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Atomic clocks provide the most accurate definition for time. The precision of atomic clock has been improved by many orders of magnitude since the first atomic clock was built. However, the interatomic interaction usually suppress the precision of atomic clock. As a result, it is especially meaningful to study the interaction effect in atomic clock, which is considered to be helpful in improving the precision and accuracy of atomic clock. In order to characterize the collision effect induced clock shift, we theoretically study the collision clock shift in the Rabi spectrum, caused by the short-range interaction between two Fermi atoms in harmonic potential. Given that the short-range interatomic interaction is generally weak, and that the parameters of external lattice laser field are in the Lamb-Dicke regime, we make an approximation that the spatial wave-function of the Fermi atoms does not change, and then derive the motion equation for the internal wave-function under the external Rabi driving field. We solve the equation of motion by the perturbative method, and obtain the solution to first order, and thus derive the expression of the collision clock shift of the Rabi spectrum in terms of the interatomic interaction and the external Rabi driving laser field parameters for specific spatial wave-functions of atoms. Finally, we use the exact expression of the Green’s function in harmonic potential to obtain the averaged clock shift of collision at finite temperatures. Our results relate the atomic interaction with atomic clock shift, and provide a unified description of all partial waves of atomic interaction induced clock shift. Therefore, it becomes much more convenient to study the contributions of different partial waves to atomic clock shift. On the other hand, our results indicate that through precisely measuring the clock shift, the information about the interatomic interactions can also be obtained. In addition, our results for two interacting atoms can inspire the future study of real many-body interacting system which will be the next research topic.
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Keywords:
- Fermion system /
- collision shift /
- atomic clock
[1] 阮军, 王叶兵, 常宏, 刘涛, 董瑞芳, 张首刚 2015 物理学报 64 160308
Google Scholar
Ruan G, Wang Y B, Chang H, Jiang H F, Liu T, Dong R F, Zhang S G 2015 Acta Phys. Sin. 64 160308
Google Scholar
[2] Ludlow A D, Boyd M M, Ye J, Peik E, Schmidt P O 2015 Rev. Mod. Phys. 87 637
Google Scholar
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Google Scholar
[4] Zhu B, Gadway B, Foss-Feig M, Schachenmayer J, Wall M L, Hazzard K R A, Yan B, Moses S A, Covey J P, Jin D S, Ye J, Holland M, Rey A M 2014 Phys. Rev. Lett. 112 070404
[5] Moses S A, Covey J P, Miecnikowski M T, Yan B, Gadway B, Ye J, Jin D S 2015 Science 350 659
Google Scholar
[6] Labuhn H, Barredo D, Ravets S, de Léséleuc S, Macrì T, Lahaye T, Browaeys A 2016 Nature 534 667
Google Scholar
[7] Aikawa K, Baier S, Frisch A, Mark M, Ravensbergen C, Ferlaino F 2014 Science 345 1484
Google Scholar
[8] Burdick N Q, Tang Y, Lev B L 2016 Phys. Rev. X 6 031022
[9] Kadau H, Schmitt M, Wenzel M, Wink C, Maier T, Ferrier-Barbut I, Pfau T 2016 Nature 530 194
Google Scholar
[10] Heller E J, Falconer I S, Dewar R L 2002 Proceedings of the XVIII International Conference on Atomic Physics: the Expanding Frontier of Atomic Physics Cambridge, Massachusett, USA, July 28–August 2, 2002 p363
[11] Zwierlein M W, Hadzibabic Z, Gupta S, Ketterle W 2003 Phys. Rev. Lett. 91 250404
Google Scholar
[12] Campbell G K, Boyd M M, Thomsen J W, et al. 2009 Science 324 360
Google Scholar
[13] Harber D M, Lewandowski H J, Mcguirk J M, Cornell E A 2002 Phys. Rev. A 66 053616
[14] Fuchs J N, Gangardt D M, Laloe F 2002 Phys. Rev. Lett. 88 230404
Google Scholar
[15] Kadio D, Band Y B 2006 Phys. Rev. A 74 053609
[16] Kurt G 2009 Phys. Rev. Lett. 103 113202
Google Scholar
[17] Hazlett E L, Zhang Y, Stites R W, Gibble K, O'Hara K M 2013 Phys. Rev. Lett. 110 160801
[18] Lemke N D, Stecher J V, Sherman J A, Rey A M, Oates C W, Ludlow A D 2011 Phys. Rev. Lett. 107 103902
Google Scholar
[19] Rey A M, Martin M J, Swallows M D, Bishof M, Benko C, Blatt S, Stecher J Von, Gorshkov A, Ye J 2012 IEEE International Frequency Control Symposium (FCS): Probing Many-body Spin Interactions with an Optical Lattice Clock Baltimore, Maryland, USA, May 21–24, 2012 p1
[20] Campbell S L, Hutson R B, Marti G E, Goban A, Oppong N D, Mcnally R L, Sonderhouse L, Robinson J M, Zhang W, Bloom B J 2017 Science 358 90
Google Scholar
[21] Liu G C, Huang Y, Cheng Z, Chen Z R, Yu Z H 2020 Phys. Rev. A 101 012504
Google Scholar
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图 1 光钟频移系数(a)
$A\;(\delta_{\rm R}/\varOmega)$ 与(b)$ B\;(\delta_{\rm R}/\varOmega) $ Figure 1. Coefficient (a)
$A\;(\delta_{\rm R}/\varOmega)$ and (b)$ B\;(\delta_{\rm R}/\varOmega) $ for clock shift.
