10.1103/PhysRevA.80.052507 Stanley A. Hagstrom [email protected]
21. Stanke M, Komasa J, Kedziera D, Bubin S, Adamowicz L, Phys Rev A, 78(2008)052507; doi.org/10.1103/PhysRevA.78.052507 : [email protected] [email protected]
22. Bushaw B A, Nortershauser W, Drake G W F, and Kluge H-J, Phys Rev A, 75 (2007)052503.
23. Stanke M, Komasa J, Kedziera D, Bubin S, and Adamowicz L, Phys Rev A, 77 (2008)062509.
24. Sharkey K L, Bubin S, and Adamowicz L, Phys Rev A, 83 (2011) 012506.
25. Bubin S, and Adamowicz L, J Chem Phys, 136(2012)134305.
26. Sims J S and Hagstrom S A, Phys Rev A, 83 (2011) 032518.
27. Stanke M, Komasa J, Bubin S, Adamowicz L, Phys Rev A, 80 (2009) 022514.
28. Puchalski M, Komasa J, Pachucki K, Phys Rev A, 92 (2015) 062501.
29. Puchalski M and Pachucki K, Phys. Rev. Lett. 113 (2014) 073004.
30. Puchalski M, Pachucki K, Phys Rev A, 92 (2015) 012513.
31. Puchalski M, Pachucki K, Phys Rev A, 80 (2009) 032521.
32. Puchalski M, Pachucki K, Phys Rev A, 81(2010)052505.
33. Breit G, Phys. Rev. 34 (1929) 553; 39(1932)616.
34. Stone A P, Proc. Phys. Soc. (London) 77 (1961) 786; 81 (1963) 868.
35. Douglas M, Kroll N M, Annals of Physics 82 (1974) 89.
36. Araki H, Prog. Theor Phys,17 (1957) 619.
37. Sucher J, Phys. Rev. 109 (1958) 1010.
38. Zhang T, Drake G W F, Phys Rev A, 54 (1996) 4882.
39. Caswell W E, Lepage G P, Phys Lett B, 167 (1986) 437.
40. Pachucki K, Phys Rev A, 56 (1997) 297.
41. (a) Pachucki K, J Phys B, 31(1998)5123;
(b) Pachucki K, J Phys B, 32(1999)137.
42. Pachucki K, Phys Rev A, 71(2005)012503.
43. Pachucki K, Phys. Rev. Lett. 97 (2006) 013002.
44. Pelzl P J, Smethells G J, and King F W, Phys. Rev. E, 65 (2002) 036707.
45. Yan Z-C and Drake G W F, Can. J. Phys, 72 (1994) 822.
46. Pachucki K, Puchalski M, Phys Rev A, 71 (2005) 032514.
47. King F W, Adv. At. Mol. Opt. Phys, 40 (1999) 57.
48. Fromm D M, Hill R N, Phys Rev A, 36(1987) 1013.
49. Drake G W F, in Encyclopedia of Applied Physics, Vol. 23 (WILEY-VCH Verlag GmbH) 1998, p121.
50. Hylleraas E A, Undheim B, Z. Phys. 65 (1930) 759.
51. MacDonald J K L, Phys. Rev. 43 (1933) 830.
52. Dalgarno A and Stewart A L, Proc. R. Soc. A 238 (1956) 269.
53. Drake G W F, Nucl. Instrum. Methods Phys. Res. B 31 (1988) 7.
54. McKenzie D K and Drake G W F, Phys Rev, 44 (1991) R6973; 48 (1993) 4803(E).
55. Mitroy J et al., Rev. Mod. Phys. 85 (2013) 693.
56. Kato T, Commun. Pure Appl. Math. 10 (1957) 151.
57. Drake G W F, Nortershauser W, and Yan Z-C, Can. J. Phys. 83 (2005) 311.
58. Pelzl P J, King F W, Phys Rev, 57(1998)7268.
59. Ohrn Y and Nordling J, J. Chem. Phys. 39 (1963) 1864.
60. Li C, Wang L M, and Yan Z-C, Int. J. Quantum Chem. 113 (2013) 1307.
61. Li C, Wang L M, and Yan Z-C, Phys Rev A, 88 (2013) 052513.
62. Harris F E, Adv. Quantum Chem. 50 (2005) 61.
63. Quinn M J, Parallel Programming in C with MPI and OpenMP. (McGraw-Hill) 2003.
64. Sims J S and Hagstrom S A, J Chem Phys, 124 (2006) 094101.
65. Bubin S et al., Chem. Rev. 113 (2013) 36.
66. Wang L M, Yan Z-C, Qiao H X, Drake G W F, Phys Rev A, 83 (2011) 034503.
67. Wang L M, Yan Z-C, Qiao H X, Drake G W F, unpublished.
68. Wang L M, Li C, Yan Z-C, and Drake G W F, Phys. Rev. Lett. 113 (2014) 263007.
69. Wang L M, Li C, Yan Z-C, and Drake G W F, unpublished.
70. Golub G H and Van Loan C F, Matrix Computations. (The Johns Hopkins University Press, Baltimore, Fourth edition) 2013.
