Quantum spin squeezing

Physics Reports - Tập 509 - Trang 89-165 - 2011
Jian Ma1,2, Xiaoguang Wang1,2, C.P. Sun1,3, Franco Nori1,4
1Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan
2Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027, China
3Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
4Physics Department, The University of Michigan, Ann Arbor, MI 48109-1040, USA

Tài liệu tham khảo

Kitagawa, 1993, Squeezed spin states, Phys. Rev. A, 47, 5138, 10.1103/PhysRevA.47.5138 Wineland, 1992, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A, 46, R6797, 10.1103/PhysRevA.46.R6797 Wineland, 1994, Squeezed atomic states and projection noise in spectroscopy, Phys. Rev. A, 50, 67, 10.1103/PhysRevA.50.67 Sørensen, 2001, Many-particle entanglement with Bose–Einstein condensates, Nature, 409, 63, 10.1038/35051038 Bigelow, 2001, Quantum engineering—squeezing entanglement, Nature, 409, 27, 10.1038/35051193 Guehne, 2009, Entanglement detection, Phys. Rep., 474, 1, 10.1016/j.physrep.2009.02.004 Polzik, 2008, Quantum physics—the squeeze goes on, Nature, 453, 45, 10.1038/453045a Cronin, 2009, Optics and interferometry with atoms and molecules, Rev. Modern Phys., 81, 1051, 10.1103/RevModPhys.81.1051 Amico, 2008, Entanglement in many-body systems, Rev. Modern Phys., 80, 517, 10.1103/RevModPhys.80.517 Horodecki, 2009, Quantum entanglement, Rev. Modern Phys., 81, 865, 10.1103/RevModPhys.81.865 Nielsen, 2000 Stolze, 2008 Ulam-Orgikh, 2001, Spin squeezing and decoherence limit in Ramsey spectroscopy, Phys. Rev. A, 64, 052106, 10.1103/PhysRevA.64.052106 Wootters, 1998, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett., 80, 2245, 10.1103/PhysRevLett.80.2245 Wang, 2003, Spin squeezing and pairwise entanglement for symmetric multiqubit states, Phys. Rev. A, 68, 012101, 10.1103/PhysRevA.68.012101 Hald, 1999, Spin squeezed atoms: a macroscopic entangled ensemble created by light, Phys. Rev. Lett., 83, 1319, 10.1103/PhysRevLett.83.1319 Orzel, 2001, Squeezed states in a Bose–Einstein condensate, Science, 291, 2386, 10.1126/science.1058149 Estève, 2008, Squeezing and entanglement in a Bose–Einstein condensate, Nature, 455, 1216, 10.1038/nature07332 Gross, 2010, Nonlinear atom interferometer surpasses classical precision limit, Nature, 464, 1165, 10.1038/nature08919 Riedel, 2010, Atom-chip-based generation of entanglement for quantum metrology, Nature, 464, 1170, 10.1038/nature08988 Julsgaard, 2001, Experimental long-lived entanglement of two macroscopic objects, Nature, 413, 400, 10.1038/35096524 Fernholz, 2008, Spin squeezing of atomic ensembles via nuclear–electronic spin entanglement, Phys. Rev. Lett., 101, 073601, 10.1103/PhysRevLett.101.073601 Appel, 2009, Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit, Proc. Natl. Acad. Sci., 106, 10960, 10.1073/pnas.0901550106 Louchet-Chauvet, 2010, Entanglement-assisted atomic clock beyond the projection noise limit, New J. Phys., 12, 065032, 10.1088/1367-2630/12/6/065032 Takano, 2009, Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half, Phys. Rev. Lett., 102, 033601, 10.1103/PhysRevLett.102.033601 Korbicz, 2005, Spin squeezing inequalities and entanglement of N qubit states, Phys. Rev. Lett., 95, 120502, 10.1103/PhysRevLett.95.120502 Korbicz, 2006, Generalized spin-squeezing inequalities in N-qubit systems: theory and experiment, Phys. Rev. A, 74, 052319, 10.1103/PhysRevA.74.052319 Tóth, 2009, Spin squeezing and entanglement, Phys. Rev. A, 79, 042334, 10.1103/PhysRevA.79.042334 Buluta You, 2005, Superconducting circuits and quantum information, Phys. Today, 58, 42, 10.1063/1.2155757 You, 2011, Atomic physics and quantum optics using superconducting circuits, Nature, 474, 589, 10.1038/nature10122 Shevchenko, 2010, Landau–Zener–Stuckelberg interferometry, Phys. Rep., 492, 1, 10.1016/j.physrep.2010.03.002 Buluta, 2009, Quantum simulators, Science, 326, 108, 10.1126/science.1177838 Bollinger, 1996, Optimal frequency measurements with maximally correlated states, Phys. Rev. A, 54, R4649, 10.1103/PhysRevA.54.R4649 Agarwal, 1996, Ramsey spectroscopy with nonclassical light sources, Phys. Rev. A, 53, 467, 10.1103/PhysRevA.53.467 1997 Xu, 1999, State-selective Rabi and Ramsey magnetic resonance line shapes, Phys. Rev. A, 59, R922, 10.1103/PhysRevA.59.R922 Meyer, 2001, Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions, Phys. Rev. Lett., 86, 5870, 10.1103/PhysRevLett.86.5870 Smith, 2004, Continuous weak measurement and nonlinear dynamics in a cold spin ensemble, Phys. Rev. Lett., 93, 163602, 10.1103/PhysRevLett.93.163602 Döring, 2010, Quantum-projection-noise-limited interferometry with coherent atoms in a Ramsey-type setup, Phys. Rev. A, 81, 043633, 10.1103/PhysRevA.81.043633 Oblak, 2005, Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition, Phys. Rev. A, 