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在玻色-爱因斯坦凝聚体中实现自旋压缩和量子纠缠, 对于提高原子干涉测量相位灵敏度和原子钟精度有着非常重要的意义. 基于一种新的平面自旋分量的不确定性关系, 介绍了如何利用两分量玻色-爱因斯坦凝聚系统中原子间相互作用提供的非线性效应和原子内部能级间线性耦合, 实现量子平面自旋压缩(挤压)和模式纠缠. 描述了一项关于平面压缩态的理论工作, 该工作利用哈密顿量的精确对角化求解系统基态, 优化非线性作用和线性耦合强度比值, 使得包含平均自旋方向在内的两个正交自旋分量的不确定度同时压缩, 因此在平面上所有相位角度的涨落都受到压制, 而在与该平面垂直的第三个自旋分量方向反压缩. 利用传统自旋压缩判定纠缠, 只能判断多个不可分辨的原子处于纠缠态, 而平面自旋压缩可以检测两个可区分模式(比如, 原子内态)间的纠缠, 从而在不同模式间进行量子信息处理. 同时, 为实现超越标准量子极限的原子干涉相位精密测量, 传统方式是利用单个自旋分量压缩, 但需要对待测相位角度有很好的估计, 或者可以进行多次测量以逐渐逼近可获得的最大压缩极限, 这就要求量子态可以被精确的重复制备. 而利用平面自旋压缩, 对任意未知相位角度只需要测量两个垂直自旋分量就可以实现高的相位测量灵敏度.Reduction of quantum noise in one spin component is a significant tool for enhancing the sensitivities of interferometers and atomic clocks. It has been recently implemented for ultra-cold atomic Bose-Einstein condensate (BEC) interferometer. This type of quantum noise reduction reduces the measurement noise near some predetermined phase. However, if the phase is completely unknown prior to measurement, then it is not known which phase quadrature should be in a squeezed state. We introduce a novel planar squeezing uncertainty relation for spin variance in a plane, and analyze how to obtain such a planar quantum squeezed (PQS) state by using a double-well single component BEC, through the use of local nonlinear S-wave scattering interaction between trapped atoms. Here, we consider the PQS that is generated by using two hyperfine states in a two components BEC system, which is useful for quantum metrology. By comparison with the case of two spatial wells, the Hamiltonian parameters can be controlled in a more efficient way. The spin component can be measured by detecting the occupation number difference between the two internal modes, while one needs to observe a spatial interference pattern in the double well BEC case. This is the major difference between the internal and external cases. Another difference is that one can use the Rabi frequency Ω instead of the Josephson parameters to switch the Hamiltonian parameters through using a diabatic technique. Therefore the coupling could be switched off or on to study the different evolutions. PQS simultaneously reduces the quantum noises of two orthogonal spin projections below the standard quantum limit, while increases the noise in the third dimension. This allows the improvement in phase measurement at any phase-angle. PQS states that reductions of fluctuations everywhere in a plane have potential utility in "one-shot" phase measurement, where iterative or repeated measurement strategies cannot be utilized. The improved interferometric phase measurements and planar uncertainty relations are useful for detecting the entanglement in mesoscopic system between two distinguished modes regardless of the third component.