71. Faddeeva V N, Computational Methods of Linear Algebra. (Dover, New York) 1959, p81.
72. Chi X B, Math. Num. Sin. 15 (1993) 289 (in Chinese).
73. Dalgarno A, Lewis J T, Proc. R. Soc. London A 233 (1955) 70.
74. Puchalski M. Pachucki K, Phys Rev A, 78 (2008) 052511.
75. Puchalski M, Kedziera D, Pachucki K, Phys Rev A, 87 (2013) 032503.
76. Bylicki M and Pestka G, J. Phys. B 29 (1996) L353.
77. Kristensen P et al., Phys Rev A, 55 (1997) 978; Erratum Phys Rev A, 56 (1997) 1674.
78. (a) Hiller J, Sucher J and Feinberg G, Phys Rev A, 18 (1978) 2399. Errata Phys Rev A, 22 (1980) 2293;
(b) Phys Rev A, 20 (1979) 378.
79. Drachman R J, J. Phys. B 14 (1981) 2733.
80. Pachucki K, Cencek W, Komasa J, J Chem Phys, 122(2005)184101.
81. Yan Z-C and Drake G W F, Phys Rev A, 61(2000)022504;
82. Nortershauser W et al., Phys Rev A, 83 (2011) 012516.
83. Kabir P K and Salpeter E E, Phys Rev, 108(1957)1256.
84. Pachucki K, J. Phys. B 31 (1998) 5123.
85. Yan Z-C, Drake G W F, Phys. Rev. Lett. 91 (2003) 113004.
86. Drake G W F, Goldman S P, Can. J. Phys. 77 (1999) 835.
87. Pachucki K, Komasa J, Phys Rev A, 68 (2003) 042507.
88. Schwartz C, Phys. Rev. 123 (1961) 1700.
89. Yan Z-C, Nortershauser W, and Drake G W F, Phys. Rev. Lett. 100 (2008) 243002. Erratum Phys. Rev. Lett. 102 (2009) 249903.
90. Yan Z-C. Drake G W F, Phys Rev A, 66 (2002) 042504.
91. Sansonetti C J, Richou B, Engleman R (Jr), Radziemski L J, Phys Rev A, 52(1995)2682.
92. Sansonetti C J et al., Phys. Rev. Lett. 107 (2011) 023001. Erratum Phys. Rev. Lett. 109 (2012) 259901.
93. Brown R C et al., Phys Rev A, 87 (2013) 032504; Erratum Phys Rev A, 88 (2013) 069902.
94. Bushaw B A, Nortershauser W, Ewald G, Dax A, and Drake G W F, Phys. Rev. Lett. 91 (2003) 043004.
95. NIST Atomic Spectra Database: http://physics.nist.gov/asd3.
96. Nakamura T et al., Phys Rev A, 74 (2006) 052503.
97. Yan Z-C, Drake G W F, Phys. Rev. Lett, 79 (1997) 1646.
98. Puchalski M, Pachucki K, Phys Rev A, 79 (2009) 032510.
99. Brog K C, Eck T G, and Wieder H, Phys Rev, 153(1967)91.
100. Orth H, Ackermann H, Otten E W, Z. Phys. A 273 (1975) 221.
101. Noble G A, Schultz B E, Ming H, and van Wijngaarden W A, Phys Rev A, 74 (2006) 012502.
102. Walls J, Ashby R, Clarke J J, Lu B, and van Wijngaardena W A, Eur. Phys. J. D 22 (2003)159.
103. Das D and Natarajan V, Phys Rev A, 75 (2007) 052508; doi.
104. Morgan III J D, Cohen J S, in Handbook of Atomic, Molecular, and Optical Physics, edited by Drake G W F (Springer Science+Business Media, Inc.) 2006, p1355.
105. Drake G W F, in Long-Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, edited by Levin F S, Micha D A. (Plenum, New York) 1993, p107.
106. Marin F, Minardi F, Pavone F, Inguscio M, Drake G W F, Z Phys D, 32(1995)285; doi.
107. Shiner D, Dixson R and Vedantham V, Phys. Rev. Lett, 74 (1995)3553; doi.
108. Wang L-B et al., Phys Rev Lett, 93 (2004) 142501.
109. Morton D C, Wu Q, Drake G W F, Phys Rev A, 73(2006)034502.
110. Mueller P et al., Phys Rev Lett, 99 (2007) 252501.
111. van Rooij R et al., Nature 333 (2011) 196.
