Abstract

In this paper, we introduce the Hermite polynomial’s coherent state (HPCS) |αH, which is defined as Hn(X)|α up to a normalization constant and where Hn(X) is the coordinate operator’s Hermite polynomial of order n and |α=exp((1/2)|α|2+αa)|0. This state may be produced by the superposition of some different photon added coherent states when n=2. The mathematical and physical properties of HPCS are also studied. It is shown that HPCS has remarkable nonclassical state features such as sub-Poissonian and squeezing properties.

© 2012 Optical Society of America

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  1. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).
  2. X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
    [CrossRef]
  3. L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
    [CrossRef]
  4. Roy J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
    [CrossRef]
  5. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
    [CrossRef]
  6. J. R. Klauder, “Continuous-representation theory. III. On functional quantization of classical systems,” J. Math. Phys. 5, 177–186 (1964).
    [CrossRef]
  7. C. C. Gerry, “Proposal for generating even and odd coherent states,” Opt. Commun. 91, 247–251 (1992).
    [CrossRef]
  8. R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
    [CrossRef]
  9. V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
    [CrossRef]
  10. A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
    [CrossRef]
  11. D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
    [CrossRef]
  12. H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
    [CrossRef]
  13. S. D. Bartlett and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
    [CrossRef]
  14. G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
    [CrossRef]
  15. G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
    [CrossRef]
  16. F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
    [CrossRef]
  17. A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
    [CrossRef]
  18. M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
    [CrossRef]
  19. P. Marek, H. Jeong, and M. S. Kim, “Generating ‘squeezed’ superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008).
    [CrossRef]
  20. S. Y. Lee and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
    [CrossRef]
  21. H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010).
    [CrossRef]
  22. H. Y. Fan, H. L. Lu, and Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
    [CrossRef]
  23. J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, Singapore, 1985).
  24. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, 1984), p. 12.
  25. V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
    [CrossRef]
  26. V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994).
    [CrossRef]
  27. V. V. Dodonov and V. I. Manko, Invariants and Evolution of Nonstationary Quantum Systems, M. A. Markov, ed. (Nova Science,1989).
  28. C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic field,” Phys. Rev. A 32, 974–982 (1985).
    [CrossRef]
  29. J. Lee, J. Kim, and H. Nha, “Demonstrating higher-order nonclassical effects by photon-added classical states: realistic schemes,” J. Opt. Soc. Am. B 26, 1363–1369 (2009).
    [CrossRef]
  30. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
    [CrossRef]
  31. H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
    [CrossRef]

2012 (1)

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

2010 (4)

X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
[CrossRef]

L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

S. Y. Lee and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010).
[CrossRef]

2009 (1)

2008 (2)

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
[CrossRef]

P. Marek, H. Jeong, and M. S. Kim, “Generating ‘squeezed’ superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008).
[CrossRef]

2007 (3)

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

2006 (2)

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

H. Y. Fan, H. L. Lu, and Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
[CrossRef]

2004 (1)

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

2003 (1)

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

2002 (1)

S. D. Bartlett and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

1996 (1)

V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
[CrossRef]

1994 (1)

V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994).
[CrossRef]

1992 (2)

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef]

C. C. Gerry, “Proposal for generating even and odd coherent states,” Opt. Commun. 91, 247–251 (1992).
[CrossRef]

1991 (1)

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

1987 (1)

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

1985 (1)

C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic field,” Phys. Rev. A 32, 974–982 (1985).
[CrossRef]

1979 (1)

1964 (1)

J. R. Klauder, “Continuous-representation theory. III. On functional quantization of classical systems,” J. Math. Phys. 5, 177–186 (1964).
[CrossRef]

1963 (2)

Roy J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

Albano, L.

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

Barbieri, M.

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

Bartlett, S. D.

S. D. Bartlett and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

Bellini, M.

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Blandino, R.

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

Browne, D. E.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

Carmichael, H. J.

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

Chefles, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

De Siena, S.

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

Dell’Anno, F.

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

Dirac, P. A. M.

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, 1984), p. 12.

Dodonov, V. V.

V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
[CrossRef]

V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994).
[CrossRef]

V. V. Dodonov and V. I. Manko, Invariants and Evolution of Nonstationary Quantum Systems, M. A. Markov, ed. (Nova Science,1989).

Eisert, J.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

Ekert, A.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

Fan, H. Y.

