Abstract

We introduce the photon-subtracted squeezed coherent state (PSSCS), which is theoretically constructed by repeatedly subtracting photons from the squeezed coherent state (SCS) with squeezing parameter r and displacement amplitude α=|α|eiφ. Employing the normal ordering form of density operator of the SCS, we study the nonclassicality of the PSSCS by analyzing Mandel’s Q-parameter, quadratures squeezing, photon-number distribution (PND), and Wigner function (WF). We find that the PND in a PSSCS is a periodic function of φ with a period π and exhibits more remarkable oscillations than that of a SCS in the case of strong squeezing. The partial negative region of the WF is sensitive to r and |α|. The fidelity between PSSCS and SCS is analyzed, which manifests that larger photon subtraction number may result in lower fidelity. By virtue of the thermal entangled state representation the decoherence of the PSSCS in thermal environment is studied through the time evolution of the WF. The negative volume of the WF gradually diminishes with the increase of evolution time and thermal photon number, respectively. The study of the PSSCS shows that generating new photon-number-controllable nonclassical states from a weak coherent light may be realized by subtracting suitable photons from a SCS.

© 2012 Optical Society of America

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2011 (3)

2010 (3)

L. Y. Hu, X. X. Xu, and H. Y. Fan, “Statistical properties of photon-subtracted two-mode squeezed vacuum and its decoherence in thermal environment,” J. Opt. Soc. Am. B 27, 286–299 (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]

L. Y. Hu and H. Y. Fan, “Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment,” J. Mod. Opt. 57, 1344–1354 (2010).
[CrossRef]

2009 (5)

2008 (3)

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]

L. Y. Hu and H. Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008).
[CrossRef]

H. Y. Fan, “Newton-Leibniz integration for ket-bra operators in quantum mechanics (IV)–Integrations within Weyl ordered product of operators and their application,” Ann. Phys. 323, 500–526 (2008).
[CrossRef]

2007 (4)

W. L. You, Y. W. Li, and S. J. Gu, “Fidelity, dynamic structure factor, and susceptibility in critical phenomena,” Phys. Rev. E 76, 022101 (2007).
[CrossRef]

A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (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]

V. Parigi, A. Zavatta, M. 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]

2006 (2)

A. Luis, “Squeezed coherent states as feasible approximations to phase-optimized states,” Phys. Lett. A 354, 71–78 (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]

2005 (3)

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[CrossRef]

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

S. L. Braunstein and P. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

2004 (3)

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

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

A. Kenfack and K. Zyczkowski, “Negativity of the Wigner function as an indicator of nonclassicality,” J. Opt. B 6, 396–404 (2004).
[CrossRef]

2003 (2)

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]

M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003).
[CrossRef]

2002 (1)

V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
[CrossRef]

2000 (1)

G. S. Kumar and V. C. Kuriakose, “Squeezed coherent states representation of scalar field and particle production in the early universe,” Int. J. Theor. Phys. 39, 351–361 (2000).
[CrossRef]

1997 (1)

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

1996 (1)

H. Y. Fan and M. Xiao, “A spacial type of squeezed coherent state,” Phys. Lett. A 220, 81–86 (1996).
[CrossRef]

1994 (1)

M. Selvadoray, M. S. Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
[CrossRef]

1993 (2)

1991 (2)

H. Y. Fan and V. J. Linde, “Similarity transformations in one- and two-mode Fock space,” J. Phys. A 24, 2529–2538(1991).

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]

1990 (1)

H. Y. Fan, “Squeezed states: Operators for two types of one- and two-mode squeezing transformations,” Phys. Rev. A 41, 1526–1532 (1990).

1985 (1)

B. Yurke, “Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors,” Phys. Rev. A 32, 300–310 (1985).
[CrossRef]

1983 (1)

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983).
[CrossRef]

1982 (1)

H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102 (1982).
[CrossRef]

1979 (2)

1970 (1)

D. Stoler, “ Equivalence classes of minimum uncertainty packets,” Phys. Rev. D 1, 3217–3219 (1970).
[CrossRef]

Agarwal, G. S.