112. Pastor P C, Consolino L, Giusfredi G, Natale P D, Inguscio M, Yerokhin V A, Pachucki K, Phys Rev Lett, 108(2012)143001; doi.org/10.1103/PhysRevLett.108.143001 [email protected], [email protected]
113. Lu Z T et al., Rev. Mod. Phys. 85 (2013) 1383.
114. Puchalski M, Moro A M, Pachucki K, Phys. Rev. Lett. 97 (2006) 133001.
115. Ewald G et al., Phys. Rev. Lett. 93 (2004) 113002. Erratum Phys. Rev. Lett. 94 (2005 039901.
116. Sanchez R et al., Phys. Rev. Lett. 96 (2006) 033002.
117. Nortershauser W, et al., Phys. Rev. Lett. 102 (2009) 062503.
118. Nortershauser W, Ne T, Sanchez R, and Sick I, Phys. Rev. C 84 (2011) 024307.
119. Krieger A et al., Phys Rev Lett, 108 (2012) 142501.
120. Kato T, Perturbation Theory for Linear Operators. (Springer-Verlag, Berlin) 1980.
121. Simon B, J. Math. Phys. 41 (2000) 3523.
122. Reed M and Simon B, Methods of modern mathematical physics, IV: Analysis of operators. (Academic Press, New York) 1978.
123. Reed M and Simon B, Methods of modern mathematical physics, I: Functional analysis. (Academic Press, New York, Revised edition) 1980.
124. Kato T, Trans. Amer. Math. Soc. 70 (1951) 212.
125. Zhislin G M, Tr. Mosk. Mat. Obs. 9 (1960) 81.
126. Zhislin G M, Teor. Mat. Fiz. 7 (1971) 571.
127. Sigal I M, Commun. Math. Phys. 85 (1982) 309.
128. Reed M and Simon B, Methods of modern mathematical physics, II: Fourier Analysis, Self- Adjointness. (Academic Press, New York) 1975.
129. Maz’ya V and Shubin M, Ann. of Math. 162 (2005) 919.
130. Hill R N, Phys. Rev. Lett. 38 (1977) 643.
131. Brown G E and Ravenhall D G, Proc. Roy. Soc. (London) A 208 (1951) 552.
132. Zhislin G M, SIGMA 2 (2006) 024.
133. Morozov S, and Vugalter S, Ann. Henri Poincare 7 (2006) 661.
134. Matte O, Rev. Math. Phys. 22 (2010) 1.
135. Hardekopf G, Sucher J, Phys Rev A, 31 (1985) 2020.
136. Evans W D, Perry P, Siedentop H, Commun Math Phys, 178 (1996) 733.
137. Sucher J, Phys. Rev. A 22 (1980) 348. Phys Rev A, 23 (1981) 388.
138. Fierz M and Pauli W, Proc. Roy. Soc. (London) A 173 (1939) 211.
139. Bruneau L and Derezinski J, Rep. Math. Phys. 54 (2004) 169; doi.
140. Bach V, Fröhlich J, Sigal I M, Adv. in Math,137(1998)299; doi.
141. Bach V, Fröhlich J, Sigal I M, Commun Math Phys, 207 (1999)249-290.
142. Lieb E H, Loss M, Adv Theor Math Phys, 7(2003)667-710.
143. Klahn B, Bingel W A, Theoret Chim Acta (Berl), 44(1977)9-26.
144. Klahn B, Bingel W A, Theoret Chim Acta (Berl), 44 (1977)27-43.
145. Coolidge A S, James H M, Phys Rev, 51(1937)855; doi.org/10.1103/PhysRev.51.85
146. Klahn B and Morgan III J D, J Chem Phys, 81 (1984) 410; doi.
147. Hill R N, J Chem Phys, 83 (1985) 1173; doi.
148. Drake G W F, in Handbook of Atomic, Molecular, and Optical Physics, edited by Drake G W F (Springer Science+Business Media, Inc.) (2006), p199.
149. James H M and Coolidge A S, J Chem Phys, 1 (1933) 825.
150. Drake G W F, Phys Rev A, 18 (1978) 820.
151. Myers C R, Umrigar C J, Sethna J P and Morgan III J D, Phys Rev A, 44 (1991) 5537.
152. Pack R T, Brown W B, J Chem Phys, 45 (1966) 556.
153. (a) Fock V A, IZV. Akad. Nauk SSSR, Ser. Fiz. 18 (1954) 1961;
(b) Kgl. Norske Videnskab. Selskabs Forh. 31(1958)138.
154. White R J, Stillinger F H, Phys Rev A, 3(1971)1521; doi.org/10.1103/PhysRevA.3.1521
155. Babuska I, Osborn J E, Eigenvalue problems, In: Ciarlet P G, Lions J L (eds.), Handbook of Numerical Analysis, vol.II, (North Holland, Amsterdam). 1991, p641.