71, 043807, 10.1103/PhysRevA.71.043807 Sørensen, 1999, Spin–spin interaction and spin squeezing in an optical lattice, Phys. Rev. Lett., 83, 2274, 10.1103/PhysRevLett.83.2274 Meiser, 2008, Spin squeezing in optical lattice clocks via lattice-based QND measurements, New J. Phys., 10, 073014, 10.1088/1367-2630/10/7/073014 Andre, 2004, Stability of atomic clocks based on entangled atoms, Phys. Rev. Lett., 92, 230801, 10.1103/PhysRevLett.92.230801 Leroux, 2010, Orientation-dependent entanglement lifetime in a squeezed atomic clock, Phys. Rev. Lett., 104, 250801, 10.1103/PhysRevLett.104.250801 Walls, 1981, Enhanced sensitivity of a gravitational-wave detector, Phys. Lett. A, 85, 118, 10.1016/0375-9601(81)90238-3 Dunningham, 2004, Sub-shot-noise-limited measurements with Bose–Einstein condensates, Phys. Rev. A, 70, 033601, 10.1103/PhysRevA.70.033601 Goda, 2008, A quantum-enhanced prototype gravitational-wave detector, Nature Phys., 4, 472, 10.1038/nphys920 Hammerer, 2010, Quantum interface between light and atomic ensembles, Rev. Modern Phys., 82, 1041, 10.1103/RevModPhys.82.1041 Palma, 1989, Phase-sensitive population decay: the two-atom Dicke model in a broadband squeezed vacuum, Phys. Rev. A, 39, 1962, 10.1103/PhysRevA.39.1962 Banerjee, 1996, Generation of atomic-squeezed states in an optical cavity with an injected squeezed vacuum, Phys. Rev. A, 54, 5327, 10.1103/PhysRevA.54.5327 Kuzmich, 1997, Spin squeezing in an ensemble of atoms illuminated with squeezed light, Phys. Rev. Lett., 79, 4782, 10.1103/PhysRevLett.79.4782 Sørensen, 1998, Quantum noise of an atomic spin polarization measurement, Phys. Rev. Lett., 80, 3487, 10.1103/PhysRevLett.80.3487 Mølmer, 1999, Twin-correlations in atoms, Eur. Phys. J. D, 5, 301, 10.1007/s100530050259 Hald, 2000, Entanglement transfer from light to atoms, J. Modern Opt., 47, 2599, 10.1080/09500340008232184 Vernac, 2000, Spin squeezing in two-level systems, Phys. Rev. A, 62, 063812, 10.1103/PhysRevA.62.063812 Vernac, 2001, Quantum state transfer from light beams to atomic ensembles, Eur. Phys. J. D, 17, 125, 10.1007/s100530170045 Hald, 2001, Mapping a quantum state of light onto atoms, J. Opt. B: Quantum Semiclassical Opt., 3, S83, 10.1088/1464-4266/3/1/365 Vernac, 2002, Collective atomic spin squeezing and control, Eur. Phys. J. D, 18, 129, 10.1140/e10053-002-0014-7 Dantan, 2003, Atomic spin squeezing in a Lambda system, Phys. Rev. A, 67, 045801, 10.1103/PhysRevA.67.045801 Dantan, 2005, Long-lived quantum memory with nuclear atomic spins, Phys. Rev. Lett., 95, 123002, 10.1103/PhysRevLett.95.123002 Dantan, 2006, Generation and storage of quantum states using cold atoms, J. Modern Opt., 53, 2235, 10.1080/09500340600894048 Civitarese, 2009, Spin squeezing in the presence of dissipation, Phys. Lett. A, 373, 754, 10.1016/j.physleta.2008.12.040 Duan, 2000, Quantum communication between atomic ensembles using coherent light, Phys. Rev. Lett., 85, 5643, 10.1103/PhysRevLett.85.5643 Fleischhauer, 2000, Dark-state polaritons in electromagnetically induced transparency, Phys. Rev. Lett., 84, 5094, 10.1103/PhysRevLett.84.5094 Lukin, 2000, Entanglement of atomic ensembles by trapping correlated photon states, Phys. Rev. Lett., 84, 4232, 10.1103/PhysRevLett.84.4232 Dantan, 2003, EIT-assisted atomic squeezing, Eur. Phys. J. D, 27, 193, 10.1140/epjd/e2003-00253-y Akamatsu, 2004, Electromagnetically induced transparency with squeezed vacuum, Phys. Rev. Lett., 92, 203602, 10.1103/PhysRevLett.92.203602 Dantan, 2004, Quantum-state transfer between fields and atoms in electromagnetically induced transparency, Phys. Rev. A, 69, 043810, 10.1103/PhysRevA.69.043810 Dantan, 2005, Atomic quantum memory: cavity versus single-pass schemes, Phys. Rev. A, 71, 043801, 10.1103/PhysRevA.71.043801 Dantan, 2006, Spin squeezing and light entanglement in coherent population trapping, Phys. Rev. Lett., 97, 023605, 10.1103/PhysRevLett.97.023605 Honda, 2008, Storage and retrieval of a squeezed vacuum, Phys. Rev. Lett., 100, 093601, 10.1103/PhysRevLett.100.093601 Gong, 2010, Adiabatic creation of atomic squeezing in dark states versus decoherences, Phys. Rev. A, 82, 012112, 10.1103/PhysRevA.82.012112 Smith, 2003, Faraday spectroscopy in an optical lattice: a continuous probe of atom dynamics, J. Opt. B: Quantum Semiclassical Opt., 5, 323, 10.1088/1464-4266/5/4/301 Kuzmich, 1998, Atomic quantum non-demolition measurements and squeezing, Europhys. Lett., 42, 481, 10.1209/epl/i1998-00277-9 Takahashi, 1999, Quantum nondemolition measurement of spin via the paramagnetic Faraday rotation, Phys. Rev. A, 60, 4974, 10.1103/PhysRevA.60.4974 Kuzmich, 1999, Quantum nondemolition measurements of collective atomic spin, Phys. Rev. A, 60, 2346, 10.1103/PhysRevA.60.2346 Kuzmich, 