A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (2007).
[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]

Anhut, T.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Bellini, M.

V. Parigi, A. Zavatta, M. 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. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Biswas, A.

A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (2007).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein and P. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

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]

Dakna, M.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[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]

Dodonov, V. V.

V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
[CrossRef]

Dutta, B.

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]

Fan, H. Y.

Z. Wang, H. C. Yuan, and H. Y. Fan, “Nonclassicality of the photon addition-then subtraction coherent state and its decoherence in the photon-loss channel,” J. Opt. Soc. Am. B 28, 1964–1972 (2011).
[CrossRef]

S. Wang, X. X. Xu, H. C. Yuan, L. Y. Hu, and H. Y. Fan, “Coherent operation of photon subtraction and addition for squeezed thermal states: analysis of nonclassicality and decoherence,” J. Opt. Soc. Am. B 28, 2149–2158 (2011).
[CrossRef]

L. Y. Hu, X. X. Xu, and H. Y. Fan, “Statistical properties of photon-subtracted two-mode squeezed vacuum and its decoherence in thermal environment,” J. Opt. Soc. Am. B 27, 286–299 (2010).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment,” J. Mod. Opt. 57, 1344–1354 (2010).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Infinite-dimensional Kraus operators for describing amplitude-damping channel and laser process,” Opt. Commun. 282, 932–935 (2009).
[CrossRef]

H. Y. Fan and L. Y. Hu, “Time evolution of Wigner function in laser process derived by entangled state representation,” Opt. Commun. 282, 4379–4383 (2009).
[CrossRef]

H. Y. Fan, “Newton-Leibniz integration for ket-bra operators in quantum mechanics (IV)–Integrations within Weyl ordered product of operators and their application,” Ann. Phys. 323, 500–526 (2008).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008).
[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]

H. Y. Fan and M. Xiao, “A spacial type of squeezed coherent state,” Phys. Lett. A 220, 81–86 (1996).
[CrossRef]

H. Y. Fan and V. J. Linde, “Similarity transformations in one- and two-mode Fock space,” J. Phys. A 24, 2529–2538(1991).

H. Y. Fan, “Squeezed states: Operators for two types of one- and two-mode squeezing transformations,” Phys. Rev. A 41, 1526–1532 (1990).

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]

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]

Gu, S. J.

W. L. You, Y. W. Li, and S. J. Gu, “Fidelity, dynamic structure factor, and susceptibility in critical phenomena,” Phys. Rev. E 76, 022101 (2007).
[CrossRef]

Hirano, T.

M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003).
[CrossRef]

Hu, L. Y.

S. Wang, X. X. Xu, H. C. Yuan, L. Y. Hu, and H. Y. Fan, “Coherent operation of photon subtraction and addition for squeezed thermal states: analysis of nonclassicality and decoherence,” J. Opt. Soc. Am. B 28, 2149–2158 (2011).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment,” J. Mod. Opt. 57, 1344–1354 (2010).
[CrossRef]

L. Y. Hu, X. X. Xu, and H. Y. Fan, “Statistical properties of photon-subtracted two-mode squeezed vacuum and its decoherence in thermal environment,” J. Opt. Soc. Am. B 27, 286–299 (2010).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Infinite-dimensional Kraus operators for describing amplitude-damping channel and laser process,” Opt. Commun. 282, 932–935 (2009).
[CrossRef]

H. Y. Fan and L. Y. Hu, “Time evolution of Wigner function in laser process derived by entangled state representation,” Opt. Commun. 282, 4379–4383 (2009).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008).
[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]

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[CrossRef]

Ji, S. W.

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

S. Y. Lee, J. Park, S. W. Ji, C. H. R. Ooi, and H. W. Lee, “Nonclassicality generated by photon annihilation-then-creation and creation-then-annihilation operations,” J. Opt. Soc. Am. B 26, 1532–1537 (2009).
[CrossRef]

Kenfack, A.

