Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Measurement of gravity acceleration by cold atoms in a harmonic trap using Kapitza-Dirac pulses

He Tian-Chen Li Ji

Citation:

Measurement of gravity acceleration by cold atoms in a harmonic trap using Kapitza-Dirac pulses

He Tian-Chen, Li Ji
PDF
HTML
Get Citation
  • The interferometry of two Kapitza-Dirac (KD) pulses acting on cold atoms in a harmonic oscillator potential well is investigated by Feynman path integral method. The wave function and density distribution function of the system at a given time are calculated analytically by using the propagator under the action of an external field. The first KD pulse acts on cold atoms to produce a large number of modes in the harmonic oscillator potential well. The maximum value of wave packet of mode 0 is larger than those of other modes. These modes evolve along different paths. The external field changes the phase of each mode and makes the evolution path of the mode deviate from that without the external field. When the second KD pulse is added, it splits the mode of the first KD pulse, and thus generates more modes. These modes will evolve along different paths under the action of external field and harmonic potential well, and interfere with each other. At the moment of measurement, all the wave packets are separated without overlapping. The effect of the external field does not change the magnitude of the density distribution at the time of measurement, but makes the wave packet of each mode shift. The phase difference between adjacent modes decreases linearly with the increase of field intensity. When the external field is a gravity field, we calculate the Fisher information and the Cramer-Rao lowér bound. The Fisher information is proportional to the mass of atoms and inversely to the third power of harmonic potential well frequency. We can improve the measurement accuracy of interferometer by reducing the frequency of harmonic potential well and increasing atomic mass. When the initial state is the ground state of the harmonic potential well, the accuracy of the gravity acceleration measured by the interference device can be obtained to be 10–9 by using the experimental parameters. The initial state is the ground state of the harmonic potential well and the external field, and the calculation result indicates that the measurement accuracy will decrease. At the same time, the enhancement of inter-atomic repulsion and attraction interaction will also lead the measurement accuracy to increase.
      Corresponding author: Li Ji, liji163love@163.com
    • Funds: Project supported by the Scientific and Technologial Innovation Program of Higher Education Institutions in Shanxi, China (Grant Nos. 2019L0785, 2019L0813) and the Beijing Natural Science Foundation, China (Grant No. 1182009).
    [1]

    Fang J, Hu J, Chen X, Zhu H, Zhou L, Zhong J, Wang J, Zhan M 2018 Opt. Express 26 1586Google Scholar

    [2]

    Lu S B, Yao Z W, Li R B, Luo J, Barthwal S, Chen H H, Lu Z X, Wang J, Zhan M S 2018 Opt. Commun. 429 158Google Scholar

    [3]

    Fang B, Mielec N, Savoie D, Altorio M, Landragin A, Geiger R 2018 New J. Phys. 20 023020Google Scholar

    [4]

    Jaffe M, Xu V, Haslinger P, Müller H, Hamilton P 2018 Phys. Rev. Lett. 121 040402Google Scholar

    [5]

    Carey M, Saywell J, Elcock D, Belal M, Freegarde T 2019 Phys. Rev. A 99 023631Google Scholar

    [6]

    Wigley P B, Hardman K S, Freier C, Everitt P J, Legge S, Manju P, Close J D, Robins N P 2019 Phys. Rev. A 99 023615Google Scholar

    [7]

    Arias A, Lochead G, Wintermantel T M, Helmrich S, Whitlock S 2019 Phys. Rev. Lett. 122 053601Google Scholar

    [8]

    Zhou L, Xiong Z Y, Yang W, Tang B, Peng W C, Wang Y B, Xu P, Wang J, Zhan M S 2011 Chin. Phys. Lett. 28 013701Google Scholar

    [9]

    Imanishi Y, Sato T, Higashi T, Sun W, Okubo S 2004 Science 306 476Google Scholar

    [10]

    Kibble B P 1991 Proc. IEE: Science, Measurement and Technology 138 187Google Scholar

    [11]

    Blakely R J, Jachens R C 1991 Geological Society of America Bulletin 103 795Google Scholar

    [12]

    Peters A, Chung K Y, Chu S 2001 Metrologia 38 25Google Scholar

    [13]

    Rasel E M, Oberthaler M K, Batelaan H, Schmiedmayer J, Zeilinger A 1995 Phys. Rev. Lett. 75 2633Google Scholar

    [14]

    Giltner D M, McGowan R W, Lee S A 1995 Phys. Rev. Lett. 75 2638Google Scholar

    [15]