H. Y. Fan, H. L. Lu, and Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
[CrossRef]

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

Fan, H.-Y.

H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010).
[CrossRef]

X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
[CrossRef]

Fan, Y.

H. Y. Fan, H. L. Lu, and Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
[CrossRef]

Ferreyrol, F.

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

Gerry, C. C.

C. C. Gerry, “Proposal for generating even and odd coherent states,” Opt. Commun. 91, 247–251 (1992).
[CrossRef]

Glauber, Roy J.

Roy J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Grangier, P.

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

Grangier, Ph.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

Hong, C. K.

C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic field,” Phys. Rev. A 32, 974–982 (1985).
[CrossRef]

Hu, L.-Y.

L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
[CrossRef]

Illuminati, F.

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

Jeong, H.

P. Marek, H. Jeong, and M. S. Kim, “Generating ‘squeezed’ superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008).
[CrossRef]

Kim, J.

Kim, M. S.

P. Marek, H. Jeong, and M. S. Kim, “Generating ‘squeezed’ superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008).
[CrossRef]

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
[CrossRef]

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Kitagawa, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Klauder, J. R.

J. R. Klauder, “Continuous-representation theory. III. On functional quantization of classical systems,” J. Math. Phys. 5, 177–186 (1964).
[CrossRef]

J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, Singapore, 1985).

Korennoy, Y. A.

V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
[CrossRef]

Lee, J.

Lee, S. Y.

S. Y. Lee and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

Lu, H. L.

H. Y. Fan, H. L. Lu, and Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
[CrossRef]

Mandel, L.

C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic field,” Phys. Rev. A 32, 974–982 (1985).
[CrossRef]

L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979).
[CrossRef]

Manko, V. I.

V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
[CrossRef]

V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994).
[CrossRef]

V. V. Dodonov and V. I. Manko, Invariants and Evolution of Nonstationary Quantum Systems, M. A. Markov, ed. (Nova Science,1989).

Marek, P.

P. Marek, H. Jeong, and M. S. Kim, “Generating ‘squeezed’ superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008).
[CrossRef]

Moukhin, Y. A.

V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
[CrossRef]

Nha, H.

S. Y. Lee and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

J. Lee, J. Kim, and H. Nha, “Demonstrating higher-order nonclassical effects by photon-added classical states: realistic schemes,” J. Opt. Soc. Am. B 26, 1363–1369 (2009).
[CrossRef]

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

Ourjoumtsev, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

Parigi, V.

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Plenio, M. B.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

Polynkin, P. G.

V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994).
[CrossRef]

Sanders, B. C.

S. D. Bartlett and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

Sasaki, M.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Scheel, S.

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

Skargerstam, B. S.

J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, Singapore, 1985).

Sudarshan, E. C. G.

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[CrossRef]

Takeoka, M.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

Tara, K.

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

Tualle-Brouri, R.

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

Wang, Z.-S.

L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

Xu, X.-F.

L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

Xu, X.-X.

L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
[CrossRef]

H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010).
[CrossRef]

Yuan, H.-C.

H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010).
[CrossRef]

Zaidi, H. R.

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

Zavatta, A.

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Zeilinger, A.

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

Ann. Phys. (1)

H. Y. Fan, H. L. Lu, and Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
[CrossRef]

Chin. Phys. B (1)

H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010).
[CrossRef]

J. Math. Phys. (1)

J. R. Klauder, “Continuous-representation theory. III. On functional quantization of classical systems,” J. Math. Phys. 5, 177–186 (1964).
[CrossRef]

J. Opt. B (1)

V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008).
[CrossRef]

New J. Phys. (1)

R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012).
[CrossRef]

Opt. Commun. (2)

C. C. Gerry, “Proposal for generating even and odd coherent states,” Opt. Commun. 91, 247–251 (1992).
[CrossRef]

X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (2)

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987).
[CrossRef]

V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994).
[CrossRef]

Phys. Rev. (1)

Roy J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[CrossRef]

Phys. Rev. A (10)

L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010).
[CrossRef]

D. E. Browne, J. Eisert, S. Scheel, and M. B. Plenio, “Driving non-Gaussian to Gaussian states with linear optics,” Phys. Rev. A 67, 062320 (2003).
[CrossRef]

S. D. Bartlett and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002).
[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical properties of states generated by the excitations on a coherent state,” Phys. Rev. A 43, 492–497 (1991).
[CrossRef]