2000, Generation of spin squeezing via continuous quantum nondemolition measurement, Phys. Rev. Lett., 85, 1594, 10.1103/PhysRevLett.85.1594 Thomsen, 2002, Continuous quantum nondemolition feedback and unconditional atomic spin squeezing, J. Phys. B: At. Mol. Opt. Phys., 35, 4937, 10.1088/0953-4075/35/23/316 Bouchoule, 2002, Preparation of spin-squeezed atomic states by optical-phase-shift measurement, Phys. Rev. A, 66, 043811, 10.1103/PhysRevA.66.043811 Zhang, 2003, Backaction-induced spin-squeezed states in a detuned quantum-nondemolition measurement, Phys. Rev. A, 68, 035802, 10.1103/PhysRevA.68.035802 Saito, 2003, Measurement-induced spin squeezing in a cavity, Phys. Rev. A, 68, 043820, 10.1103/PhysRevA.68.043820 Auzinsh, 2004, Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?, Phys. Rev. Lett., 93, 173002, 10.1103/PhysRevLett.93.173002 Madsen, 2004, Spin squeezing and precision probing with light and samples of atoms in the Gaussian description, Phys. Rev. A, 70, 052324, 10.1103/PhysRevA.70.052324 Kuzmich, 2004, Nonsymmetric entanglement of atomic ensembles, Phys. Rev. Lett., 92, 030407, 10.1103/PhysRevLett.92.030407 de Echaniz, 2005, Conditions for spin squeezing in a cold Rb-87 ensemble, J. Opt. B: Quantum Semiclassical Opt., 7, S548, 10.1088/1464-4266/7/12/016 Petersen, 2005, Magnetometry with entangled atomic samples, Phys. Rev. A, 71, 012312, 10.1103/PhysRevA.71.012312 Genes, 2006, Generating conditional atomic entanglement by measuring photon number in a single output channel, Phys. Rev. A, 73, 013801, 10.1103/PhysRevA.73.013801 Smith, 2006, Efficient quantum-state estimation by continuous weak measurement and dynamical control, Phys. Rev. Lett., 97, 180403, 10.1103/PhysRevLett.97.180403 Cviklinski, 2007, Conditional squeezing of an atomic alignment, Phys. Rev. A, 76, 033830, 10.1103/PhysRevA.76.033830 Nielsen, 2008, Atomic spin squeezing in an optical cavity, Phys. Rev. A, 77, 063811, 10.1103/PhysRevA.77.063811 Teper, 2008, Backaction noise produced via cavity-aided nondemolition measurement of an atomic clock state, Phys. Rev. A, 78, 051803, 10.1103/PhysRevA.78.051803 Windpassinger, 2008, Inhomogeneous light shift effects on atomic quantum state evolution in non-destructive measurements, New J. Phys., 10, 053032, 10.1088/1367-2630/10/5/053032 Windpassinger, 2009, Squeezing of atomic quantum projection noise, J. Modern Opt., 56, 1993, 10.1080/09500340903033682 Saffman, 2009, Spin squeezing of atomic ensembles by multicolor quantum nondemolition measurements, Phys. Rev. A, 79, 023831, 10.1103/PhysRevA.79.023831 Kubasik, 2009, Polarization-based light–atom quantum interface with an all-optical trap, Phys. Rev. A, 79, 043815, 10.1103/PhysRevA.79.043815 Shah, 2010, High bandwidth atomic magnetometery with continuous quantum nondemolition measurements, Phys. Rev. Lett., 104, 013601, 10.1103/PhysRevLett.104.013601 Kurucz, 2010, Multilevel Holstein–Primakoff approximation and its application to atomic spin squeezing and ensemble quantum memories, Phys. Rev. A, 81, 032314, 10.1103/PhysRevA.81.032314 Marek, 2010, Noise-resilient quantum interface based on quantum nondemolition interactions, Phys. Rev. A, 81, 042325, 10.1103/PhysRevA.81.042325 Wasilewski, 2010, Quantum noise limited and entanglement-assisted magnetometry, Phys. Rev. Lett., 104, 133601, 10.1103/PhysRevLett.104.133601 Schleier-Smith, 2010, States of an ensemble of two-level atoms with reduced quantum uncertainty, Phys. Rev. Lett., 104, 073604, 10.1103/PhysRevLett.104.073604 Koschorreck, 2010, Sub-projection-noise sensitivity in broadband atomic magnetometry, Phys. Rev. Lett., 104, 093602, 10.1103/PhysRevLett.104.093602 Koschorreck, 2010, Quantum nondemolition measurement of large-spin ensembles by dynamical decoupling, Phys. Rev. Lett., 105, 093602, 10.1103/PhysRevLett.105.093602 Klimov, 2005, Classical evolution of quantum fluctuations in spin-like systems: squeezing and entanglement, J. Opt. B: Quantum Semiclassical Opt., 7, 183, 10.1088/1464-4266/7/6/004 Pathak, 2008, The quadratic spin squeezing operators, J. Phys. A-Math. Theor., 41, 145302, 10.1088/1751-8113/41/14/145302 Agarwal, 1997, Atomic schrodinger cat states, Phys. Rev. A, 56, 2249, 10.1103/PhysRevA.56.2249 Klimov, 1998, The Dicke model dynamics in a high detuning limit, Phys. Lett. A, 247, 14, 10.1016/S0375-9601(98)00529-5 Shindo, 2004, Dynamical squeezing enhancement in the off-resonant Dicke model, J. Opt. B: Quantum Semiclassical Opt., 6, 34, 10.1088/1464-4266/6/1/006 Deb, 2006, Spin squeezing and entanglement in a dispersive cavity, Phys. Rev. A, 73, 053817, 10.1103/PhysRevA.73.053817 Chaudhury, 2007, Quantum control of the hyperfine spin of a Cs atom ensemble, Phys. Rev. Lett., 99, 163002, 10.1103/PhysRevLett.99.163002 Ueda, 1996, Synchronous collapses