    吴彬, 程冰, 付志杰, 朱栋, 周寅, 翁堪兴, 王肖隆, 林强 2018 物理学报 67 190302Google Scholar

    Wu B, Cheng B, Fu Z J, Zhu D, Zhou Y, Wong K X, Wang X L, Lin Q 2018 Acta Phys. Sin. 67 190302Google Scholar

    [16]

    McGuirk J M, Foster G T, Fixler J B, Snadden M J, Kasevich M A 2002 Phys. Rev. A 65 033608Google Scholar

    [17]

    Fixler J B, Foster G T, McGuirk J M, Kasevich M A 2007 Science 315 74Google Scholar

    [18]

    Li W D, He T, Smerzi A 2014 Phys. Rev. Lett. 113 023003Google Scholar

    [19]

    杨志安 2013 物理学报 62 110302Google Scholar

    Yang Z A 2013 Acta Phys. Sin. 62 110302Google Scholar

    [20]

    He T C, Niu P B 2017 Phys. Lett. A 381 108

    [21]

    Cheng R, He T, Li W, Smerzi A 2016 J. Mod. Phys. 7 2043Google Scholar

    [22]

    Sapiro R E, Zhang R, Raithel G 2009 Phys. Rev. A 79 043630Google Scholar

    [23]

    Keller C, Schmiedmayer J, Zeilinger A, Nonn T, Dürr S, Rempe G 1999 Appl. Phys. B: Lasers Opt. 69 303Google Scholar

    [24]

    Dong G J, Zhu J, Zhang W P, Malomed B A 2013 Phys. Rev. Lett. 110 250401Google Scholar

    [25]

    Zhu J, Dong G J, Shneider M N, Zhang W P 2011 Phys. Rev. Lett. 106 210403Google Scholar

    [26]

    Chwedenczuk J, Piazza F, Smerzi A 2013 Phys. Rev. A 87 033607Google Scholar

    [27]

    Shin Y, Saba M, Schirotzek A, Pasquini T A, Leanhardt A E, Pritchard D E, Ketterle W 2004 Phys. Rev. Lett. 92 150401Google Scholar

    [28]

    Lehtovaara L, Toivanen J, Eloranta J 2007 J. Comput. Phys. 221 148Google Scholar

    [29]

    Bandrauk A D, Shen H 1994 J. Phys. A 27 7147Google Scholar

    [30]

    Fattori M, D’Errico C, Roati G, Zaccanti M, Jona-Lasinio M, Modugno M, Inguscio M, Modugno G 2008 Phys. Rev. Lett. 100 080405Google Scholar

  • 图 1  简谐势阱中冷原子受到两次KD脉冲的示意图 在测量时刻${t_{\rm{f}}} ={\text{π}}/\omega $, 不同模式相干叠加, $\beta $为外场

    Figure 1.  Diagram of cold atoms with two KD pulses in harmonic oscillator potential. At the measurement time ${t_{\rm{f}}} = {\text{π}}/\omega $, the coherent superposition of different modes occurs. $\beta $ is the external field.

    图 2  没有外场的情况下($\beta = 0$), 系统态密度分布函数的演化规律 无量纲参数为$V = 1,\; k = 10$, 测量时刻在$t = {t_{\rm{f}}} = {\text{π}}$, 两次KD脉冲都用红色箭头表示, 态密度演化图右边的彩色条表示态密度分布函数值由低(蓝色)变到高(红色)

    Figure 2.  In the absence of an external field ($\beta = 0$), the density distribution function of system varies with time. The dimensionless parameter are $V = 1,\; k = 10$. The measurement time is at $t = {t_{\rm{f}}} ={\text{π}}$. Both KD pulses are represented by red arrows. The color bar on the right side of the density of states evolution diagram indicates that the value of the density distribution function changes from low (blue) to high (red).

    图 3  在外场$\beta = 1$的情况下, 系统态密度分布函数的演化规律 图中除$\beta $之外的其他无量纲参数与图2相同, 红色箭头为KD脉冲, 测量时刻在$t = {t_{\rm{f}}} = {\text{π}}$

    Figure 3.  In the case of external field $\beta = 1$, the evolution of density distribution function of the system is obtained. The dimensionless parameters in this figure are the same as those in Figure 2. The red arrow are KD pulses. The measurement time is at $t = {t_{\rm{f}}} = {\text{π}}$.

    图 4  在外场$\beta = 2$的情况下, 系统态密度分布函数的演化规律 图中除$\beta $之外的其他无量纲参数与图2相同, 红色的箭头为KD脉冲, 测量时刻在$t = {t_{\rm{f}}} = {\text{π}}$

    Figure 4.  In the case of external field $\beta = 2$, the evolution of density distribution function of the system is obtained. The dimensionless parameters in this figure are the same as those in Figure 2. The red arrow are KD pulses. The measurement time is at $t = {t_{\rm{f}}} = {\text{π}}$.