G. S. Agarwal and K. Tara, “Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics,” Phys. Rev. A 46, 485–488 (1992).
[CrossRef]

F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007).
[CrossRef]

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, “Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states,” Phys. Rev. A 73, 042310 (2006).
[CrossRef]

C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic field,” Phys. Rev. A 32, 974–982 (1985).
[CrossRef]

P. Marek, H. Jeong, and M. S. Kim, “Generating ‘squeezed’ superpositions of coherent states using photon addition and subtraction,” Phys. Rev. A 78, 063811 (2008).
[CrossRef]

S. Y. Lee and H. Nha, “Quantum state engineering by a coherent superposition of photon subtraction and addition,” Phys. Rev. A 82, 053812 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004).
[CrossRef]

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, “Increasing entanglement between Gaussian states by coherent photon subtraction,” Phys. Rev. Lett. 98, 030502 (2007).
[CrossRef]

E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963).
[CrossRef]

Science (1)

V. Parigi, A. Zavatta, M. S. Kim, and M. Bellini, “Probing quantum commutation rules by addition and subtraction of single photons to/from a light field,” Science 317, 1890–1893 (2007).
[CrossRef]

Other (4)

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).

J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, Singapore, 1985).

P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, 1984), p. 12.

V. V. Dodonov and V. I. Manko, Invariants and Evolution of Nonstationary Quantum Systems, M. A. Markov, ed. (Nova Science,1989).

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Figures (10)

Fig. 1.
Fig. 1.

Quadrature distributions P of HPCS P as a function of x for different values of n with α=0.15. The solid curve refers to n=0. The dashed curve indicates n=1, and n=3 is the dotted–dashed curve.

Fig. 2.
Fig. 2.

x quadrature distributions P of HPCS as a function of x for different α with n=5. The solid curve, dashed curve, and dotted–dashed curve refer to α=0.15, 0.5, 2, respectively.

Fig. 3.
Fig. 3.

Squeezing coefficient s as a function of α with n=1 (dotted curve), n=3 (dotted–dashed curve), and n=4 (dashed curve). In the primary and secondary figure, the horizontal lines from top to bottom are s=1/2 and s=1 (when n=0), respectively.

Fig. 4.
Fig. 4.

Function D in Eq. (30) as a function of α with different n. The curves corresponding to n=0, 1, 3, 4 from bottom to top. The bottom horizontal line is D=1/4.

Fig. 5.
Fig. 5.

Degree of squeezing Sopt for the HPCS as a function of the parameter α with different parameters n. The bottom horizontal line is sopt=1, meaning the maximum degree of squeezing. The dotted curve, dotted–dashed curve, and solid curve refer to n=1, 2, 3, respectively. In the auxiliary figure, we plot the function for the parameter α in the range of [0.8,10].

Fig. 6.
Fig. 6.

Q-parameter QH as a function of α with n=1 (solid curve), n=2 (dashed curve), n=4 (dotted–dashed curve) and n=6 (dotted curve). When n=0, QH=0, i.e., the standard coherent state.

Fig. 7.
Fig. 7.

Second-order correlation function g2 of the HPCS as a function of α with n=1 (solid curve), n=2 (dashed curve), n=4 (dotted–dashed curve), and n=6 (dotted curve). The top line stands for g2=1 when n=0.

Fig. 8.
Fig. 8.

Photon-number distributions of the HPCS PH(m) as a function of m with α=0.5, n=10.

Fig. 9.
Fig. 9.

Q function of the HPCS, α=2, n=1.

Fig. 10.
Fig. 10.

Wigner function of HPCS in (γ1,γ2) phase space with α=0.1 and n=2.

Equations (45)