and revivals of atomic dipole fluctuations and photon fano factor beyond the standard quantum limit, Phys. Rev. Lett., 76, 2045, 10.1103/PhysRevLett.76.2045 Sørensen, 2002, Entangling atoms in bad cavities, Phys. Rev. A, 66, 022314, 10.1103/PhysRevA.66.022314 Yukalov, 2004, Atomic squeezing under collective emission, Phys. Rev. A, 70, 053828, 10.1103/PhysRevA.70.053828 Ramon, 1999, Governing dynamics by squeezing in a system of cold trapped ions, Phys. Rev. A, 59, 736, 10.1103/PhysRevA.59.736 Saito, 1997, Quantum-controlled few-photon state generated by squeezed atoms, Phys. Rev. Lett., 79, 3869, 10.1103/PhysRevLett.79.3869 Saito, 1999, Squeezed few-photon states of the field generated from squeezed atoms, Phys. Rev. A, 59, 3959, 10.1103/PhysRevA.59.3959 Poulsen, 2001, Squeezed light from spin-squeezed atoms, Phys. Rev. Lett., 87, 123601, 10.1103/PhysRevLett.87.123601 Law, 2001, Coherent control of spin squeezing, Phys. Rev. A, 63, 055601, 10.1103/PhysRevA.63.055601 Poulsen, 2001, Positive-P simulations of spin squeezing in a two-component Bose condensate, Phys. Rev. A, 64, 013616, 10.1103/PhysRevA.64.013616 Raghavan, 2001, Generation of arbitrary Dicke states in spinor Bose–Einstein condensates, Opt. Commun., 188, 149, 10.1016/S0030-4018(00)01163-9 Jenkins, 2002, Spin squeezing in a driven Bose–Einstein condensate, Phys. Rev. A, 66, 043621, 10.1103/PhysRevA.66.043621 Jaksch, 2002, Dynamically turning off interactions in a two-component condensate, Phys. Rev. A, 65, 033625, 10.1103/PhysRevA.65.033625 Jing, 2002, Mutual coherence and spin squeezing in double-well atomic condensates, Phys. Lett. A, 306, 91, 10.1016/S0375-9601(02)00131-7 Sørensen, 2002, Bogoliubov theory of entanglement in a Bose–Einstein condensate, Phys. Rev. A, 65, 043610, 10.1103/PhysRevA.65.043610 Micheli, 2003, Many-particle entanglement in two-component Bose–Einstein condensates, Phys. Rev. A, 67, 013607, 10.1103/PhysRevA.67.013607 Mølmer, 2003, Quantum atom optics with Bose–Einstein condensates, New J. Phys., 5, 55, 10.1088/1367-2630/5/1/355 Jaaskelainen, 2004, Limits to phase resolution in matter-wave interferometry, Phys. Rev. A, 70, 063612, 10.1103/PhysRevA.70.063612 Choi, 2005, Quantum squeezing and entanglement in a two-mode Bose–Einstein condensate with time-dependent Josephson-like coupling, Phys. Rev. A, 72, 033612, 10.1103/PhysRevA.72.033612 Jaaskelainen, 2005, Dynamics of Bose–Einstein condensates in double-well potentials, Phys. Rev. A, 71, 043603, 10.1103/PhysRevA.71.043603 Jin, 2007, Storage of spin squeezing in a two-component Bose–Einstein condensate, Phys. Rev. Lett., 99, 170405, 10.1103/PhysRevLett.99.170405 Jin, 2007, Spin squeezing and maximal-squeezing time, Phys. Rev. A, 76, 043621, 10.1103/PhysRevA.76.043621 Thanvanthri, 2007, Spatial dynamics and spin squeezing in Bose–Einstein condensates, Phys. Rev. A, 75, 023618, 10.1103/PhysRevA.75.023618 Jin, 2008, Relationship between spin squeezing and single-particle coherence in two-component Bose–Einstein condensates with Josephson coupling, Phys. Rev. A, 78, 063620, 10.1103/PhysRevA.78.063620 Grond, 2009, Optimizing number squeezing when splitting a mesoscopic condensate, Phys. Rev. A, 79, 021603, 10.1103/PhysRevA.79.021603 Grond, 2009, Optimal control of number squeezing in trapped Bose–Einstein condensates, Phys. Rev. A, 80, 053625, 10.1103/PhysRevA.80.053625 Helmerson, 2001, Creating massive entanglement of Bose–Einstein condensed atoms, Phys. Rev. Lett., 87, 170402, 10.1103/PhysRevLett.87.170402 Zhang, 2003, Entanglement and spin squeezing of Bose–Einstein-condensed atoms, Phys. Rev. A, 68, 043622, 10.1103/PhysRevA.68.043622 Ng, 2003, Quantum-correlated double-well tunneling of two-component Bose–Einstein condensates, Phys. Rev. A, 68, 013604, 10.1103/PhysRevA.68.013604 Deb, 2003, Entangling two Bose–Einstein condensates by stimulated Bragg scattering, Phys. Rev. A, 67, 023603, 10.1103/PhysRevA.67.023603 Gasenzer, 2002, Limitations of entanglement between photons and atoms coupled out from a Bose–Einstein condensate, Phys. Rev. A, 65, 021605, 10.1103/PhysRevA.65.021605 Yi, 2002, Single-mode approximation in a spinor-1 atomic condensate, Phys. Rev. A, 66, 011601, 10.1103/PhysRevA.66.011601 Mutecaplioglu, 2007, Quantum dynamics of a spin-1 condensate in a double-well potential, Phys. Rev. A, 75, 023605, 10.1103/PhysRevA.75.023605 Duan, 2000, Squeezing and entanglement of atomic beams, Phys. Rev. Lett., 85, 3991, 10.1103/PhysRevLett.85.3991 Pu, 2000, Creating macroscopic atomic Einstein–Podolsky–Rosen states from Bose–Einstein condensates, Phys. Rev. Lett., 85, 3987, 10.1103/PhysRevLett.85.3987 Duan, 2002, Quantum entanglement in spinor Bose–Einstein condensates, Phys. Rev. A, 65, 033619, 10.1103/PhysRevA.65.033619 Mustecaplioglu, 2002, Spin