Mean spin direction and spin squeezing in superpositions of spin coherent states

[1] B. Yurke “Input states for enhancement of fermion interferometer sensitivity”, Phys. Rev. Lett., Vol. 56, (1986), pp. 1515–1517. http://dx.doi.org/10.1103/PhysRevLett.56.151510.1103/PhysRevLett.56.1515Search in Google Scholar

[2] L.A. Wu, H.J. Kimble, J.L. Hall and H. Wu “Generation of squeezed states by parametric down conversion”, Phys. Rev. Lett., Vol. 57, (1986), pp. 2520–2523. http://dx.doi.org/10.1103/PhysRevLett.57.252010.1103/PhysRevLett.57.2520Search in Google Scholar

[3] M. Kitagawa and M. Ueda “Squeezed spin states”, Phys. Rev. A, Vol. 47, (1993), pp. 5138–5143. http://dx.doi.org/10.1103/PhysRevA.47.513810.1103/PhysRevA.47.5138Search in Google Scholar

[4] D.J. Wineland, J.J. Bollinger, W.M. Itano and D.J. Heinzen “Squeezed atomic states and projection noise in spectroscopy”, Phys. Rev. A, Vol. 50, (1994), pp. 67–88. http://dx.doi.org/10.1103/PhysRevA.50.6710.1103/PhysRevA.50.67Search in Google Scholar

[5] D.J. Wineland “Spin squeezing and reduced quantum noise in spectroscopy”, Phys. Rev. A, Vol. 46, (1992), pp. R6797–R6800. http://dx.doi.org/10.1103/PhysRevA.46.R679710.1103/PhysRevA.46.R6797Search in Google Scholar

[6] G.S. Agarwal and R.R. Puri “Cooperative behavior of atoms irradiated by broadband squeezed light”, Phys. Rev. A, Vol. 41, (1990), pp. 3782–3791. http://dx.doi.org/10.1103/PhysRevA.41.378210.1103/PhysRevA.41.3782Search in Google Scholar

[7] M.D. Lukin, S.F. Yelin and M. Fleischhauer “Entanglement of atomic ensembles by trapping correlated photon states”, Phys. Rev. Lett., Vol. 84, (2000), pp. 4232–4235; A. André and M. D. Lukin: “Atom correlations and spin squeezing near the Heisenberg limit: Finite-size effect and decoherence”, Phys. Rev. A, Vol. 65, (2002), art. 053819. http://dx.doi.org/10.1103/PhysRevLett.84.4232Search in Google Scholar

[8] L. Vernac, M. Pinard and E. Giacobino “Spin squeezing in two-level systems”, Phys. Rev. A, Vol. 62, (2000), art. 063812. Search in Google Scholar

[9] A. Kuzmich, N.P. Bigelow and L. Mandel “Atomic quantum non-demolition measurements and squeezing”, Europhys. Lett., Vol. 43, (1998), pp. 481–486; A. Kuzmich, K. Molmer and E. S. Polzik: “Spin squeezing in an ensemble of atoms illuminated with squeezed light”, Phys. Rev. Lett., Vol. 79, (1997), pp. 4782–4785; A. Kuzmich, L. Mandel, N.P. Bigelow: “Generation of spin squeezing via continuous quantum nondemolition measurement”, Phys. Rev. Lett., Vol. 85, (2000), pp. 1594–1597; A. Kozhekin, K. Molmer and E.S. Polzik: “Quantum memory for light”, Phys. Rev. A, Vol. 62, (2000), art. 033809; J. Wesenberg and K. Molmer: “Mixed collective states of many spins”, Phys. Rev. A, Vol. 65, (2002), art. 062304. http://dx.doi.org/10.1209/epl/i1998-00277-9Search in Google Scholar

[10] X. Wang, A. S. Sorensen and K. Molmer “Spin squeezing in the Ising model”, Phys. Rev. A, Vol. 64, (2001), art. 053815. Search in Google Scholar

[11] J. Liao, X.G. Wang, L.A. Wu and S.H. Pan “Real and imaginary negative binomial states”, J. Opt. B: Quantum Semiclass.Opt., Vol. 3, (2001) pp. 303–307. http://dx.doi.org/10.1088/1464-4266/3/5/30310.1088/1464-4266/3/5/303Search in Google Scholar

[12] X. Wang “Coherence and squeezing in superpositions of spin coherent states”, Opt. Commun., Vol. 200, (2001), pp. 277–282. http://dx.doi.org/10.1016/S0030-4018(01)01631-510.1016/S0030-4018(01)01631-5Search in Google Scholar

[13] A. Sorensen and K. Molmer “Spin-spin interaction and spin squeezing in an optical lattice”, Phys. Rev. Lett., Vol. 83, (1999), pp. 2274–2277. http://dx.doi.org/10.1103/PhysRevLett.83.227410.1103/PhysRevLett.83.2274Search in Google Scholar