156. Feng K, Qin M, Symplectic geometric algorithms for Hamiltonian systems, (Zhejiang Publishing United Group, Zhejiang Science and Technology Publishing House, Hangzhou and Springer-Verlag Berlin, Heidelberg). 2010.
157. Klahn B, Bingel W A, Int J Quant Chem, 11(1977)943-957.
158. Yan Z-C, Drake G W F, Phys Rev A, 52(1995)R4316; doi.org/10.1103/PhysRevA.52.R4316
159. Yan Z-C, McKenzie D K, Drake G W F, Phys Rev A, 54 (1996) 1322; doi
160. Drake G W F, Can J Phys, 80(2002)1195; doi
161. Zotev V S, Rebane T K, Phys Rev A, 65(2002)062501; doi
162. Yan Z-C and Drake G W F, Phys Rev Lett, 81 (1998)774; doi
163. Remiddi E, Phys Rev A, 44(1991)5492; doi
164. Harris F E, Phys Rev A, 55(1997)1820; doi
165. Li C, Wang L M, Yan Z-C, unpublished
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1207-1231 |
Precision measurements based on 40Ca+ ion optical frequency standards
Hua Guan1, 2, Yao Huang1, 2, Cheng-bin Li1, Li-yan Tang1, and Ke-lin Gao1, 2*
1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics,
Chinese Academy of Sciences, Wuhan 430071, China [1]
2Key Laboratory of Atomic Frequency Standards, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
The development of the optical frequency standard based on trapped and cold 40Ca+ with the 4s 2S1/2–3d 2D5/2 clock transition at 729 nm is reported. A single 40Ca+ ion is trapped and laser cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly. In order to realize the frequency comparison, two similar 40Ca+ optical frequency standards are established. The overall systematic uncertainties of the clock transition of two 40Ca+ optical frequency standards are evaluated to be better than 6 × 10-17. With an over-one-month measurement, the frequency difference between the two clocks is measured to be 3.2 × 10−17 with a measurement uncertainty of 5.5 × 10−17, considering both the statistic (1.9 × 10−17) and the systematic (5.1 × 10−17) uncertainties. By the frequency comparison in three days uninterruptedly, a fractional stability of 7 × 10−17 in 20 000 s of averaging time is achieved. At the same time, the absolute frequency of the clock transition is measured at 10-15 level by using an optical frequency comb referenced to a Hydrogen maser which is calibrated to the SI second through the global positioning system (GPS). The frequency value is 411042129776401.7(1.1) Hz with the correction of the systematic shifts. Moreover, additional two precision measurements based on single trapped 40Ca+ ion are carried out. One is magic wavelengths for 4s 2S1/2-3d 2D5/2 clock transition, λ|mj|=1/2 = 395.7992(7) nm and λ|mj|=3/2 = 395.7990(7) nm are measured. It’s the first time that two magic wavelengths for the 40Ca+ clock-transition are reported. And the correlation between the magic wavelengths and the polarization direction of the linearly polarized laser is preliminary studied. The other one is the 3d 2D5/2 state lifetime measurement, our result of 1174(10) ms agrees well with the experimental results reported by P. A. Barton et al. [Phys. Rev. A 62, 032503 (2000)], A. Kreuter et al. [Phys. Rev. A 71, 032504 (2005)] and the recent RCC calculation result by B. K. Sahoo [Phys. Rev. A 91, 022511 (2015)].
Total Refs : 58
Asian Journal of Physics |
Vol. 25 No 9 (2016) 1233-1245 |
Precision physics with molecules
Amar C Vutha
Department of Physics, University of Toronto, 60 St. George Street, Toronto ON M5S 1A7, Canada
Molecules have become an important resource for precisely measuring a number of fundamental physics quantities. This review provides an introduction to the properties of molecules that make them suitable for precision measurements, and surveys the state of the art in precision molecular physics experiments.© Anita Publications. All rights reserved.
Keywords: Fundamental physics quantities; Precision measurements
Total Ref: 90
1. Bloch Immanuel. Ultracold quantum gases in optical lattices, Nat Phys, 1(2005)23-30.
2. Georgescu I M, Ashhab S, Nori Franco, Quantum simulation, Rev Mod Phys, 86(2014)153-185.
3. Alexander D. Cronin, J¨org Schmiedmayer, and David E. Pritchard. Optics and interferometry with atoms and molecules, Rev. Mod.Phys., 81(3):1051–1129, jul 2009.
4. H. S. Margolis. Optical frequency standards and clocks. Contemp. Phys., 51(1):37–58, 2010.
5. Andrew D Ludlow, Martin M Boyd, Jun Ye, E Peik, and P O Schmidt. Optical atomic clocks. Rev. Mod. Phys., 87:637–701, 2015.