squeezing and entanglement in spinor condensates, Phys. Rev. A, 66, 033611, 10.1103/PhysRevA.66.033611 Yi, 2006, Magnetization, squeezing, and entanglement in dipolar spin-1 condensates, Phys. Rev. A, 73, 023602, 10.1103/PhysRevA.73.023602 Gerbier, 2006, Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition, Phys. Rev. Lett., 96, 090401, 10.1103/PhysRevLett.96.090401 Oztop, 2009, Quantum entanglement of spin-1 bosons with coupled ground states in optical lattices, J. Phys. B: At. Mol. Opt. Phys., 42, 145505, 10.1088/0953-4075/42/14/145505 Gasenzer, 2002, Limitations of squeezing due to collisional decoherence in Bose–Einstein condensates, J. Phys. B: At. Mol. Opt. Phys., 35, 2337, 10.1088/0953-4075/35/10/312 Dunningham, 2002, Interferometry below the standard quantum limit with Bose–Einstein condensates, Phys. Rev. Lett., 89, 150401, 10.1103/PhysRevLett.89.150401 Li, 2008, Optimum spin squeezing in Bose–Einstein condensates with particle losses, Phys. Rev. Lett., 100, 210401, 10.1103/PhysRevLett.100.210401 Li, 2009, Spin squeezing in a bimodal condensate: spatial dynamics and particle losses, Eur. Phys. J. B, 68, 365, 10.1140/epjb/e2008-00472-6 Poulsen, 2001, Quantum states of Bose–Einstein condensates formed by molecular dissociation, Phys. Rev. A, 63, 023604, 10.1103/PhysRevA.63.023604 Yi, 2001, Creating entangled atomic pairs by photodissociation, J. Phys. B: At. Mol. Opt. Phys., 34, 5087, 10.1088/0953-4075/34/24/310 Lee, 2006, Adiabatic Mach–Zehnder interferometry on a quantized Bose–Josephson junction, Phys. Rev. Lett., 97, 150402, 10.1103/PhysRevLett.97.150402 Jaaskelainen, 2006, Coherence dynamics of two-mode condensates in asymmetric potentials, Phys. Rev. A, 73, 013602, 10.1103/PhysRevA.73.013602 Jo, 2007, Long phase coherence time and number squeezing of two Bose–Einstein condensates on an atom chip, Phys. Rev. Lett., 98, 030407, 10.1103/PhysRevLett.98.030407 Li, 2007, Extended coherence time with atom-number squeezed states, Phys. Rev. Lett., 98, 040402, 10.1103/PhysRevLett.98.040402 Vengalattore, 2007, High-resolution magnetometry with a spinor Bose–Einstein condensate, Phys. Rev. Lett., 98, 200801, 10.1103/PhysRevLett.98.200801 Benatti, 2010, Sub-shot-noise quantum metrology with entangled identical particles, Ann. Phys., 325, 924, 10.1016/j.aop.2010.01.005 F. Benatti, R. Floreanini, U. Marzolino, Squeezing inequalities and entanglement for identical particles, 2010. arXiv:1009.0995. Wang, 2001, Spin squeezing in the Ising model, Phys. Rev. A, 64, 053815, 10.1103/PhysRevA.64.053815 Wang, 2004, Entanglement and spin squeezing in the three-qubit transverse Ising model, Phys. Lett. A, 331, 164, 10.1016/j.physleta.2004.08.019 Reboiro, 2007, Study of squeezing in spin clusters, Phys. Lett. A, 366, 241, 10.1016/j.physleta.2007.02.007 Agarwal, 1994, Atomic states with spectroscopic squeezing, Phys. Rev. A, 49, 4968, 10.1103/PhysRevA.49.4968 Yuen, 1976, Two-photon coherent states of the radiation field, Phys. Rev. A, 13, 2226, 10.1103/PhysRevA.13.2226 Walls, 1994 Scully, 1997 Dodonov, 2002, ‘Nonclassical’ states in quantum optics: a ‘squeezed’ review of the first 75 years, J. Opt. B: Quantum Semiclassical Opt., 4, R1, 10.1088/1464-4266/4/1/201 Caves, 1981, Quantum-mechanical noise in an interferometer, Phys. Rev. D, 23, 1693, 10.1103/PhysRevD.23.1693 Bondurant, 1984, Squeezed states in phase-sensing interferometers, Phys. Rev. D, 30, 2548, 10.1103/PhysRevD.30.2548 Hu, 1996, Squeezed phonon states: modulating quantum fluctuations of atomic displacements, Phys. Rev. Lett., 76, 2294, 10.1103/PhysRevLett.76.2294 Hu, 1996, Quantum phonon optics: coherent and squeezed atomic displacements, Phys. Rev. B, 53, 2419, 10.1103/PhysRevB.53.2419 Hu, 1997, Phonon squeezed states generated by second-order Raman scattering, Phys. Rev. Lett., 79, 4605, 10.1103/PhysRevLett.79.4605 Hu, 1999, Phonon squeezed states: quantum noise reduction in solids, Physica B, 263–264, 16, 10.1016/S0921-4526(98)01483-5 Xue, 2007, Two-mode squeezed states and entangled states of two mechanical resonators, Phys. Rev. B, 76, 064305, 10.1103/PhysRevB.76.064305 Lambert, 2010, Unified single-photon and single-electron counting statistics: from cavity-QED to electron transport, Phys. Rev. A, 82, 063840, 10.1103/PhysRevA.82.063840 Zagoskin, 2008, Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit, Phys. Rev. Lett., 101, 253602, 10.1103/PhysRevLett.101.253602 Zhang, 2009, Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control, Phys. Rev. A, 79, 052102, 10.1103/PhysRevA.79.052102 Barut, 1971, New coherent states associated with non-compact groups, Comm. Math. Phys., 21, 41, 10.1007/BF01646483 Gilmore, 1972, Geometry of symmetrized states, Ann. Phys., 74, 391, 10.1016/0003-4916(72)90147-9 Perelomov, 1972, Coherent