quantum spin squeezing

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  • Physics Reports 509 (2011) 89165 Contents lists available at SciVerse ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep Quantum spin squeezing Jian Maa,b, , Xiaoguang Wanga,b , C.P. Suna,c , Franco Noria,d a Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan b Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China c Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China d Physics Department, The University of Michigan, Ann Arbor, MI 48109-1040, USA a r t i c l e i n f o Article history: Accepted 27 June 2011 Available online 31 August 2011 editor: G.I. Stegeman a b s t r a c t This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to SU(2) rotations, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin- squeezed states produced with nonlinear twisting Hamiltonians. Afterward, we explain pairwise correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin squeezing. Finally, we review several experimental realizations of spin squeezing, as well as their corresponding theoretical backgrounds, including: producing spin-squeezed states via particle collisions in BoseEinstein condensates, transferring photon squeezing to atomic ensembles, and generating spin squeezing via quantum non- demolition measurements. 2011 Elsevier B.V. All rights reserved. Contents 1. Introduction.......................................................................................................................................................................................... 90 1.1. Generating spin squeezing in atomic ensembles via atomphoton interactions................................................................ 91 1.2. Generating spin squeezing in a BEC via atomic collisions .................................................................................................... 91 1.3. Organization of this review..................................................................................................................................................... 92 2. Definitions of spin squeezing .............................................................................................................................................................. 92 2.1. Coherent state and bosonic squeezing ................................................................................................................................... 92 2.1.1. Coherent state........................................................................................................................................................... 93 2.1.2. Generation of bosonic squeezed states ................................................................................................................... 93 2.2. Coherent spin state.................................................................................................................................................................. 94 2.3. Spin-squeezing parameters based on the Heisenberg uncertainty relation........................................................................ 95 2.4. Squeezing parameter 2 S given by Kitagawa and Ueda ......................................................................................................... 96 2.5. Squeezing parameter 2 R given by Wineland et al. ................................................................................................................ 98 2.6. Other spin-squeezing parameters .......................................................................................................................................... 100 2.7. Rotationally-invariant extensions of squeezing parameters ................................................................................................ 101 2.8. Spin-squeezing parameters for states with parity ................................................................................................................ 103 2.8.1. Spin-squeezing parameters 2 S and 2 R .................................................................................................................... 103 Corresponding author at: Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China. E-mail addresses: majian84@gmail.com (J. Ma), xgwang@zimp.zju.edu.cn (X. Wang). 0370-1573/$ see front matter 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physrep.2011.08.003
  • 90 J. Ma et al. / Physics Reports 509 (2011) 89165 2.8.2. Spin-squeezing parameter 2 E .................................................................................................................................. 104 2.8.3. Dicke states ............................................................................................................................................................... 105 2.9. Relations between spin squeezing and bosonic squeezing................................................................................................... 105 3. Generation of spin squeezing with nonlinear twisting Hamiltonians.............................................................................................. 106 3.1. One-axis twisting Hamiltonian............................................................................................................................................... 106 3.1.1. One-axis twisted states ............................................................................................................................................ 107 3.1.2. One-axis twisting with a transverse field ............................................................................................................... 108 3.1.3. One-axis twisting in BoseEinstein condensates ................................................................................................... 109 3.1.4. One-axis twisting from large-detuned atomfield interaction ............................................................................. 110 3.2. Two-axis twisted states........................................................................................................................................................... 111 4. Spin squeezing, negative pairwise correlations, and entanglement ................................................................................................ 112 4.1. Spin squeezing and pairwise correlations.............................................................................................................................. 112 4.1.1. Spin-squeezing parameter 2 S and correlation Gn,n ............................................................................................ 113 4.1.2. Spin-squeezing parameter 2 E and correlation G1n,2n ............................................................................................. 113 4.2. Spin squeezing and pairwise entanglement .......................................................................................................................... 114 4.3. Spin squeezing and many-body entanglement ..................................................................................................................... 117 4.4. Spin-squeezing inequalities for higher spin-j systems ......................................................................................................... 118 4.5. Two-mode spin-squeezed states ............................................................................................................................................ 118 5. Spin squeezing, Fisher information, and quantum metrology.......................................................................................................... 119 5.1. Quantum Fisher information .................................................................................................................................................. 119 5.2. Spin squeezing and quantum Fisher information ................................................................................................................. 120 5.3. Spin squeezing, Fisher information and metrology............................................................................................................... 121 5.4. MachZehnder interferometer as an optical version of Ramsey interferometry................................................................ 124 6. Spin squeezing, quantum phase transitions, and quantum chaos.................................................................................................... 125 6.1. Spin squeezing and quantum phase transitions in the LipkinMeshkovGlick model ...................................................... 125 6.2. Spin squeezing and quantum chaos in the quantum kicked-top model.............................................................................. 126 6.3. Spin squeezing and quantum chaos in the Dicke model....................................................................................................... 128 7. Spin squeezing under decoherence .................................................................................................................................................... 130 7.1. Decoherence and spin squeezing generation ................................................................................................

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