6. B C Regan, Eugene D Commins, Christian J Schmidt, and DavidPhys. Rev. Lett., 88(7):71805, feb 2002.
7. C. S. Wood, S. C. Bennett, D. Cho, B. P. Masterson, J. L. Roberts, C. E. Tanner, and C. E. Wieman. Measurement of Parity Nonconservation and an Anapole Moment in Cesium. Science (80-. )., 275(5307):1759–1763, mar 1997.
8. Nicholas R. Hutzler, Hsin-I Lu, and John M. Doyle. The Buffer Gas Beam: An Intense, Cold, and Slow Source for Atoms and Molecules, Chem. Rev., 112(9):4803–4827, 2012.
9. E S Shuman, J F Barry, and D Demille. Laser cooling of a diatomic molecule. Nature, 467(2010):820-823, oct
10. Matthew T. Hummon, Mark Yeo, Benjamin K. Stuhl, Alejandra L. Collopy, Yong Xia, and Jun Ye. 2D magneto-optical trapping of diatomic molecules. Phys. Rev. Lett., 110(2013):143001, .
11. V. Zhelyazkova, A. Cournol, T. E. Wall, A. Matsushima, J. J. Hudson, E. A. Hinds, M. R. Tarbutt, and B. E. Sauer. Laser cooling and slowing of CaF molecules. Phys. Rev. A, 89(5):053416, may 2014.
12. J. F. Barry, D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille. Magneto-optical trapping of a diatomic molecule. Nature, 512(7514):286–289, aug 2014.
13. D. J. McCarron, E. B. Norrgard, M. H. Steinecker, and D. DeMille. Improved magneto-optical trapping of a diatomic molecule. New J. Phys., 17(3):1–12, mar 2015.
14. Cheng Chin, Rudolf Grimm, Paul Julienne, and Eite Tiesinga. Feshbach resonances in ultracold gases. Rev. Mod. Phys., 82(2010)1225-1286.
15. Jones Kevin M, Tiesinga Eite, Lett Paul D, Julienne Paul S, Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering, Rev Mod Phys, 78(2006)483-535.
16. Ospelkaus S, Péer A, Ni K.-K, Zirbel J J, Neyenhuis B, Kotochigova S, Julienne P S, Ye J, Jin D S, Efficient state transfer in an ultracold dense gas of heteronuclear molecules, Nat Phys, 4(2008)622-626.
17. Tetsu Takekoshi, Lukas Reichs llner, Andreas Schindewolf, Jeremy M. Hutson, C. Ruth Le Sueur, Olivier Dulieu, Francesca Ferlaino, Rudolf Grimm, and Hanns Christoph N??gerl. Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state. Phys Rev Lett, 113(2014)205301,
18. Jee Woo Park, Sebastian A. Will, Martin W. Zwierlein. Ultracold Dipolar Gas of Fermionic Na<sup>23</sup>K<sup>40</sup> Molecules in Their Absolute Ground State, Phys Rev Lett, 114(20):205302, may 2015.
19. Fudong Wang, Xiaodong He, Xiaoke Li, Bing Zhu, Jun Chen, Dajun Wang. Formation of ultracold NaRb Feshbach molecules, New J Phys, 17(2015)035003.
20. Hendrick Bethlem, Giel Berden, and Gerard Meijer. Decelerating Neutral Dipolar Molecules, Phys Rev Lett, 83(1999)1558-1561.
21. Hendrick Bethlem, Floris Crompvoets, Rienk Jongma, Sebastiaan van de Meerakker, and Gerard Meijer. Deceleration and trapping of ammonia usingtime-varying electric fields. Phys. Rev. A, 65(5):1–20, may 2002.
22. Sebastiaan Y.T. van de Meerakker, Nicolas Vanhaecke, and Gerard Meijer. STARK DECELERATION AND TRAPPING OF OH RADICALS. Annu.Rev. Phys. Chem., 57(1):159–190, 2006.
23. S. K. Tokunaga, J. M. Dyne, E. A. Hinds, M. R. Tarbutt, Stark deceleration of lithium hydride molecules, New J Phys, 11(2009)055038;doi.org/10.1088/1367-2630/11/5/055038 [email protected]
24. Bucicov O, Nowak M, Jung S, Meijer G, Tiemann E, Lisdat C, Cold SO2 molecules by stark deceleration, Eur Phys J D, 46(2008)463-469.
25. Martin Zeppenfeld, Barbara G. U. Englert, Rosa Gl¨ockner, Alexander Prehn, Manuel Mielenz, Christian Sommer, Laurens D.van Buuren,Michael Motsch, Gerhard Rempe, Sisyphus cooling of electrically trapped polyatomic molecules, Nature, 491(7425):570-573, nov 2012.
26. Alexander Prehn, Martin Ibr¨ugger, Rosa Gl¨ockner, Gerhard Rempe, Martin Zeppenfeld. Optoelectrical Cooling of Polar Molecules toSubmillikelvin Temperatures. Phys Rev Lett, 116(2016)063005.