    图 5  图2图3图4中测量时刻${t_{\rm{f}}} = {\text{π}}$态密度的分布规律

    Figure 5.  The density distribution functions at measuring time${t_{\rm{f}}} = {\text{π}}$ for figure 2, 3, and 4.

    图 6  外场$\beta = 1$的情况下系统基态的态密度分布函数, 不同的颜色对应不同非线性相互作用下的态密度分布函数

    Figure 6.  In the case of external field $\beta = 1$, the density distribution function of the ground state of the system. Different colors correspond to the density distribution function under different non-linear interactions.

    图 7  在外场$\beta = 1$的情况下系统基态的态密度分布函数, 不同的颜色对应不同非线性相互作用下的态密度分布函数

    Figure 7.  In the case of external field $\beta = 1$, the density distribution function of the ground state of the system. Different colors correspond to the density distribution function under different non-linear interactions.

    图 8  $V = 1,\;k = 10,\; \beta = {\rm{1}}$的情况下测量时刻的态密度分布函数, 不同的颜色对应不同非线性相互作用下的态密度分布函数

    Figure 8.  In the case of $V = 1,\;k = 10,\; \beta = {\rm{1}}$, the density distribution functions at measuring time. Different colors correspond to the density distribution function under different non-linear interactions.

    图 9  图8中0模式的放大图

    Figure 9.  Detailed diagram of 0 mode in Fig. 8.

    图 10  测量时刻系统态密度的分布函数, 除了非线性参数以外的其他无量纲参数和图8相同

    Figure 10.  The density distribution functions at measuring time, dimensionless parameters other than non-linear parameters are the same as those in Fig. 8.

    图 11  图10中0模式的放大图

    Figure 11.  Detailed diagram of 0 mode in Fig. 10.

    图 12  系统的测量精度随非线性参数的变化规律, 除了非线性参数以外的其他无量纲参数和图8相同

    Figure 12.  The variation of measuring accuracy of the system with nonlinear parameters, dimensionless parameters other than non-linear parameters are the same as those in Fig. 8.

  • [1]

    Fang J, Hu J, Chen X, Zhu H, Zhou L, Zhong J, Wang J, Zhan M 2018 Opt. Express 26 1586Google Scholar

    [2]

    Lu S B, Yao Z W, Li R B, Luo J, Barthwal S, Chen H H, Lu Z X, Wang J, Zhan M S 2018 Opt. Commun. 429 158Google Scholar

    [3]

    Fang B, Mielec N, Savoie D, Altorio M, Landragin A, Geiger R 2018 New J. Phys. 20 023020Google Scholar

    [4]

    Jaffe M, Xu V, Haslinger P, Müller H, Hamilton P 2018 Phys. Rev. Lett. 121 040402Google Scholar

    [5]

    Carey M, Saywell J, Elcock D, Belal M, Freegarde T 2019 Phys. Rev. A 99 023631Google Scholar

    [6]

    Wigley P B, Hardman K S, Freier C, Everitt P J, Legge S, Manju P, Close J D, Robins N P 2019 Phys. Rev. A 99 023615Google Scholar

    [7]

    Arias A, Lochead G, Wintermantel T M, Helmrich S, Whitlock S 2019 Phys. Rev. Lett. 122 053601Google Scholar

    [8]

    Zhou L, Xiong Z Y, Yang W, Tang B, Peng W C, Wang Y B, Xu P, Wang J, Zhan M S 2011 Chin. Phys. Lett. 28 013701Google Scholar

    [9]

    Imanishi Y, Sato T, Higashi T, Sun W, Okubo S 2004 Science 306 476Google Scholar

    [10]

    Kibble B P 1991 Proc. IEE: Science, Measurement and Technology 138 187Google Scholar

    [11]

    Blakely R J, Jachens R C 1991 Geological Society of America Bulletin 103 795Google Scholar

    [12]

    Peters A, Chung K Y, Chu S 2001 Metrologia 38 25Google Scholar

    [13]

    Rasel E M, Oberthaler M K, Batelaan H, Schmiedmayer J, Zeilinger A 1995 Phys. Rev. Lett. 75 2633Google Scholar

    [14]

    Giltner D M, McGowan R W, Lee S A 1995 Phys. Rev. Lett. 75 2638Google Scholar

    [15]