A. Kenfack and K. Zyczkowski, “Negativity of the Wigner function as an indicator of nonclassicality,” J. Opt. B 6, 396–404 (2004).
[CrossRef]

Kim, H. J.

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[CrossRef]

Kim, J.

Kim, M.

V. Parigi, A. Zavatta, M. 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]

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, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[CrossRef]

Kitagawa, A.

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

Knight, P. L.

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[CrossRef]

Knoll, L.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Kumar, G. S.

G. S. Kumar and V. C. Kuriakose, “Squeezed coherent states representation of scalar field and particle production in the early universe,” Int. J. Theor. Phys. 39, 351–361 (2000).
[CrossRef]

Kumar, M. S.

M. Selvadoray, M. S. Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
[CrossRef]

Kuriakose, V. C.

G. S. Kumar and V. C. Kuriakose, “Squeezed coherent states representation of scalar field and particle production in the early universe,” Int. J. Theor. Phys. 39, 351–361 (2000).
[CrossRef]

Lee, H. W.

Lee, J.

Lee, S. Y.

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[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]

S. Y. Lee, J. Park, S. W. Ji, C. H. R. Ooi, and H. W. Lee, “Nonclassicality generated by photon annihilation-then-creation and creation-then-annihilation operations,” J. Opt. Soc. Am. B 26, 1532–1537 (2009).
[CrossRef]

Li, F. L.

Li, X. R.

Li, Y. W.

W. L. You, Y. W. Li, and S. J. Gu, “Fidelity, dynamic structure factor, and susceptibility in critical phenomena,” Phys. Rev. E 76, 022101 (2007).
[CrossRef]

Linde, V. J.

H. Y. Fan and V. J. Linde, “Similarity transformations in one- and two-mode Fock space,” J. Phys. A 24, 2529–2538(1991).

Loock, P.

S. L. Braunstein and P. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[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]

Luis, A.

A. Luis, “Squeezed coherent states as feasible approximations to phase-optimized states,” Phys. Lett. A 354, 71–78 (2006).
[CrossRef]

Mandel, L.

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983).
[CrossRef]

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

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]

Matsuoka, M.

M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003).
[CrossRef]

Mukunda, N.

Nha, H.

S. Y. Lee, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[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]

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]

Ooi, C. H. R.

Opatrny, T.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[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. 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]

Park, E.

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[CrossRef]

Park, J.

Paul, H.

H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102 (1982).
[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]

Puri, R. R.

R. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, 2001).

Sasaki, M.

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[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]

Schleich, W. P.

W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, 2001).

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Selvadoray, M.

M. Selvadoray, M. S. Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
[CrossRef]

Shapiro, J. H.

Short, R.

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983).
[CrossRef]

Simon, R.

M. Selvadoray, M. S. Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
[CrossRef]

B. Dutta, N. Mukunda, R. Simon, and A. Subramaniam, “Squeezed states, photon-number distributions, and U(1) invariance,” J. Opt. Soc. Am. B 10, 253–264 (1993).
[CrossRef]

Stoler, D.

D. Stoler, “ Equivalence classes of minimum uncertainty packets,” Phys. Rev. D 1, 3217–3219 (1970).
[CrossRef]

Subramaniam, A.

Takeoka, M.

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

Tara, K.

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.

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]

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Wakui, K.

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[CrossRef]

Wang, Q.

Wang, S.

Wang, Z.

Welsch, D. G.

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

Xiao, M.

H. Y. Fan and M. Xiao, “A spacial type of squeezed coherent state,” Phys. Lett. A 220, 81–86 (1996).
[CrossRef]

Xu, X. X.

Yang, Y.

You, W. L.

W. L. You, Y. W. Li, and S. J. Gu, “Fidelity, dynamic structure factor, and susceptibility in critical phenomena,” Phys. Rev. E 76, 022101 (2007).
[CrossRef]

Yuan, H. C.

Yuen, H. P.

Yurke, B.

B. Yurke, “Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors,” Phys. Rev. A 32, 300–310 (1985).
[CrossRef]

Zavatta, A.

V. Parigi, A. Zavatta, M. 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. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

Zhu, K.