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|αH=Nm1/2Hn(X)|α,
et2+2tx=n=0tnn!Hn(x),
et2+2tX=n=0tnn!Hn(X).
:aa:=aa=:aa:.
n=0(2t)nn!:Xn:=:e2tX:=:e2t(a+a):=e2tae2ta.
eAeB=eA+Be12[A,B],[A,[A,B]]=[B,[A,B]]=0,
n=0(2t)nn!:Xn:=e2tXt2=n=0tnn!Hn(X).
Hn(X)=2n:Xn:.
Nm=α|H(X)H(X)|α=2nd2zπα|:(a+a)n:|zz|:(a+a)n:|α=2nd2zπ(z+α*)n(z*+α)nexp[(|z|2+|α|2)+α*z+az*].
Nm=2nd2zπznz*nexp(|z|2+2zReα+2z*Reα4Re2α)=2nn!Ln(4Re2α),
Lm(ξη)=eξηm!d2zπzmz*mexp(|z|2+ξzηz*).
|αH=Nm122n:(a+a)n:|α=Nm122ni=1nCniαniai|α,
x|α=π1/4exp(x22+2xαα22|α|22),
x|αH=Nm1/2x|Hn(X)|α=Nm1/2Hn(x)x|α=π1/4Nm1/2Hn(x)exp(x22+2xαα22|α|22).
q=a+a2,p=aa2i.
akH=2nn!Nm1r=0kCkr(α*)kr(2rRerα)Lnr,
d2zπznz*mexp[|z|2+ξzηz*]={n!ξmneξηLnmn(ξη),m>nm!(1)m+nηnmeξηLmnm(ξη),m<n
akH=2nn!Nm1r=0kCkr(α)kr(2Reα)rLnr,
aaH=2nn!Nm1[(n+1)Ln+1+|α|2Ln4(Reα)2Ln1]1,
a2a2H=2nNm1[(n+2)!Ln+2+4|α|2(n+1)!Ln+1+|α|4n!Ln4Re2α((α2+α*2)n!Ln22|α|2n!Ln12(n+1)!Ln+11)].
qH=a+a2H=12[akH+akH]|k=1,
pH=aa2iH=12i[akHakH]|k=1,
q2H=a2+a22+aa+12H=12[akH+akH]|k=2+aaH+12,
p2H=a2+a22+aa+12H=12[akH+akH]|k=2+aaH+12,
qp+pqH=i(a2+a2)H=i[akH+akH]|k=2.
σqq=q2HqH,
σpp=p2HpH,
σpq=12qp+pqHpHpH.
s=σqq+σpp[(σqq+σpp)24D]1/2,
D=σppσqqσpq2.
Sopt=2|a2a2|+2aa2|a|2.
Q=a2a2aa2aa.
g2=a2a2aa2,
PH(m)=|m|αH|2.
m|αH=2nNm1/2m|:(a+a)n:|α=2nNm1/2d2zπm|zz|:(a+a)n:|α=2nNm1/2d2zπe12|z|2zmm!(α+z*)ne12|z|212|α|2+αz*=2nm!Nm1/2exp(12|α|2)r=0nCnrαnrd2zπzmz*rexp(|z|2+αz*)=2nm!Nm1/2exp(12|α|2)r=0nCnrαnr(1)mHr,m(0,α),
(1)neξηHm,n(ξ,η)=d2zπznz*mexp[|z|2+ξzηz*],
Hm,n(ξ,η)=l=0min(m,n)m!n!(1)l(nl)!(ml)!ξmlηnll!.
PH(m)=2nm!Nm1exp(|α|2)[r=0nCnrαnrHr,m(0,α)]2.
QH(β)=β|αHHα|β.
QH(β)=2n1Nm(|α|2+|β|2+αβ+α*β*)exp[(|α|2+|β|2)+αβ*+α*β].
W(γ,γ*)=e2|γ|2πd2zπz|ρ|ze2(zγ*z*γ),
W(γ,γ*)=2ne2|γ|2πNm1exp(2|α|2+2γα*+2γ*α4|γ|2)r=0nCnr2nrr!(1)r(|α|2α2+2αγ)nrLrnr[4(γ*Reα)(γImα)].
W(γ,γ*)=2ne2|γ|2πNm1d2zπz|:(a+a)n:|αα|:(a+a)n:|ze2(zγ*z*γ)=2ne2|γ|2πNm1d2zπ(αz*)n(z+α*)nexp[(|z|2+|α|2)+(2γα)z*+(α*2γ*)z].
W(γ,γ*)=2ne2|γ|2πNm1exp(2|α|2+α2α*2+2γ*α*2γα)r=0nCnr(2α)nr(1)rd2zπz*rznexp[|z|2+(α+α*2γ*)z+(α*α+2γ)z*],
W(γ,γ*)=2ne2|γ|2πNm1exp(2|α|2+2γα*+2γ*α4|γ|2)r=0nCnr2nrr!(1)r=(|α|2α2+2αγ)nrLrnr[4(γ*Reα)(γImα)].

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