    吴彬, 程冰, 付志杰, 朱栋, 周寅, 翁堪兴, 王肖隆, 林强 2018 物理学报 67 190302Google Scholar

    Wu B, Cheng B, Fu Z J, Zhu D, Zhou Y, Wong K X, Wang X L, Lin Q 2018 Acta Phys. Sin. 67 190302Google Scholar

    [16]

    McGuirk J M, Foster G T, Fixler J B, Snadden M J, Kasevich M A 2002 Phys. Rev. A 65 033608Google Scholar

    [17]

    Fixler J B, Foster G T, McGuirk J M, Kasevich M A 2007 Science 315 74Google Scholar

    [18]

    Li W D, He T, Smerzi A 2014 Phys. Rev. Lett. 113 023003Google Scholar

    [19]

    杨志安 2013 物理学报 62 110302Google Scholar

    Yang Z A 2013 Acta Phys. Sin. 62 110302Google Scholar

    [20]

    He T C, Niu P B 2017 Phys. Lett. A 381 108

    [21]

    Cheng R, He T, Li W, Smerzi A 2016 J. Mod. Phys. 7 2043Google Scholar

    [22]

    Sapiro R E, Zhang R, Raithel G 2009 Phys. Rev. A 79 043630Google Scholar

    [23]

    Keller C, Schmiedmayer J, Zeilinger A, Nonn T, Dürr S, Rempe G 1999 Appl. Phys. B: Lasers Opt. 69 303Google Scholar

    [24]

    Dong G J, Zhu J, Zhang W P, Malomed B A 2013 Phys. Rev. Lett. 110 250401Google Scholar

    [25]

    Zhu J, Dong G J, Shneider M N, Zhang W P 2011 Phys. Rev. Lett. 106 210403Google Scholar

    [26]

    Chwedenczuk J, Piazza F, Smerzi A 2013 Phys. Rev. A 87 033607Google Scholar

    [27]

    Shin Y, Saba M, Schirotzek A, Pasquini T A, Leanhardt A E, Pritchard D E, Ketterle W 2004 Phys. Rev. Lett. 92 150401Google Scholar

    [28]

    Lehtovaara L, Toivanen J, Eloranta J 2007 J. Comput. Phys. 221 148Google Scholar

    [29]

    Bandrauk A D, Shen H 1994 J. Phys. A 27 7147Google Scholar

    [30]

    Fattori M, D’Errico C, Roati G, Zaccanti M, Jona-Lasinio M, Modugno M, Inguscio M, Modugno G 2008 Phys. Rev. Lett. 100 080405Google Scholar

