Planar quantum squeezing and atom interferometry

Huang Xin-Yao; Xiang Yu; Sun Feng-Xiao; He Qiong-Yi; Gong Qi-Huang

doi:10.7498/aps.64.160304

Abstract

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.

Keywords:

Authors and contacts

1.
State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China;
2.
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11274025, 61475006, 11121091).

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Cited By

[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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Vol. 64, Issue 16 - 2015-08-20

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