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Zyczkowski, K.

A. Kenfack and K. Zyczkowski, “Negativity of the Wigner function as an indicator of nonclassicality,” J. Opt. B 6, 396–404 (2004).
[CrossRef]

Ann. Phys. (2)

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, “Newton-Leibniz integration for ket-bra operators in quantum mechanics (IV)–Integrations within Weyl ordered product of operators and their application,” Ann. Phys. 323, 500–526 (2008).
[CrossRef]

Int. J. Theor. Phys. (1)

G. S. Kumar and V. C. Kuriakose, “Squeezed coherent states representation of scalar field and particle production in the early universe,” Int. J. Theor. Phys. 39, 351–361 (2000).
[CrossRef]

J. Mod. Opt. (1)

L. Y. Hu and H. Y. Fan, “Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment,” J. Mod. Opt. 57, 1344–1354 (2010).
[CrossRef]

J. Opt. B (2)

A. Kenfack and K. Zyczkowski, “Negativity of the Wigner function as an indicator of nonclassicality,” J. Opt. B 6, 396–404 (2004).
[CrossRef]

V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B 4, R1–R33 (2002).
[CrossRef]

J. Opt. Soc. Am. B (9)

S. Wang, X. X. Xu, H. C. Yuan, L. Y. Hu, and H. Y. Fan, “Coherent operation of photon subtraction and addition for squeezed thermal states: analysis of nonclassicality and decoherence,” J. Opt. Soc. Am. B 28, 2149–2158 (2011).
[CrossRef]

Y. Yang and F. L. Li, “Nonclassicality of photon-subtracted and photon-added-then-subtracted Gaussian states,” J. Opt. Soc. Am. B 26, 830–835 (2009).
[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]

S. Y. Lee, J. Park, S. W. Ji, C. H. R. Ooi, and H. W. Lee, “Nonclassicality generated by photon annihilation-then-creation and creation-then-annihilation operations,” J. Opt. Soc. Am. B 26, 1532–1537 (2009).
[CrossRef]

K. Zhu, Q. Wang, and X. R. Li, “Nonclassical statistical properties of fields in squeezed even and squeezed odd coherent states,” J. Opt. Soc. Am. B 10, 1287–1291 (1993).
[CrossRef]

Z. Wang, H. C. Yuan, and H. Y. Fan, “Nonclassicality of the photon addition-then subtraction coherent state and its decoherence in the photon-loss channel,” J. Opt. Soc. Am. B 28, 1964–1972 (2011).
[CrossRef]

L. Y. Hu and H. Y. Fan, “Statistical properties of photon-subtracted squeezed vacuum in thermal environment,” J. Opt. Soc. Am. B 25, 1955–1964 (2008).
[CrossRef]

L. Y. Hu, X. X. Xu, and H. Y. Fan, “Statistical properties of photon-subtracted two-mode squeezed vacuum and its decoherence in thermal environment,” J. Opt. Soc. Am. B 27, 286–299 (2010).
[CrossRef]

B. Dutta, N. Mukunda, R. Simon, and A. Subramaniam, “Squeezed states, photon-number distributions, and U(1) invariance,” J. Opt. Soc. Am. B 10, 253–264 (1993).
[CrossRef]

J. Phys. A (1)

H. Y. Fan and V. J. Linde, “Similarity transformations in one- and two-mode Fock space,” J. Phys. A 24, 2529–2538(1991).

Opt. Commun. (2)

L. Y. Hu and H. Y. Fan, “Infinite-dimensional Kraus operators for describing amplitude-damping channel and laser process,” Opt. Commun. 282, 932–935 (2009).
[CrossRef]

H. Y. Fan and L. Y. Hu, “Time evolution of Wigner function in laser process derived by entangled state representation,” Opt. Commun. 282, 4379–4383 (2009).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (2)

A. Luis, “Squeezed coherent states as feasible approximations to phase-optimized states,” Phys. Lett. A 354, 71–78 (2006).
[CrossRef]