27. Nicolas Vanhaecke, Urban Meier, Markus Andrist, Beat H. Meier, and Fr´ed´eric Merkt. Multistage Zeeman deceleration of hydrogen atoms,Phys Rev A, 75(2007)031402R;doi.org/10.1103/PhysRevA.75.031402
28. A.W. Wiederkehr, H. Schmutz, M. Motsch, and F. Merkt. Velocitytunable slow beams of cold O2 in a single spin-rovibronic state with full angular-momentum orientation by multistage Zeeman deceleration. http://dx.doi.org/10.1080/00268976.2012.681312, 2012.
29. M. A. Chieda and E. E. Eyler. Prospects for rapid deceleration of small molecules by optical bichromatic forces. Phys. Rev. A – At. Mol. Opt. Phys., 84(6):063401, dec 2011.
30. A. M. Jayich, A. C. Vutha, M. T. Hummon, J. V. Porto, W. C. Campbell. Continuous all-optical deceleration and singlephoton cooling of molecularbeams. Phys. Rev. A – At. Mol. Opt.Phys., 89(2):023425, feb 2014.
31. Ekaterina Ilinova, Jonathan Weinstein, and Andrei Derevianko, Stimulated deceleration of diatomic molecules on multiple rovibrational transitionswith coherent pulse trains, New J Phys, 17(2015)055003;
32. Rudolf Grimm, MatthiasWeidem??ller, and Yurii B. Ovchinnikov. Optical Dipole Traps for Neutral Atoms. Adv. At. Mol. Opt. Phys., 42(C):95–170, 2000.
33. DeMille D, Glenn D R, Petricka J, Microwave traps for cold polar molecules, Eur Phys J D, 31(2004)375-384.
34. Paul Wolfgang, Electromagnetic traps for charged and neutral particles, Rev Mod Phys, 62(1990)531-540.
35. Mølhave K, Drewsen M, Formation of translationally cold MgH+ and MgD+ molecules in an ion trap, Phys Rev A,62(2000)011401;
36. Koelemeij J C J, Roth B, Wicht A, Ernsting I, Schiller S,Vibrational Spectroscopy of HD+ with 2-ppb Accuracy, Phys Rev Lett, 98(2007)173002; doi:
37. Schneider T, Roth B, Duncker H, I. Ernsting, and Stephan Schiller. All-optical preparation of molecular ions in the rovibrational ground state,Nat Phys, 6(2010)275-278. o k
38. Loh H, Cossel K C, Grau M C, Ni K-K, Meyer E R, Bohn J L, Ye J, Cornell E A, Precision spectroscopy of polarized moleculesin an ion trap,Science, 342(2013)1220-1222.
39. Wan Yong, Gebert Florian, Wübbena Jannes B, Scharnhorst Nils, Amairi Sana, Leroux Ian D, Hemmerling Börge, Lörch Niels, HammererKlemens, Schmidt Piet O, Precision spectroscopy by photon-recoil signal amplification, Nat Commun, 5, jan 2014.
40. van Veldhoven Jacqueline, Bethlem Hendrick L, Meijer Gerard, ac Electric Trap for Ground-State Molecules, Phys Rev Lett, 94(2005)083001; doi:.
41. Bethlem Hendrick L, van Veldhoven Jacqueline, Schnell Melanie, Meijer Gerard, Trapping polar molecules in an ac trap, Phys Rev A – At Mol Opt Phys, 74(2006)063403; doi:.
42. Schnell Melanie, Peter L??tzow, van Veldhoven Jacqueline, Bethlem Hendrick L, K??pper Jochen, Friedrich Bretislav, Schleier-Smith Monika, Haak Henrik, Meijer Gerard, A linear AC trap for polar molecules in their ground state, J Phys Chem A, 111(2007)7411-7419.
43. Tarbutt M R, Hudson J J, Sauer B E, Hinds E A, Prospects for measuring the electric dipole moment of the electron using electrically trapped polar molecules, Faraday Discuss, 142(0):37-56; discussion 93–111, 2009.
44. Doyle John M, Friedrich Bretislav, Kim Jinha, Patterson David, Buffer-gas loading of atoms and molecules into a magnetic trap, Phys Rev A, 52(1995)R2515-R2518.
45. Weinstein Jonathan D, DeCarvalho Robert, Guillet Thierry, Friedrich Bretislav, Doyle John M, Magnetic trapping of calcium monohydride molecules at millikelvin temperatures, Nature, 395(6698)148-150.