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Keywords:
- Bose-Einstein condensate /
- spin squeezing /
- entanglement /
- atom interferometry
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[1] Wineland D J, Bollinger J J, Itano W M, Heinzen D J 1994 Phys. Rev. A 50 67
[2] Wineland D J, Bollinger J J, Itano W M, Moore F L, Heinzen D J 1992 Phys. Rev. A 46 6797
[3] Kuzmich A, Mølmer K, Polzik E S 1997 Phys. Rev. Lett. 79 4782
[4] Agarwal G S, Puri R R 1990 Phys. Rev. A 41 3782
[5] Zou H M, Fang M F, Yang B Y 2013 Chin. Phys. B 22 120303
[6] Hofmann H F, Takeuchi S 2003 Phys. Rev. A 68 032103
[7] Tóth G, Knapp C, Gühne O, Briegel H J 2009 Phys. Rev. A 79 042334
[8] Liu S Y, Zheng K M, Jia F, Hu L Y, Xie F S 2014 Acta Phys. Sin. 63 140302 (in Chinese) [刘世右, 郑凯敏, 贾芳, 胡利云, 谢芳森 2014 63 140302]
[9] Zhou B J, Peng Z H, Jia C X, Jiang C L, Liu X J 2014 Chin. Phys. B 23 120305
[10] Cavalcanti E G, Drummond P D, Bachor H A, Reid M D 2009 Opt. Express 17 18693
[11] Reid M D, Drummond P D, Bowen W P, Cavalcanti E G, Lam P K, Bachor H A, Andersen U L, Leuchs G 2009 Rev. Mod. Phys. 81 1727
[12] Cavalcanti E G, Jones S J, Wiseman H M, Reid M D 2009 Phys. Rev. A 80 032112
[13] Kitagawa M, Ueda M 1993 Phys. Rev. A 47 5138
[14] Estève J, Gross C, Weller A, Giovanazzi S, Oberthaler M K 2008 Nature 455 1216
[15] Riedel M F, Bøhi P, Li Y, Hönsch T W, Sinatra A, Treutlein P 2010 Nature 464 1170
[16] Gross C, Zibold T, Nicklas E, Estève J, Oberthaler M K 2010 Nature 464 1165
[17] Ma J, Wang X G, Sun C P, Nori F 2011 Phys. Rep. 509 89
[18] Chang F, Wang X Q, Gai Y J, Yan D, Song L J 2014 Acta Phys. Sin. 63 170302 (in Chinese) [常峰, 王晓茜, 盖永杰, 严冬, 宋立军 2014 63 170302]
[19] He Q Y, Peng S G, Drummond P D, Reid M D 2011 Phys. Rev. A 84 022107
[20] He Q Y, Vaughan T G, Drummond P D, Reid M D 2012 New J. Phys. 14 093012
[21] Smerzi A, Fantoni S 1997 Phys. Rev. Lett. 78 3589
[22] Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623
[23] Yan D, Song L J, Chen D W 2009 Acta Phys. Sin. 58 3679 (in Chinese) [严冬, 宋立军, 陈殿伟 2009 58 3679]
[24] Wu B, Niu Q 2000 Phys. Rev. A 61 23402
[25] Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404
[26] Wu B, Liu J, Niu Q 2005 Phys. Rev. Lett. 94 140402
[27] Raghavan S, Smerzi A, Fantoni S, Shenoy S R 1999 Phys. Rev. A 59 620
[28] Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 13619
[29] Liu B, Fu L B, Yang S P, Liu J 2007 Phys. Rev. A 75 33601
[30] Kasamatsu K, Tsubota M, Ueda M 2003 Phys. Rev. Lett. 91 150406
[31] Kasamatsu K, Tsubota M 2009 Phys. Rev. A 79 023606
[32] Mason P, Aftalion A 2011 Phys. Rev. A 84 033611
[33] Wang C, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403
[34] Xu Z F, Lu R, You L 2011 Phys. Rev. A 83 053602
[35] Hu H, Ramachandhran B, Pu H, Liu X J 2012 Phys. Rev. Lett. 108 010402
[36] Xu Z F, Kawaguchi Y, You L, Ueda M 2012 Phys. Rev. A 86 033628
[37] Wang C, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403
[38] Puentes G, Colangelo G, Sewell1 R J, Mitchell M W 2013 New J. Phys. 15 103031
[39] He Q Y, Drummond P D, Olsen M K, Reid M D 2012 Phys. Rev. A 86 023626
[40] He Q Y, Reid M D, Vaughan T G, Gross C, Oberthaler M, Drummond P D 2011 Phys. Rev. Lett. 106 120405
[41] Law C K, Ng H, Leung P 2001 Phys. Rev. A 63 055601
[42] Fattori M, D'Errico C, Roati G, Zaccanti M, Jona L M, Modugno M, Inguscio M, Modugno G 2008 Phys. Rev. Lett. 100 080405
[43] Hillery M, Zubairy M S 2006 Phys. Rev. Lett. 96 050503
[44] Cavalcanti E G, He Q Y, Reid M D, Wiseman H M 2011 Phys. Rev. A 84 032115
[45] Sørensen A S, Mølmer K 2001 Phys. Rev. Lett. 86 4431
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