H. Y. Fan and M. Xiao, “A spacial type of squeezed coherent state,” Phys. Lett. A 220, 81–86 (1996).
[CrossRef]

Phys. Rev. A (13)

B. Yurke, “Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors,” Phys. Rev. A 32, 300–310 (1985).
[CrossRef]

M. Selvadoray, M. S. Kumar, and R. Simon, “Photon distribution in two-mode squeezed coherent states with complex displacement and squeeze parameters,” Phys. Rev. A 49, 4957–4967 (1994).
[CrossRef]

M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003).
[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, S. W. Ji, H. J. Kim, and H. Nha, “Enhancing quantum entanglement for continuous variables by coherent superposition of photon subtraction and addition,” Phys. Rev. A 84, 012302 (2011).
[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]

M. S. Kim, E. Park, P. L. Knight, and H. Jeong, “Nonclassicality of a photon-subtracted Gaussian field,” Phys. Rev. A 71, 043805 (2005).
[CrossRef]

A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (2007).
[CrossRef]

A. Kitagawa, M. Takeoka, K. Wakui, and M. Sasaki, “Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to the dense coding scheme,” Phys. Rev. A 72, 022334 (2005).
[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]

M. Dakna, T. Anhut, T. Opatrny, L. Knoll, and D. G. Welsch, “Generating Schrodinger-cat-like states by means of conditional measurements on a beam splitter,” Phys. Rev. A 55, 3184–3194 (1997).
[CrossRef]

H. Y. Fan, “Squeezed states: Operators for two types of one- and two-mode squeezing transformations,” Phys. Rev. A 41, 1526–1532 (1990).

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. D (1)

D. Stoler, “ Equivalence classes of minimum uncertainty packets,” Phys. Rev. D 1, 3217–3219 (1970).
[CrossRef]

Phys. Rev. E (1)

W. L. You, Y. W. Li, and S. J. Gu, “Fidelity, dynamic structure factor, and susceptibility in critical phenomena,” Phys. Rev. E 76, 022101 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983).
[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]

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

Rev. Mod. Phys. (2)

S. L. Braunstein and P. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[CrossRef]

H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102 (1982).
[CrossRef]

Science (2)

A. Zavatta, S. Viciani, and M. Bellini, “Quantum-to-classical transition with single-photon-added coherent states of light,” Science 306, 660–662 (2004).
[CrossRef]

V. Parigi, A. Zavatta, M. 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 (3)

W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, 2001).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

R. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, 2001).

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Figures (9)

Fig. 1.
Fig. 1.

Mandel’s Q-parameter of PSSCS versus r with |α|=23, φ=π3 for different values of m: m=0, 1, 2, and 3, respectively.

Fig. 2.
Fig. 2.

(a) Degree of output squeezing of PSSCS changes with r with |α|=23, φ=π3 for different values of m: m=0, 1, 2, and 3, respectively. (b) Degree of output squeezing of PSSCS changes with |α| with φ=0, r=0.55 for different values of m: m=0, 1, 2, and 3, respectively.

Fig. 3.
Fig. 3.

PND of PSSCS versus n for several different values of m: (a) m=0, (b) m=1, (c) m=5 with r=0.55, |α|=23, and φ=π3.

Fig. 4.
Fig. 4.

PND of PSSCS versus n with r=2.2, |α|=23, and φ=π3 for different values of m: (a) m=0 and (b) m=1, respectively.

Fig. 5.
Fig. 5.

WF of PSSCS for different values of m with r=0.55, |α|=23, and φ=π3. (a) m=0, (b) m=1, (c) m=2, and (d) m=3, respectively.

Fig. 6.
Fig. 6.

WF of PSSCS for different values of r and α. (a) r=0.055, |α|=23, φ=π3, and (b) r=0.55, |α|=3, φ=π3, respectively.

Fig. 7.
Fig. 7.

(a) Fidelity between PSSCS and SCS versus r with |α|=23 and φ=π3 for several different values of m: m=0, 1, 2, 3, 4, and 5 (from upper to lower curves), respectively. (b) Fidelity between PSSCS and SCS versus |α| with φ=0 and r=0.55 for several different values of m: m=0, 1, 2, 3, 4, and 5 (from upper to lower curves), respectively.

