ISSN 0253-2778

CN 34-1054/N

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Entangled state representation for two particles with unequal masses and the squeezed state generation

  • 1.

    School of Physics and Optoelectronic Engineering, Weifang University, Weifang 261061, China

  • 2.

    Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.08.008
  • Received Date: 01 May 2018
  • Accepted Date: 04 July 2018
  • Rev Recd Date: 04 July 2018
  • Publish Date: 31 August 2018
    Abstract

  • Abstract

    It was found that the entangled state representation of two particles with unequal masses can be directly derived by the Weyl correspondence and the technique of integration within an ordered product of operators. The entanglement properties can be achieved through its Schmidt decomposition. With this representation, a kind of new one- and two- combination squeezed state and corresponding squeezing operator was obtained.

    Abstract

    It was found that the entangled state representation of two particles with unequal masses can be directly derived by the Weyl correspondence and the technique of integration within an ordered product of operators. The entanglement properties can be achieved through its Schmidt decomposition. With this representation, a kind of new one- and two- combination squeezed state and corresponding squeezing operator was obtained.
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    • References(17)
  • [1]
    FOX R. Quantum Optics：An Introduction[M]. Oxford: Oxford University Press. 2006:157-160.
    [2]
    TAKEDA S, MIZUTA T, FUWA M, et al. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique[J]. Nature, 2013,500:315-318.
    [3]
    KRAUTER H, SALART D, MUSCHIK C A, et al. Deterministic quantum teleportation between distant atomic objects[J]. Nature Phys, 2013,9:400-404.
    [4]
    RIEBE M, HAFFNER H, ROOS C F, et al. Deterministic quantum teleportation with atoms[J]. Nature, 2004,429:734-737.
    [5]
    PFAFF W, HENSEN J B, BERNIEN H, et al. Unconditional quantum teleportation between distant solid-state quantum bits[J]. Science, 2014, 345(6196):532-535.
    [6]
    STEFFEN L, SALATHE Y, OPPLIGER M, et al. Deterministic quantum teleportation with feed-forward in a solid state system[J]. Nature, 2013,500:319-322.
    [7]
    WANG X L, CAI X D, SU Z E, et al. Quantum teleportation of multiple degrees of freedom of a single photon[J]. Nature, 2015,518:516-519.
    [8]
    FAN H Y, KLAUDER J R. Eigenvectors of two particles’ relative position and total momentum[J].Phys Rev A, 1994, 49(2): 704-707.
    [9]
    FAN H Y, YE X. Common eigenstates of two particles’ center-of-mass coordinates and mass-weighted relative momentum[J]. Phys Rev A, 1995, 51(4):3343-3346.
    [10]
    WEYL H.Quantenmechanik and gruppentheorie[J]. Z Phys, 1927,46:1-46.
    [11]
    FAN H Y. Newton-Leibniz integration for ket-bra operators in quantum mechanics(IV)[J]. Ann Phys, 2008, 323(2):500-526.
    [12]
    FAN H Y.Weyl ordering quantum mechanical operators by virtue of the IWOP technique[J]. J Phys A Math Gen, 1992，25:3443-3447.
    [13]
    WIGNER E. On the quantum correction for thermodynamic equilibrium[J].Phys Rev, 1932,40:749-759.
    [14]
    XU Y J, FAN H Y, LIU Q Y. New equation for deriving pure state density operators by Weyl correspondence and Wigner operator[J]. Chin Phys B, 2010, 19(2):020303.
    [15]
    XU X F. Obtaining multimode entangled state representation by generalized radon trans-formation of the Wigner operator[J]. Int J Theor Phys, 2010, 49(7):1446-1551.
    [16]
    范洪义. 论由Dirac符号组成的算符之积分―从牛顿-莱布尼兹积分谈起[J]. 中国科学技术大学学报, 2007, 37(7):695-699.
    FAN Hongyi. On the integration over operators composed of Dirac’s symbols: Beyond Newton-Leibniz integration over c-number functions[J]. Journal of University of Science and Technology of China, 2007, 37(7):695-699.
    [17]
    FAN H Y. Operator ordering in quantum optics theory and the development of Dirac’s symbolic method[J]. J Opt B: Quantum Semiclass Opt, 2003,5(4): R147.)
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    [1]
    FOX R. Quantum Optics：An Introduction[M]. Oxford: Oxford University Press. 2006:157-160.
    [2]
    TAKEDA S, MIZUTA T, FUWA M, et al. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique[J]. Nature, 2013,500:315-318.
    [3]
    KRAUTER H, SALART D, MUSCHIK C A, et al. Deterministic quantum teleportation between distant atomic objects[J]. Nature Phys, 2013,9:400-404.
    [4]
    RIEBE M, HAFFNER H, ROOS C F, et al. Deterministic quantum teleportation with atoms[J]. Nature, 2004,429:734-737.
    [5]
    PFAFF W, HENSEN J B, BERNIEN H, et al. Unconditional quantum teleportation between distant solid-state quantum bits[J]. Science, 2014, 345(6196):532-535.
    [6]
    STEFFEN L, SALATHE Y, OPPLIGER M, et al. Deterministic quantum teleportation with feed-forward in a solid state system[J]. Nature, 2013,500:319-322.
    [7]
    WANG X L, CAI X D, SU Z E, et al. Quantum teleportation of multiple degrees of freedom of a single photon[J]. Nature, 2015,518:516-519.
    [8]
    FAN H Y, KLAUDER J R. Eigenvectors of two particles’ relative position and total momentum[J].Phys Rev A, 1994, 49(2): 704-707.
    [9]
    FAN H Y, YE X. Common eigenstates of two particles’ center-of-mass coordinates and mass-weighted relative momentum[J]. Phys Rev A, 1995, 51(4):3343-3346.
    [10]
    WEYL H.Quantenmechanik and gruppentheorie[J]. Z Phys, 1927,46:1-46.
    [11]
    FAN H Y. Newton-Leibniz integration for ket-bra operators in quantum mechanics(IV)[J]. Ann Phys, 2008, 323(2):500-526.
    [12]
    FAN H Y.Weyl ordering quantum mechanical operators by virtue of the IWOP technique[J]. J Phys A Math Gen, 1992，25:3443-3447.
    [13]
    WIGNER E. On the quantum correction for thermodynamic equilibrium[J].Phys Rev, 1932,40:749-759.
    [14]
    XU Y J, FAN H Y, LIU Q Y. New equation for deriving pure state density operators by Weyl correspondence and Wigner operator[J]. Chin Phys B, 2010, 19(2):020303.
    [15]
    XU X F. Obtaining multimode entangled state representation by generalized radon trans-formation of the Wigner operator[J]. Int J Theor Phys, 2010, 49(7):1446-1551.
    [16]
    范洪义. 论由Dirac符号组成的算符之积分―从牛顿-莱布尼兹积分谈起[J]. 中国科学技术大学学报, 2007, 37(7):695-699.
    FAN Hongyi. On the integration over operators composed of Dirac’s symbols: Beyond Newton-Leibniz integration over c-number functions[J]. Journal of University of Science and Technology of China, 2007, 37(7):695-699.
    [17]
    FAN H Y. Operator ordering in quantum optics theory and the development of Dirac’s symbolic method[J]. J Opt B: Quantum Semiclass Opt, 2003,5(4): R147.)
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