states for arbitrary Lie group, Comm. Math. Phys., 26, 222, 10.1007/BF01645091 Perelomov, 1986 Zhang, 1990, Coherent states: theory and some applications, Rev. Modern Phys., 62, 867, 10.1103/RevModPhys.62.867 Lukš, 1988, Principal squeezing of vacuum fluctuations, Opt. Commun., 67, 149, 10.1016/0030-4018(88)90322-7 Lukš, 1988, Principal squeezing, Acta Phys. Polon. A, 74, 713 Miranowicz, 2010, Testing nonclassicality in multimode fields: a unified derivation of classical inequalities, Phys. Rev. A, 82, 013824, 10.1103/PhysRevA.82.013824 Kitagawa, 1986, Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer, Phys. Rev. A, 34, 3974, 10.1103/PhysRevA.34.3974 Itano, 1993, Quantum projection noise: population fluctuations in two-level systems, Phys. Rev. A, 47, 3554, 10.1103/PhysRevA.47.3554 Arecchi, 1972, Atomic coherent states in quantum optics, Phys. Rev. A, 6, 2211, 10.1103/PhysRevA.6.2211 Walls, 1981, Reduced quantum fluctuations in resonance fluorescence, Phys. Rev. Lett., 47, 709, 10.1103/PhysRevLett.47.709 Prakash, 2005, Simultaneous squeezing of two orthogonal spin components, J. Opt. B: Quantum Semiclassical Opt., 7, S757, 10.1088/1464-4266/7/12/046 Prakash, 2007, Atomic squeezing in assembly of two two-level atoms interacting with a single mode coherent radiation, Eur. Phys. J. D, 42, 475, 10.1140/epjd/e2007-00042-8 Song, 2006, Spin squeezing properties in the quantum kicked top model, J. Phys. B: At. Mol. Opt. Phys., 39, 559, 10.1088/0953-4075/39/3/009 Giovannetti, 2004, Quantum-enhanced measurements: beating the standard quantum limit, Science, 306, 1330, 10.1126/science.1104149 Rivas, 2008, Characterization of quantum angular-momentum fluctuations via principal components, Phys. Rev. A, 77, 022105, 10.1103/PhysRevA.77.022105 Rivas, 2008, Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics, Phys. Rev. A, 78, 043814, 10.1103/PhysRevA.78.043814 Wang, 2010, Sudden vanishing of spin squeezing under decoherence, Phys. Rev. A, 81, 022106, 10.1103/PhysRevA.81.022106 Devi, 2003, Spin squeezing criterion with local unitary invariance, Quantum Inf. Process., 2, 207, 10.1023/B:QINP.0000004125.12489.f4 Wang, 2001, Spin squeezing in nonlinear spin-coherent states, J. Opt. B: Quantum Semiclassical Opt., 3, 93, 10.1088/1464-4266/3/3/304 Liu, 1996, The squeezed component of the atomic collective phase quadrature operators with respect to a two-level atomic coherent state, Phys. Lett. A, 221, 384, 10.1016/0375-9601(96)00565-8 Wang, 2003, Relations between bosonic quadrature squeezing and atomic spin squeezing, Phys. Rev. A, 68, 033821, 10.1103/PhysRevA.68.033821 Chumakov, 1999, Finite Kerr medium: macroscopic quantum superposition states and Wigner functions on the sphere, Phys. Rev. A, 60, 1817, 10.1103/PhysRevA.60.1817 Holstein, 1940, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev., 58, 1098, 10.1103/PhysRev.58.1098 Sanders, 1989, Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement, Phys. Rev. A, 40, 2417, 10.1103/PhysRevA.40.2417 Wesenberg, 2002, Mixed collective states of many spins, Phys. Rev. A, 65, 062304, 10.1103/PhysRevA.65.062304 Ocak, 2003, The effective potential of squeezed spin states, Phys. Lett. A, 308, 17, 10.1016/S0375-9601(02)01796-6 Takeuchi, 2005, Spin squeezing via one-axis twisting with coherent light, Phys. Rev. Lett., 94, 023003, 10.1103/PhysRevLett.94.023003 Jin, 2009, Spin squeezing in a generalized one-axis twisting model, New J. Phys., 11, 073049, 10.1088/1367-2630/11/7/073049 Leroux, 2010, Implementation of cavity squeezing of a collective atomic spin, Phys. Rev. Lett., 104, 073602, 10.1103/PhysRevLett.104.073602 Schleier-Smith, 2010, Squeezing the collective spin of a dilute atomic ensemble by cavity feedback, Phys. Rev. A, 81, 021804, 10.1103/PhysRevA.81.021804 Rojo, 2003, Optimally squeezed spin states, Phys. Rev. A, 68, 013807, 10.1103/PhysRevA.68.013807 Andre, 2002, Atom correlations and spin squeezing near the Heisenberg limit: finite-size effect and decoherence, Phys. Rev. A, 65, 053819, 10.1103/PhysRevA.65.053819 Bouchoule, 2002, Spin squeezing of atoms by the dipole interaction in virtually excited Rydberg states, Phys. Rev. A, 65, 041803, 10.1103/PhysRevA.65.041803 Jafarpour, 2008, Entanglement and squeezing of multi-qubit systems using a two-axis countertwisting Hamiltonian with an external field, Phys. Lett. A, 372, 2374, 10.1016/j.physleta.2007.12.021 Andre, 2002, Coherent atom interactions mediated by dark-state polaritons, Phys. Rev. Lett., 88, 243602, 10.1103/PhysRevLett.88.243602 Wang, 2002, Pairwise entanglement in symmetric multi-qubit systems, Eur. Phys. J. D, 18, 385, 10.1140/epjd/e20020045 Yan, 2005, Spin squeezing and entanglement of many-particle spin-half states, Chin. Phys. Lett., 22, 271, 10.1088/0256-307X/22/2/002 Zeng, 