Fig. 8.
Fig. 8.

WF of SPSSCS for different values of κt with r=0.55, n¯=1, |α|=23, and φ=π3. (a) κt=0.01, (b) κt=0.03, (c) κt=0.05, and (d) κt=0.15, respectively.

Fig. 9.
Fig. 9.

(a) The evolution of negative volume of the WF versus κt with n¯=1, r=0.55, |α|=23, and φ=π3 for several different values of m: m=2, 1, 3, and 4 (from upper to lower curves), respectively. (b) The evolution of negative volume of the WF versus n¯ with κt=0.01, r=0.55, |α|=23, and φ=π3 for several different values of m: m=2, 1, 3, and 4 (from upper to lower curves), respectively.

Equations (47)

Equations on this page are rendered with MathJax. Learn more.

|m,r,α=(Nm)12amS(r)|α,
ρ=(Nm)1amρsam,
ρs=2σ1σ2:exp[1σ12(Qτ1)21σ22(Pτ2)2]:,
ρ=(Nm)12σ1σ2am:exp[1σ12(Qτ1)21σ22(Pτ2)2]:am.
Nm=(14sinh2r)mn=0m(2tanhr)nn![m!(mn)!]2|Hmn(iχ)|2,
χ=cothr2α+tanhr2α*.
aa=(Nm)1Tr(am+1ρsam+1)=Nm+1Nm,
a2a2=(Nm)1Tr(am+2ρsam+2)=Nm+2Nm.
QM=a2a2aaaa,
QM=Nm+2Nm+1Nm+1Nm.
a=(Nm)1Tr(amρsam+1)=i(Nm)1(14sinh2r)m+12n=0m(2tanhr)nn!×m!(m+1)!(mn)!(m+1n)!Hmn(iχ*)Hm+1n(iχ),
a2=(Nm)1Tr(amρsam+2)=(Nm)1(14sinh2r)m+1n=0m(2tanhr)nn!×m!(m+2)!(mn)!(m+2n)!Hmn(iχ*)Hm+2n(iχ).
Sm:Δ2Xθ:min=2|a2a2|+2aa2|a|2.
P(n)=Tr(ρ|nn|),
P(n)=n|ρ|n=2Nmσ1σ21n!d2(m+n)dz1*m+ndz2m+nexp[α*coshrz1*+12z1*2tanhr+αcoshrz2+12z2*2tanhr|α|212(α*2+α2)tanhr]|z1*,z2=0.
Hn(x)=ntnexp(2xtt2)|t=0,
P(n)=1Nmn!coshr(tanhr2)m+n|Hm+n(iα*sinh2r)|2×exp[|α|212(α2+α*2)tanhr].
P(n)=1Nmn!coshr(tanhr2)m+n|Hm+n(i|α|eiφsinh2r)|2×exp(|α|2tanhrcos2φ)=1Nmn!coshr(tanhr2)m+n|Hm+n[i|α|ei(φπ)sinh2r]|2×exp[|α|2tanhrcos2(φπ)],
W(β,β*)=d2zπ2z|ρ|zexp[2|β|22(β*zβz*)].
W(β,β*)=(Nm)11π2mμmνmexp[μνsinh2r+Δ*μ+Δν+14(μ2+ν2)sinh2r2|α|22|β|2cosh2r+2(αcoshrα*sinhr)β+2(α*coshrαsinhr)β*+(β2+β*2)sinh2r]|μ,ν=0,
Δ=αcoshrα*sinhr+βsinh2r2β*sinh2r.
W(β,β*)=Fm(β,β*)W0(β,β*),