46. Lu Hsin I, Kozyryev Ivan, Hemmerling Boerge, Piskorski Julia, Doyle John M, Magnetic trapping of molecules via optical loading and magnetic slowing, Phys Rev Lett, 112(2014)113006;doi:
47. Campbell Wesley C, Tsikata Edem, Lu Hsin I, van Buuren Laurens D, Doyle John M, Magnetic trapping and Zeeman relaxation of NH, Phys Rev Lett, 98(2007)213001; doi:
48. Stoll Michael, Bakker Joost M, Steimle Timothy C, Meijer Gerard, Peters Achim, Cryogenic buffer-gas loading and magnetic trapping of CrH and MnH molecules, Phys Rev A – At Mol Opt Phys, 78(2008)032707; doi:
49. Sawyer Brian C, Lev Benjamin L, Hudson Eric R, Stuhl Benjamin K, Lara Manuel, Bohn John L, Ye Jun, Magnetoelectrostatic trapping of ground state OH molecules, Phys Rev Lett, 98(2007)253002;doi:
50. DeMille D, Cahn S B, Murphree D, Rahmlow D A, Kozlov M G, Using Molecules to Measure Nuclear Spin-Dependent Parity Violation, Phys Rev Lett, 100(2008)023003, .
51. Zelevinsky T, Kotochigova S, Ye Jun, Precision test of mass ratio variations with lattice-confined ultracold molecules, Phys Rev Lett, 100(2008)043201;doi:
52. Chin Cheng, Flambaum V V, Kozlov M G, Ultracold molecules: New probes on the variation of fundamental constants, New J Phys, 11(2009)055048;doi:
53. Ho Paul T P, Townes Charles H , Interstellar Ammonia, Annu Rev Astron Astrophys, 21(1983)239-270.
54. Flambaum V V, Kozlov M G, Limit on the cosmological variation of mp/me from the inversion spectrum of ammonia, Phys Rev Lett, 98(2007)240801;doi:.
55. Kozlov M G, Lambda-doublet spectra of diatomic radicals and their dependence on fundamental constants, Phys Rev A – At Mol Opt Phys, 80(2009)022118;doi:
56. Kozlov M G, Levshakov Sergei A, Microwave and submillimeter molecular transitions and their dependence on fundamental constants, Ann Phys, 525(2013)452-471.
57. Winnewisser G, Herbst E, Interstellar molecules, Reports Prog Phys, 56(1993)1209-1273, .
58. Herbst Eric, The chemistry of interstellar space, Chem Soc Rev, 30(2001)168-176.
59. Hudson Eric R, Lewandowski H J, Sawyer Brian C, Ye Jun, Cold molecule spectroscopy for constraining the evolution of the fine structure constant,
Phys Rev Lett, 96(2006)143004;;doi:
60. Truppe S, Hendricks R J, Tokunaga S K, Lewandowski H J, Kozlov M G, Christian Henkel, E a Hinds, and M R Tarbutt. A search for varying fundamental constants using hertz-level frequency measurements of cold CH molecules, Nat Commun, 4(2013)2600
61. Bagdonaite J, Ubachs W, Murphy M T, Whitmore J B, Constraint on a Varying Proton-Electron Mass Ratio 1.5 Billion Years after the Big Bang, Phys Rev Lett, 114(2015):071301; http://dx.doi.org/10.1103/PhysRevLett.114.071301
62. Levshakov S A, Kozlov M G, Reimers D, Methanol as a Tracer of Fundamental Constants, Astrophys J, 738(2011)26; doi
63. Bagdonaite Julija, Jansen P, Henkel C, Bethlem H L, Menten K M, Ubachs W, A stringent limit on a drifting proton-339(6115)46-8, 2013.
64. Kanekar N, Ubachs W, Menten K M, Bagdonaite J, Brunthaler A, Henkel C, Muller S, Bethlem H L, Dapra M, Constraints on changes in the proton-electron mass ratio using methanol lines. Mon. Not. R. Astron. Soc. Lett., 448(2015)L104-L108.
65. Jansen Paul, Bethlem Hendrick L, Ubachs Wim, Perspective:Tipping the scales: Search for drifting constants from molecular spectra, J Chem Phys, 140(2014)010901; doi:
66. Commins Eugene D, Electric Dipole Moments of Leptons, Adv. At. Mol. Opt. Phys, 40(1999)1-55.
67. Commins Eugene D, Jackson J D, DeMille David P, The electric dipole moment of the electron: An intuitive explanation for the evasion
of Schiff’s theorem, Am J Phys, 75(2007)532;doi
68. Hinds Edward A, Sandars P G H. Experiment to search for P – and T -violating interactions in the hyperfine structure of thallium fluoride, Phys Rev A, 21(1980)480-487
69. Wilkening Dean A, Ramsey Norman F, Larson Daniel J, Search for P and T violations in the hyperfine structure of thallium fluoride, Phys Rev A, 29(1984)425-4384.
70. Hunter L R, Peck S K, Greenspon A S, Alam S Saad, De- Mille D, Prospects for laser cooling TlF, Phys Rev A, 85(2012)012511.