  • [1] Zhai Hui. Non-equilibrium quantum many-body physics with ultracold atoms. Acta Physica Sinica, 2023, 72(23): 230701. doi: 10.7498/aps.72.20231375
    [2] Tian Li-Man, Wen Yong-Li, Wang Yun-Fei, Zhang Shan-Chao, Li Jian-Feng, Du Jing-Song, Yan Hui, Zhu Shi-Liang. Research progress of measurement of propagators in path integrals. Acta Physica Sinica, 2023, 72(20): 200305. doi: 10.7498/aps.72.20230902
    [3] Zhang Su-Zhao, Sun Wen-Jun, Dong Meng, Wu Hai-Bin, Li Rui, Zhang Xue-Jiao, Zhang Jing-Yi, Cheng Yong-Jun. Vacuum pressure measurement based on 6Li cold atoms in a magneto-optical trap. Acta Physica Sinica, 2022, 71(9): 094204. doi: 10.7498/aps.71.20212204
    [4] Luo Yu-Chen, Li Xiao-Peng. Quantum simulation of interacting fermions. Acta Physica Sinica, 2022, 71(22): 226701. doi: 10.7498/aps.71.20221756
    [5] Li Mo, Chen Fei-Liang, Luo Xiao-Jia, Yang Li-Jun, Zhang Jian. Fundamental principles, key enabling technologies, and research progress of atom chips. Acta Physica Sinica, 2021, 70(2): 023701. doi: 10.7498/aps.70.20201561
    [6] Cheng Bing, Zhou Yin, Chen Pei-Jun, Zhang Kai-Jun, Zhu Dong, Wang Kai-Nan, Weng Kan-Xing, Wang He-Lin, Peng Shu-Ping, Wang Xiao-Long, Wu Bin, Lin Qiang. Absolute gravity measurement based on atomic gravimeter under mooring state of a ship. Acta Physica Sinica, 2021, 70(4): 040304. doi: 10.7498/aps.70.20201522
    [7] Wu Bin, Zhou Yin, Cheng Bing, Zhu Dong, Wang Kai-Nan, Zhu Xin-Xin, Chen Pei-Jun, Weng Kan-Xing, Yang Qiu-Hai, Lin Jia-Hong, Zhang Kai-Jun, Wang He-Lin, Lin Qiang. Static measurement of absolute gravity in truck based on atomic gravimeter. Acta Physica Sinica, 2020, 69(6): 060302. doi: 10.7498/aps.69.20191765
    [8] Wu Bin, Cheng Bing, Fu Zhi-Jie, Zhu Dong, Zhou Yin, Weng Kan-Xing, Wang Xiao-Long, Lin Qiang. Measurement of absolute gravity based on cold atom gravimeter at large tilt angle. Acta Physica Sinica, 2018, 67(19): 190302. doi: 10.7498/aps.67.20181121
    [9] Wei Chun-Hua, Yan Shu-Hua, Yang Jun, Wang Guo-Chao, Jia Ai-Ai, Luo Yu-Kun, Hu Qing-Qing. Design and control of large-detuned optical lattice based on 87Rb atoms. Acta Physica Sinica, 2017, 66(1): 010701. doi: 10.7498/aps.66.010701
    [10] Yuan Du-Qi. Thermodynamics of trapped finite unitary Fermi gas. Acta Physica Sinica, 2016, 65(18): 180302. doi: 10.7498/aps.65.180302
    [11] Yuan Du-Qi. Boundary effects of Bose-Einstein condensation in a three-dimensional harmonic trap. Acta Physica Sinica, 2014, 63(17): 170501. doi: 10.7498/aps.63.170501
    [12] Xiong Zong-Yuan, Yao Zhan-Wei, Wang Ling, Li Run-Bin, Wang Jin, Zhan Ming-Sheng. Control of atomic path in projectile cold atom gyroscope. Acta Physica Sinica, 2011, 60(11): 113201. doi: 10.7498/aps.60.113201
    [13] Qiu Ying, He Jun, Wang Yan-Hua, Wang Jing, Zhang Tian-Cai, Wang Jun-Min. Loading and cooling of cesium atoms in 3D optical lattice. Acta Physica Sinica, 2008, 57(10): 6227-6232. doi: 10.7498/aps.57.6227
    [14] Jiang Kai-Jun, Li Ke, Wang Jin, Zhan Ming-Sheng. Dependence of number of trapped atoms on the experimental parameters of Rb magneto-optical trap. Acta Physica Sinica, 2006, 55(1): 125-129. doi: 10.7498/aps.55.125
    [15] Tang Lin, Huang Jian-Hua, Duan Zheng-Lu, Zhang Wei-Ping, Zhou Zhao-Ying, Feng Yan-Ying, Zhu Rong. Quantum tunnelling time of cold atom passing through a laser beam. Acta Physica Sinica, 2006, 55(12): 6606-6611. doi: 10.7498/aps.55.6606
    [16] Geng Tao, Yan Shu-Bin, Wang Yan-Hua, Yang Hai-Jing, Zhang Tian-Cai, Wang Jun-Min. Temperature measurement of cold atoms in a cesium magneto-optical trap by means of short-distance time-of-flight absorption spectrum. Acta Physica Sinica, 2005, 54(11): 5104-5108. doi: 10.7498/aps.54.5104
    [17] Yin Jian-Ling, Liu Cheng-Yi, Yang You-Yuan, Liu Jiang, Fan Guang-Han. Effective ABCD formulation of the propagation of the atom laser. Acta Physica Sinica, 2004, 53(2): 356-361. doi: 10.7498/aps.53.356
    [18] Wang Ping, Yang Xin-E, Song Xiao-Hui. Exact solution for a harmonic oscillator with a time-dependent inverse square po tential by path-integral. Acta Physica Sinica, 2003, 52(12): 2957-2960. doi: 10.7498/aps.52.2957
    [19] Luo You-Hua, Huang Zheng, Wang Yu-Zhu. . Acta Physica Sinica, 2002, 51(8): 1706-1710. doi: 10.7498/aps.51.1706
    [20] LING RUI-LIANG. PROPAGATOR AND EXACT WAVE FUNCTION OF THE TIME DEPENDENTLY DAMPED HARMONIC OSCILLATOR. Acta Physica Sinica, 2001, 50(8): 1421-1424. doi: 10.7498/aps.50.1421
Metrics
  • Abstract views:  6378
  • PDF Downloads:  73
  • Cited By: 0
Publishing process
  • Received Date:  17 May 2019
  • Accepted Date:  06 August 2019
  • Available Online:  01 October 2019
  • Published Online:  20 October 2019

/

返回文章
返回