2005, Entanglement and spin-squeezing properties for three bosons in two modes, Phys. Rev. A, 71, 042317, 10.1103/PhysRevA.71.042317 Messikh, 2003, Spin squeezing as a measure of entanglement in a two-qubit system, Phys. Rev. A, 68, 064301, 10.1103/PhysRevA.68.064301 Messikh, 2003, Entanglement and spin squeezing in the two-atom Dicke model, J. Opt. B: Quantum Semiclassical Opt., 5, L1, 10.1088/1464-4266/5/2/101 Tóth, 2007, Optimal spin squeezing inequalities detect bound entanglement in spin models, Phys. Rev. Lett., 99, 250405, 10.1103/PhysRevLett.99.250405 Vidal, 2006, Phys. Rev. A, 73, 062318, 10.1103/PhysRevA.73.062318 X. Yin, X. Wang, J. Ma, X.G. Wang, Spin squeezing and concurrence, 2009. arXiv:0912.1752. Coffman, 2000, Distributed entanglement, Phys. Rev. A, 61, 052306, 10.1103/PhysRevA.61.052306 Sackett, 2000, Experimental entanglement of four particles, Nature, 404, 256, 10.1038/35005011 Seevinck, 2001, Sufficient conditions for three-particle entanglement and their tests in recent experiments, Phys. Rev. A, 65, 012107, 10.1103/PhysRevA.65.012107 Sørensen, 2001, Entanglement and extreme spin squeezing, Phys. Rev. Lett., 86, 4431, 10.1103/PhysRevLett.86.4431 Tóth, 2004, Entanglement detection in optical lattices of bosonic atoms with collective measurements, Phys. Rev. A, 69, 052327, 10.1103/PhysRevA.69.052327 Kuzmich, 2000, Atomic quantum state teleportation and swapping, Phys. Rev. Lett., 85, 5639, 10.1103/PhysRevLett.85.5639 Berry, 2002, Quantum teleportation and entanglement swapping for spin systems, New J. Phys., 4, 8 Duan, 2000, Inseparability criterion for continuous variable systems, Phys. Rev. Lett., 84, 2722, 10.1103/PhysRevLett.84.2722 Simon, 2000, Peres–Horodecki separability criterion for continuous variable systems, Phys. Rev. Lett., 84, 2726, 10.1103/PhysRevLett.84.2726 Berry, 2005, Equivalence between two-mode spin squeezed states and pure entangled states with equal spin, J. Phys. A: Math. Theor., 38, L205, 10.1088/0305-4470/38/14/L01 Raymer, 2003, Separability criterion for separate quantum systems, Phys. Rev. A, 67, 052104, 10.1103/PhysRevA.67.052104 Berry, 2002, Near-optimal two-mode spin squeezing via feedback, Phys. Rev. A, 66, 012313, 10.1103/PhysRevA.66.012313 Helstrom, 1976 Holevo, 1982 Kok, 2010 Pezzé, 2009, Entanglement, nonlinear dynamics, and the Heisenberg limit, Phys. Rev. Lett., 102, 100401, 10.1103/PhysRevLett.102.100401 Ma, 2009, Fisher information and spin squeezing in the Lipkin–Meshkov–Glick model, Phys. Rev. A, 80, 012318, 10.1103/PhysRevA.80.012318 Hyllus, 2010, Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles, Phys. Rev. Lett., 105, 120501, 10.1103/PhysRevLett.105.120501 Jin, 2010, Polarization squeezing and many-body entanglement of triphoton states, J. Opt. Soc. Amer. B, 27, A105, 10.1364/JOSAB.27.00A105 Braunstein, 1994, Statistical distance and the geometry of quantum states, Phys. Rev. Lett., 72, 3439, 10.1103/PhysRevLett.72.3439 Bures, 1969, An extension of Kakutani’s theorem on infinite product measures to the tensor product of siemifinite w∗-algebras, Trans. Amer. Math. Soc., 135, 199 You, 2007, Fidelity, dynamic structure factor, and susceptibility in critical phenomena, Phys. Rev. E, 76, 022101, 10.1103/PhysRevE.76.022101 Sanders, 1995, Optimal quantum measurements for phase estimation, Phys. Rev. Lett., 75, 2944, 10.1103/PhysRevLett.75.2944 Giovannetti, 2006, Quantum metrology, Phys. Rev. Lett., 96, 010401, 10.1103/PhysRevLett.96.010401 Boixo, 2008, Quantum metrology: dynamics versus entanglement, Phys. Rev. Lett., 101, 040403, 10.1103/PhysRevLett.101.040403 Zanardi, 2008, Quantum criticality as a resource for quantum estimation, Phys. Rev. A, 78, 042105, 10.1103/PhysRevA.78.042105 Burgarth, 2009, Coupling strength estimation for spin chains despite restricted access, Phys. Rev. A, 79, 020305, 10.1103/PhysRevA.79.020305 Leibfried, 2004, Toward Heisenberg-limited spectroscopy with multiparticle entangled states, Science, 304, 1476, 10.1126/science.1097576 Sachdev, 1999 Haake, 1999 Gu, 2010, Fidelity approach to quantum phase transitions, Internat. J. Modern Phys. B, 24, 4371, 10.1142/S0217979210056335 Heller, 1984, Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits, Phys. Rev. Lett., 53, 1515, 10.1103/PhysRevLett.53.1515 Schack, 1994, Hypersensitivity to perturbation in the quantum kicked top, Phys. Rev. E, 50, 972, 10.1103/PhysRevE.50.972 Chaudhury, 2009, Quantum signatures of chaos in a kicked top, Nature, 461, 768, 10.1038/nature08396 Lipkin, 1965, Validity of many-body approximation methods for a solvable model (I). Exact solutions and perturbation theory, Nuclear Phys., 62, 188, 10.1016/0029-5582(65)90862-X Vidal, 2004, Entanglement in a second-order quantum phase transition, Phys. Rev. A, 69, 022107, 