71. Isaev T A, Hoekstra S, Berger R, Laser-cooled RaF as a promising candidate to measure molecular parity violation, Phys Rev A 82(2010)052521.
72. Hinds Edward A, Sandars P G H, Electric dipole hyperfine structure of TIF, Phys Rev A, 21(1980)471-479.
73. Kudashov A D, Petrov A N, Skripnikov L V, Mosyagin N S, Isaev T A, Berger R, Titov A V. <i>Ab initio</i>study of radium monofluoride (RaF)
as a candidate to search for parity and time-and-parityviolation effects, Phys Rev A, 90(2014)052513.
74. Engel Jonathan, Ramsey-Musolf Michael J, van Kolck U, Electric dipole moments of nucleons, nuclei, and atoms: The Standard Model and beyond, Prog Part Nucl Phys, 71(2013)21-74,
75. Hudson J J, Kara D M, Smallman I J, Sauer B E, Tarbutt M R, Hinds E A, Improved measurement of the shape of the electron, Nature, 473(2011)493-496.
76. Vutha A C, Campbell W C, Gurevich Y V, Hutzler N R, Parsons M, D Patterson, Petrik E, Spaun B, Doyle J M, Gabrielse G, De-Mille D, Search for the electric dipole moment of the electron with thorium monoxide, J Phys B At Mol Opt Phys, 43(2010)074007;
77. Lee J , Meyer E R , Paudel R, Bohn J L, Leanhardt A F, An electron electric dipole moment search in the X ˆ3Delta 1 ground state of tungsten carbide molecules, J Mod Opt, 56(2009)2005-2012,
78. Shafer-Ray Neil E, Possibility of 0- g -factor paramagnetic molecules for measurement of the electron’s electric dipole moment,Phys Rev A, 73(2006)034102,
79. Prasannaa V S, Vutha A C, Abe M, Das B P, Mercury Monohalides: Suitability for Electron Electric Dipole Moment Searches,Phys Rev Lett, 114(2015)183001;
80. Kozlov M G, Derevianko Andrei, Proposal for a Sensitive Search for the Electric Dipole Moment of the Electron with Matrix-Isolated Radicals,Phys Rev Lett, 97(2006)063001;
81. Sasmal Sudip, Pathak Himadri, Nayak Malaya K, Vaval Nayana, Pal Sourav, Search for parity and time reversal violating effects in HgH:Relativistic coupled-cluster study, J Chem Phys, 144(2016)124307; doi.org/10.1063/1.4944673
82. Meyer E R, Bohn J L, Electron electric-dipolemoment searches based on alkali-metal- or alkaline-earthmetal-bearing molecules,Phys Rev A, 80(2009)042508; doi.org/10.1103/PhysRevA.80.042508
83. Baron J, Campbell W C, D DeMille, J M Doyle, G Gabrielse, Y V Gurevich, PWHess, NR Hutzler, E Kirilov, I Kozyryev, B R O’Leary,Panda C D, Parsons M F, Petrik E S, Spaun B, Vutha A C, West A D, Order of magnitude smaller limit on the electric dipole moment of the electron,Science, 343(2014)269-272.
84. Flambaum VV V, DeMille D, Kozlov M G G, Time-Reversal Symmetry Violation in Molecules Induced by Nuclear Magnetic Quadrupole Moments,Phys Rev Lett, 113(2014)103003doi.
85. Cahn S B, Ammon J, Kirilov E, Gurevich Y V, Murphree D, Paolino R, Rahmlow D A, Kozlov M G, DeMille D, Zeeman-Tuned RotationalLevel-Crossing Spectroscopy in a Diatomic Free Radical, Phys Rev Lett, 112(2014)163002;
86. Bouchiat Marie-Anne, Bouchiat Claude, Parity violation in atoms, Reports Prog Phys, 60(1999)1351-1396.
87. Kellogg J M B, Rabi I I, Ramsey N F, Zacharias J R. The Magnetic Moments of the Proton and the Deuteron. The Radiofrequency Spectrum ofH2 in Various Magnetic Fields, Phys Rev, 56(1939)728-743.
88. J. M. B. Kellogg, I. I. Rabi, N. F. Ramsey, and J. R. Zacharias. An Electrical Quadrupole Moment of the Deuteron. Phys Rev, 55(1939)318-319.
89. Perry Adam J, Hodges James N, Markus Charles R, Kocheril G Stephen, McCall Benjamin J, Communication: High precision sub-Doppler infrared spectroscopy of the HeH+ ion, J Chem Phys, 141(2014)101101,
90. Kozyryev Ivan, Baum Louis, Matsuda Kyle, Hemmerling Boerge, MDoyle John, Radiation Pressure Force from Optical Cycling on a Polyatomic Molecule, J Phys B At Mol Opt Phys, 49(2016)1–7,