W0(β,β*)=1πexp[2|α|22|β|2cosh2r+(β2+β*2)sinh2r+2(αcoshrα*sinhr)β+2(α*coshrαsinhr)β*],
Fm(β,β*)=(Nm)1(14sinh2r)mn=0m(2tanhr)nn!×[m!(mn)!]2|Hmn(iΔsinh2r)|2.
F1(β,β*)=(N1)1(|Δ|2sinh2r).
F=|m,r,α|S(r)|α|2=(Nm)1|α|S(r)amS(r)|α|2=(Nm)1(14sinh2r)m|Hm(iχ*)|2,
S(r)aS(r)=asinhr+acoshr
(ξa+ζa)m=(iξζ2)m:Hm(iξ2ζa+iζ2ξa):
dρdt=κ(n¯+1)(2aρaaaρρaa)+κn¯(2aρaaaρρaa),
W(β,β*,t)=2(2n¯+1)Td2zπW(z,z*,0)×exp(2(2n¯+1)T|βzeκt|2),
W(β,β*,t)=(Nm)12π(2n¯+1)TR(14sinh2r)m×n=0m(2tanhr)nn![m!(mn)!]22(mn)μmnνmnexp{Eμν2iQsinh2rμ+2iQsinh2rνA0(μ2+ν2)+A1|β|2+A2(β2+β*2)+(A3α*+A4α)β+(A3α+A4α*)β*+A5|α|2A6(α2+α*2)}|μ,ν=0,
E=16tanhrR[1+cosh2r(2n¯+1)TRe2κt],Q=coshr[116sinh2r(2n¯+1)TRe2κt]αsinhr[8R(1+cosh2r(2n¯+1)Te2κt)1]α*4sinh2r(2n¯+1)TR[1+e2κt(2n¯+1)T]eκtβ8sinh2r(2n¯+1)TR[1e2κt(2n¯+1)T]eκtβ*,A0=116sinh2r(2n¯+1)TRe2κt,A1=2(2n¯+1)T[4(e2κt(2n¯+1)T+coshr)(2n¯+1)TRe2κt1],A2=4sinh2r(2n¯+1)2T2Re2κt,A3=8(1e2κt(2n¯+1)T)sinhr(2n¯+1)TReκt,A4=8(1+e2κt(2n¯+1)T)coshr(2n¯+1)TReκt,A5=2[4R(1+cosh2r(2n¯+1)Te2κt)1],A6=4sinh2r(2n¯+1)TRe2κt,R=4(e4κt(2n¯+1)2T2+2cosh2r(2n¯+1)Te2κt+1).
W(β,β*,t)=Fm(β,β*,t)W0(β,β*,t),
W0(β,β*,t)=1π(2n¯+1)TRexp[A1|β|2+A2β2+A2β*2+(A3α*+A4α)β+(A3α+A4α*)β*+A5|α|2A6(α2+α*2)],
Fm(β,β*,t)=(Nm)1(14A0sinh2r)mn=0mk=0mn(2A0tanhr)nn!(EA0)kk![m!(mnk)!]2×|Hmnk(iQA0sinh2r)|2.
δ=12dqdp[|W(q,p)|W(q,p)].
|αα|exp(|α|2+αa+α*aaa):.
O=2d2βπβ|O|β::exp[2(aβ*aβ+aa)]::,
|αα|=2::exp[2(αa)(α*a)]::.
ρs=2::exp[2|α(12erQ+i2erP)|2]::,
2exp[2|α(12erq+i2erp)|2].
Δ(q,p)=1π:exp[(qQ)2(pP)2]:,
F(Q,P)=dpdqf(q,p)Δ(q,p),
Nm=Tr(d2z1d2z2π2am|z1z1|ρs|z2z2|am)=2σ1σ22mtmτmd2z1d2z2π2exp[|z1|2+(z2*+t)z1+α*coshrz1*+12z1*2tanhr|z2|2+αcoshrz2+τz2*+12z22tanhr12(α2+α*2)tanhr|α|2]|t,τ=0.
d2zπexp(ζ|z|2+ξz+ηz*+fz2+gz*2)=1ζ24fgexp(ζξη+ξ2g+η2fζ24fg),
Nm=2mtmτmexp[tτsinh2r+At+A*τ+14(t2+τ2)sinh2r]|t,τ=0,
dldxlHn(x)=2ln!(nl)!Hnl(x),

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