10.1103/PhysRevA.69.022107 Miranowicz, 2002, Generation of maximum spin entanglement induced by cavity field in quantum-dot systems, Phys. Rev. A, 65, 062321, 10.1103/PhysRevA.65.062321 Miranowicz, 2007, Quantum entanglement and teleportation of quantum-dot states in microcavities, e-J. Surf. Sci. Nanotechnol., 5, 51, 10.1380/ejssnt.2007.51 Botet, 1982, Size scaling for infinitely coordinated systems, Phys. Rev. Lett., 49, 478, 10.1103/PhysRevLett.49.478 Cirac, 1998, Quantum superposition states of Bose–Einstein condensates, Phys. Rev. A, 57, 1208, 10.1103/PhysRevA.57.1208 Tsomokos, 2008, Fully connected network of superconducting qubits in a cavity, New J. Phys., 10, 113020, 10.1088/1367-2630/10/11/113020 Draayer, 1999, Analytical solutions for the LMG model, Phys. Lett. B, 451, 1, 10.1016/S0370-2693(99)00191-4 Links, 2003, Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose–Einstein condensates and metallic nanograins, J. Phys. A: Math. Gen., 36, R63, 10.1088/0305-4470/36/19/201 Dusuel, 2005, Continuous unitary transformations and finite-size scaling exponents in the Lipkin–Meshkov–Glick model, Phys. Rev. B, 71, 224420, 10.1103/PhysRevB.71.224420 Wichterich, 2010, Universality of the negativity in the Lipkin–Meshkov–Glick model, Phys. Rev. A, 81, 032311, 10.1103/PhysRevA.81.032311 Orús, 2008, Equivalence of critical scaling laws for many-body entanglement in the Lipkin–Meshkov–Glick model, Phys. Rev. Lett., 101, 025701, 10.1103/PhysRevLett.101.025701 Vidal, 2007, Entanglement entropy in collective models, J. Stat. Mech. Theory Exp., P01015 Lambert, 2004, Entanglement and the phase transition in single-mode superradiance, Phys. Rev. Lett., 92, 073602, 10.1103/PhysRevLett.92.073602 Lambert, 2009, Quantum chaos and critical behavior on a chip, Phys. Rev. B, 80, 165308, 10.1103/PhysRevB.80.165308 Furuya, 1998, Quantum dynamical manifestation of chaotic behavior in the process of entanglement, Phys. Rev. Lett., 80, 5524, 10.1103/PhysRevLett.80.5524 Song, 2009, Spin squeezing as an indicator of quantum chaos in the Dicke model, Phys. Rev. E, 79, 046220, 10.1103/PhysRevE.79.046220 Deaguiar, 1992, Chaos in a spin boson system—classical analysis, Ann. Phys., 216, 291, 10.1016/0003-4916(92)90178-O Weiss, 1999 Gardiner, 2000 Breuer, 2002 Schlosshauer, 2007 Stockton, 2003, Characterizing the entanglement of symmetric many-particle spin-1/2 systems, Phys. Rev. A, 67, 022112, 10.1103/PhysRevA.67.022112 Huelga, 1997, Improvement of frequency standards with quantum entanglement, Phys. Rev. Lett., 79, 3865, 10.1103/PhysRevLett.79.3865 Rey, 2007, Quantum-limited measurements of atomic scattering properties, Phys. Rev. A, 76, 053617, 10.1103/PhysRevA.76.053617 Koschorreck, 2009, Unified description of inhomogeneities, dissipation and transport in quantum light–atom interfaces, J. Phys. B, 42, 195502, 10.1088/0953-4075/42/19/195502 Simon, 2002, Robustness of multiparty entanglement, Phys. Rev. A, 65, 052327, 10.1103/PhysRevA.65.052327 J. Preskill, Lecture Notes for Physics 219: Quantum Information and Computation, Caltech, Pasadena, CA, 1999. Bartkowiak, 2011, Sudden vanishing and reappearance of nonclassical effects, Phys. Rev. A, 83, 053814, 10.1103/PhysRevA.83.053814 Kominis, 2008, Sub-shot-noise magnetometry with a correlated spin-relaxation dominated alkali-metal vapor, Phys. Rev. Lett., 100, 073002, 10.1103/PhysRevLett.100.073002 Greiner, 2002, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, 419, 51, 10.1038/nature00968 Sun, 2003, Quasi-spin-wave quantum memories with a dynamical symmetry, Phys. Rev. Lett., 91, 147903, 10.1103/PhysRevLett.91.147903 Wang, 2010, Robust and scalable optical one-way quantum computation, Phys. Rev. A, 81, 052332, 10.1103/PhysRevA.81.052332 Fleischhauer, 1995, Pulse matching and correlation of phase fluctuations in Lambda systems, Phys. Rev. A, 51, 2430, 10.1103/PhysRevA.51.2430 Thomsen, 2002, Spin squeezing via quantum feedback, Phys. Rev. A, 65, 061801, 10.1103/PhysRevA.65.061801 Bowen, 2002, Polarization squeezing of continuous variable stokes parameters, Phys. Rev. Lett., 88, 093601, 10.1103/PhysRevLett.88.093601 Heersink, 2003, Polarization squeezing of intense pulses with a fiber-optic Sagnac interferometer, Phys. Rev. A, 68, 013815, 10.1103/PhysRevA.68.013815 Corney, 2006, Many-body quantum dynamics of polarization squeezing in optical fibers, Phys. Rev. Lett., 97, 023606, 10.1103/PhysRevLett.97.023606 Luis, 2006, Polarization squeezing and nonclassical properties of light, Phys. Rev. A, 74, 043817, 10.1103/PhysRevA.74.043817 Marquardt, 2007, Quantum reconstruction of an intense polarization squeezed optical state, Phys. Rev. Lett., 99, 220401, 10.1103/PhysRevLett.99.220401 Shalm, 2009, Squeezing and over-squeezing of triphotons, Nature, 10.1038/nature07624