图 2 系数
$ C_\ell $ 随温度的变化 (a) C1; (b) C2Figure 2. Coefficient
$ C_\ell $ versus temperature: (a) C1; (b) C2.
图 3 当温度较高时, 系数
$ C_\ell $ 随温度的变化, 这里横轴和纵轴都取对数 (a)线性拟合表达式为$y = 5.54203 x- 3.83918$ ; (b)线性拟合表达式为$ y = 6.5296 x-0.119146 $ Figure 3. Coefficient
$ C_\ell $ versus temperature for higher temperature. The horizontal coordinate and the vertical coordinate are logarithmic here: (a) Linear fitting function is$ y = 5.54203 x-3.83918 $ ; (b) linear fitting function is$ y = 6.5296 x-0.119146 $ .
图 C1 同时考虑s波至d波时的钟频移
$ {\bar\delta}_{\rm s}\;(\ell = 2) $ 与只考虑s波和p波时的钟频移$ {\bar\delta}_{\rm s}\;(\ell = 1) $ 的相对误差Figure C1. Relative error of clock shifts between considering s, p, d partial waves (
$ {\bar\delta}_{\rm s}\;(\ell = 2) $ ) and only considering s, p partial waves ($ {\bar\delta}_{\rm s}\; (\ell = 1) $ ). -
[1] 阮军, 王叶兵, 常宏, 刘涛, 董瑞芳, 张首刚 2015 物理学报 64 160308
Google Scholar
Ruan G, Wang Y B, Chang H, Jiang H F, Liu T, Dong R F, Zhang S G 2015 Acta Phys. Sin. 64 160308
Google Scholar
[2] Ludlow A D, Boyd M M, Ye J, Peik E, Schmidt P O 2015 Rev. Mod. Phys. 87 637
Google Scholar
[3] Blatt S, Thomsen J W, Campbell G K, et al. 2009 Phys. Rev. A 80 052703
Google Scholar
[4] Zhu B, Gadway B, Foss-Feig M, Schachenmayer J, Wall M L, Hazzard K R A, Yan B, Moses S A, Covey J P, Jin D S, Ye J, Holland M, Rey A M 2014 Phys. Rev. Lett. 112 070404
[5] Moses S A, Covey J P, Miecnikowski M T, Yan B, Gadway B, Ye J, Jin D S 2015 Science 350 659
Google Scholar
[6] Labuhn H, Barredo D, Ravets S, de Léséleuc S, Macrì T, Lahaye T, Browaeys A 2016 Nature 534 667
Google Scholar
[7] Aikawa K, Baier S, Frisch A, Mark M, Ravensbergen C, Ferlaino F 2014 Science 345 1484
Google Scholar
[8] Burdick N Q, Tang Y, Lev B L 2016 Phys. Rev. X 6 031022
[9] Kadau H, Schmitt M, Wenzel M, Wink C, Maier T, Ferrier-Barbut I, Pfau T 2016 Nature 530 194
Google Scholar
[10] Heller E J, Falconer I S, Dewar R L 2002 Proceedings of the XVIII International Conference on Atomic Physics: the Expanding Frontier of Atomic Physics Cambridge, Massachusett, USA, July 28–August 2, 2002 p363
[11] Zwierlein M W, Hadzibabic Z, Gupta S, Ketterle W 2003 Phys. Rev. Lett. 91 250404
Google Scholar
[12] Campbell G K, Boyd M M, Thomsen J W, et al. 2009 Science 324 360
Google Scholar
[13] Harber D M, Lewandowski H J, Mcguirk J M, Cornell E A 2002 Phys. Rev. A 66 053616
[14] Fuchs J N, Gangardt D M, Laloe F 2002 Phys. Rev. Lett. 88 230404
Google Scholar
[15] Kadio D, Band Y B 2006 Phys. Rev. A 74 053609
[16] Kurt G 2009 Phys. Rev. Lett. 103 113202
Google Scholar
[17] Hazlett E L, Zhang Y, Stites R W, Gibble K, O'Hara K M 2013 Phys. Rev. Lett. 110 160801
[18] Lemke N D, Stecher J V, Sherman J A, Rey A M, Oates C W, Ludlow A D 2011 Phys. Rev. Lett. 107 103902
Google Scholar
[19] Rey A M, Martin M J, Swallows M D, Bishof M, Benko C, Blatt S, Stecher J Von, Gorshkov A, Ye J 2012 IEEE International Frequency Control Symposium (FCS): Probing Many-body Spin Interactions with an Optical Lattice Clock Baltimore, Maryland, USA, May 21–24, 2012 p1
[20] Campbell S L, Hutson R B, Marti G E, Goban A, Oppong N D, Mcnally R L, Sonderhouse L, Robinson J M, Zhang W, Bloom B J 2017 Science 358 90
Google Scholar
[21] Liu G C, Huang Y, Cheng Z, Chen Z R, Yu Z H 2020 Phys. Rev. A 101 012504
Google Scholar
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