[14] K. Helmerson and L. You “Creating massive entanglement of Bose-Einstein condensed atoms”, Phys. Rev. Lett., Vol. 87, (2001), art. 170402; Ö. E. Müstecaplioğlu, M. Zhang and L. You: “Spin squeezing and entanglement in spinor condensates”, Phys. Rev. A, Vol. 66, (2002), art. 033611; S. Yi, Ö.E. Müstecaplioğlu, C.P. Sun and L. You: “Single-mode approximation in a spinor-1 atomic condensate”, Phys. Rev. A, Vol. 66, (2002), art. 011601; Ö.E. Müstecaplioğlu, M. Zhang and L. You: “Spin squeezing and entanglement in spinor condensates”, Phys. Rev. A, Vol. 66, (2002), art. 033611. Search in Google Scholar

[15] D. Yan, X. Wang and L.A. Wu “Spin squeezing and entanglement of many-particle spin-half states”, Chin. Phys. Lett, Vol. 22, (2005), pp. 271–274. http://dx.doi.org/10.1088/0256-307X/22/2/00210.1088/0256-307X/22/2/002Search in Google Scholar

[16] D. Yan, X. Wang and L.A. Wu “Squeezing in the real and imaginary spin coherent states”, Chin. Phys. Lett, Vol. 22, (2005), pp. 521–524. http://dx.doi.org/10.1088/0256-307X/22/3/00110.1088/0256-307X/22/3/001Search in Google Scholar

[17] X. Wang and B.C. Sanders “Spin squeezing and pairwise entanglement for symmetric multiqubit states”, Phys. Rev. A, Vol. 68, (2003), art. 012101. Search in Google Scholar

[18] A. Sorensen, L.M. Duan, J.I. Cirac and P. Zoller “Many-particle entanglement with Bose-Einstein condensates”, Nature, Vol. 409, (2001), pp. 63–66. http://dx.doi.org/10.1038/3505103810.1038/35051038Search in Google Scholar

[19] H. Barnum, E. Knill, G. Ortiz, R. Somma and L. Viola “A subsystem-independent generalization of entanglement”, Phys. Rev. Lett., Vol. 92, (2004), art. 107902. Search in Google Scholar

[20] M.A. Can, A.A. Klyachko and A.S. Shumovsky “Single-particle entanglement”, J. Opt. B: Quant. Semiclass. Opt., Vol. 7, (2005), pp. L1–L3. http://dx.doi.org/10.1088/1464-4266/7/2/L0110.1088/1464-4266/7/2/L01Search in Google Scholar

[21] A.A. Klyachko and A.S. Shumovsky “General entanglement”, J. Phys: Conf. Series, Vol. 36, (2006), pp. 87–93. http://dx.doi.org/10.1088/1742-6596/36/1/01510.1088/1742-6596/36/1/015Search in Google Scholar

[22] S. Binicioğlu, M. A. Can, A. A. Klyachko and A. S. Shumovsky: “Entanglement of a single spin-1 object: an example of ubiquitous entanglement”, Preprint:arXiv: quant-ph/0604182 Search in Google Scholar

[23] L. J. Song, X. Wang, D. Yan and Z. G. Zong “Spin squeezing properties in the quantum kicked top model”, J. Phys. B: At. Mol. Opt. Phys., Vol. 39, (2006), pp. 559–568. http://dx.doi.org/10.1088/0953-4075/39/3/00910.1088/0953-4075/39/3/009Search in Google Scholar

[24] J. M. Radcliffe “Some properties of coherent spin states”, J. Phys. A: Gen. Phys., Vol. 4, (1971), pp. 313–323; F. T. Arecchi, E. Courtens, R. Gilmore and H. Thomas: “Atomic Coherent States in Quantum Optics”, Phys. Rev. A, Vol. 6, (1972), pp. 2211–2237; R. Gilmore, C. M. Bowden and L. M. Narducci: “Classical-quantum correspondence for multilevel systems”, Phys. Rev. A, Vol. 12, (1975), pp. 1019–1031; L. M. Narducci, C. M. Bowden, V. Bluemel, G. P. Garrazana and R. A. Tuft: “Multitime-correlation functions and the atomic coherent-state representation”, Phys. Rev. A, Vol. 11, (1975), pp. 973–980; G. S. Agarwal: “Relation between atomic coherent-state representation, state multipoles and generalized phase-space distributions”, Phys. Rev. A, Vol. 24, (1981), pp. 2889–2896. http://dx.doi.org/10.1088/0305-4470/4/3/009Search in Google Scholar

[25] V. Bužek and P. L. Knight “Quantum interference, superpositions states of light and nonclassical effects”, In: E. Wolf (Ed.): Progress in Optics XXXIV, Academic Press, Amsterdam, Elsevier, 1995, pp. 12–87. Search in Google Scholar

[26] V. V. Dodonov, S. Y. Kalmykov and V. I. Man’ko “Statistical properties of Schrödinger real and imaginary cat states", Phys. Lett. A, Vol. 199, (1995), pp. 123–130. http://dx.doi.org/10.1016/0375-9601(95)00048-810.1016/0375-9601(95)00048-8Search in Google Scholar

[27] Y. J. Xia and G. C. Guo “Nonclassical properties of even and odd coherent states”, Phys. Lett. A, Vol. 136, (1989), pp. 281–283. http://dx.doi.org/10.1016/0375-9601(89)90815-310.1016/0375-9601(89)90815-3Search in Google Scholar

[28] D. Stoler, B. E. A. Saleh and M. C. Teich “Binomial states of the quantized radiation field”, Opt. Acta, Vol. 32, (1985), pp. 345–355. Search in Google Scholar