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

• Authors: Dong Yan , Xiaoguang Wang , Lijun Song , Zhanguo Zong
• Languages of publication: EN

Abstracts

EN

We consider the mean spin direction (MSD) of superpositions of two spin coherent states (SCS) | ± μ〉, and superpositions of | μ〉 and | μ*〉 with a relative phase. We find that the azimuthal angle exhibits a π transition for both states when we vary the relative phase. The spin squeezing of the states, and the bosonic counterpart of the mean spin direction are also discussed.

Keywords

EN

spin squeezing; mean spin direction

Discipline

• 03.65.Ud: Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)(for entanglement production and manipulation, see 03.67.Bg; for entanglement measures, witnesses etc., see 03.67.Mn; for entanglement in Bose-Einstein condensates, see 03.75.Gg)
• 42.50.Dv: Quantum state engineering and measurements(see also 03.65.Ud Entanglement and quantum nonlocality, e.g., EPR paradox, Bells inequalities, GHZ states, etc.)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2007
• Volume: 5
• Issue: 3
• Pages: 367-376

Dates

published

1 - 9 - 2007

online

9 - 6 - 2007

Contributors

author

Dong Yan

author

Xiaoguang Wang

• Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, HangZhou, 310027, P.R. China

author

Lijun Song

author

Zhanguo Zong

• Institute of Applied Physics, Changchun University, Changchun, 130022, P.R. China

References

• [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.56.1515[Crossref]
• [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.57.2520[Crossref]
• [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.47.5138[Crossref]
• [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.50.67[Crossref]
• [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.R6797[Crossref]
• [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.41.3782[Crossref]
• [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.84.4232[Crossref]
• [8] L. Vernac, M. Pinard and E. Giacobino “Spin squeezing in two-level systems”, Phys. Rev. A, Vol. 62, (2000), art. 063812.
• [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/i1998-00277-9[Crossref]
• [10] X. Wang, A. S. Sorensen and K. Molmer “Spin squeezing in the Ising model”, Phys. Rev. A, Vol. 64, (2001), art. 053815.
• [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/10.1088/1464-4266/3/5/303[Crossref]
• [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)01631-5[Crossref]
• [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.83.2274[Crossref]
• [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.
• [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/22/2/002[Crossref]
• [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/22/3/001[Crossref]
• [17] X. Wang and B.C. Sanders “Spin squeezing and pairwise entanglement for symmetric multiqubit states”, Phys. Rev. A, Vol. 68, (2003), art. 012101. [Crossref]
• [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/10.1038/35051038[Crossref]
• [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.
• [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/L01[Crossref]
• [21] A.A. Klyachko and A.S. Shumovsky “General entanglement”, J. Phys: Conf. Series, Vol. 36, (2006), pp. 87–93. http://dx.doi.org/10.1088/1742-6596/36/1/015[Crossref]
• [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
• [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/10.1088/0953-4075/39/3/009[Crossref]
• [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/10.1088/0305-4470/4/3/009[Crossref]
• [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.
• [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)00048-8[Crossref]
• [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)90815-3[Crossref]
• [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. [Crossref]

Identifiers

DOI

10.2478/s11534-007-0029-2