Abstract

We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.

© 2012 Optical Society of America

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2012 (1)

2011 (4)

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

T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
[CrossRef]

S. Sivakumar, “Photon-added coherent states in parametric down-conversion,” Phys. Rev. A 83, 035802 (2011).
[CrossRef]

Ya. A. Korennoy and V. I. Man’ko, “Optical tomography of photon-added coherent states, even and odd coherent states, and thermal states,” Phys. Rev. A 83, 053817 (2011).
[CrossRef]

2010 (4)

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

H. Takahashi, J. S. Neergaard-Nielsenl, M. Takeuchil, M. Takeokal, K. Hayasakal, A. Furusawa, and M. Sasakil, “Entanglement distillation from Gaussian input states,” Nat. Photon. 4, 178–181 (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]

M. G. Genoni and M. G. A. Paris, “Quantifying non-Gaussianity for quantum information,” Phys. Rev. A 82, 052341 (2010).
[CrossRef]

2009 (3)

J. Niset, J. Fiurášek, and N. J. Cerf, “No-Go theorem for Gaussian quantum error correction,” Phys. Rev. Lett. 102, 120501 (2009).
[CrossRef]

S.-Y. Lee, J. Y. 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]

Y. Yang and F.-L. Li, “Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement,” Phys. Rev. A 80, 022315 (2009).
[CrossRef]

2008 (8)

X. G. Wang, C.-S. Yu, and X. X. Yi, “An alternative quantum fidelity for mixed states of qudits,” Phys. Lett. A 373, 58–60 (2008).
[CrossRef]

P. van Loock, W. J. Munro, K. Nemoto, T. P. Spiller, T. D. Ladd, S. L. Braunstein, and G. J. Milburn, “Hybrid quantum computation in quantum optics,” Phys. Rev. A 78, 022303 (2008).
[CrossRef]

A. P. Lund, T. C. Ralph, and H. L. Haselgrove, “Fault-tolerant linear optical quantum computing with small-amplitude coherent states,” Phys. Rev. Lett. 100, 030503 (2008).
[CrossRef]

H. Y. Fan and L. Y. Hu, “New approach for analyzing time evolution of density operator in a dissipative channel by the entangled state representation,” Opt. Commun. 281, 5571–5573 (2008).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Quantifying the non-Gaussian character of a quantum state by quantum relative entropy,” Phys. Rev. A 78, 060303 (2008).
[CrossRef]

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

V. Parigi, A. Zavatta, and M. Bellini, “Manipulating thermal light states by the controlled addition and subtraction of single photons,” Laser Phys. Lett. 5, 246–251 (2008).
[CrossRef]

X. G. Meng, J. S. Wang, and B. L. Liang, “Two-mode excited squeezed vacuum state and its properties,” Commun. Theor. Phys. 49, 1299–1304 (2008).
[CrossRef]

2007 (5)

H.-R. Li, F.-L. Li, and S.-Y. Zhu, “Inseparability of photon-added Gaussian states,” Phys. Rev. A 75, 062318 (2007).
[CrossRef]

A. Zavatta, V. Parigi, and M. Bellini, “Experimental nonclassicality of single-photon-added thermal light states,” Phys. Rev. A 75, 052106 (2007).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Measure of the non-Gaussian character of a quantum state,” Phys. Rev. A 76, 042327 (2007).
[CrossRef]

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

K. Wakui, H. Takahashi, A. Furusawa, and M. Sasaki, “Photon subtracted squeezed states generated with periodically poled KTiOPO4,” Opt. Express 15, 3568–3574 (2007).
[CrossRef]

2006 (4)

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, “Generating optical Schrödinger kittens for quantum information processing,” Science 312, 83–86 (2006).
[CrossRef]

J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, “Generation of a superposition of odd photon number states for quantum information networks,” Phys. Rev. Lett. 97, 083604 (2006).
[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]

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 (4)

V. V. Dodonov and L. A. de Souza, “Decoherence of superpositions of displaced number states,” J. Opt. B Quant. Semiclass. Opt. 7, S490–S499 (2005).
[CrossRef]

A. Zavatta, S. Viciani, and M. Bellini, “Single-photon excitation of a coherent state: catching the elementary step of stimulated light emission,” Phys. Rev. A 72, 023820 (2005).
[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]

N. J. Cerf, O. Krüger, P. Navez, R. F. Werner, and M. M. Wolf, “Non-Gaussian cloning of quantum coherent states is optimal,” Phys. Rev. Lett. 95, 070501 (2005).
[CrossRef]

2004 (4)

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[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]

J. Wenger, R. Tualle-Brouri, and P. Grangier, “Non-Gaussian statistics from individual pulses of squeezed light,” Phys. Rev. Lett. 92, 153601 (2004).
[CrossRef]

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

2003 (2)

P. Marian, T. A. Marian, and H. Scutaru, “Bures distance as a measure of entanglement for two-mode squeezed thermal states,” Phys. Rev. A 68, 062309 (2003).
[CrossRef]

T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A 68, 042319 (2003).
[CrossRef]

2002 (3)

J. Eisert, S. Scheel, and M. B. Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys. Rev. Lett. 89, 137903 (2002).
[CrossRef]

G. Giedke and J. I. Cirac, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316 (2002).
[CrossRef]

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

2001 (1)

X.-B. Wang, L. C. Kwek, Y. Liu, and C. H. Oh, “Non-classical effects of two-mode photon-added displaced squeezed states,” J. Phys. B At. Mol. Opt. Phys. 34, 1059–1078 (2001).
[CrossRef]

2000 (1)

S. Sivakumar, “Studies on nonlinear coherent states,” J. Opt. B Quant. Semiclass. Opt. 2, R61–R75 (2000).
[CrossRef]

1998 (2)

V. V. Dodonov, M. A. Marchiolli, Y. A. Korennoy, V. I. Man’ko, and Y. A. Moukhin, “Dynamical squeezing of photon-added coherent states,” Phys. Rev. A 58, 4087–4094 (1998).
[CrossRef]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

M. Ban, “Photon statistics of conditional output states of lossless beam splitter,” J. Mod. Opt. 43, 1281–1303 (1996).
[CrossRef]

1995 (1)

C. T. Lee, “Theorem on nonclassical states,” Phys. Rev. A 52, 3374–3376 (1995).
[CrossRef]

1992 (1)

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]

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]

1990 (1)

C. T. Lee, “Many-photon antibunching in generalized pair coherent states,” Phys. Rev. A 41, 1569–1575 (1990).
[CrossRef]

1988 (1)

W. Schleich, D. F. Walls, and J. A. Wheeler, “Area of overlap and interference in phase space versus Wigner pseudoprobabilities,” Phys. Rev. A 38, 1177–1186 (1988).
[CrossRef]

1987 (3)

W. Schleich and J. A. Wheeler, “Oscillations in photon distribution of squeezed states and interference in phase space,” Nature 326, 574–577 (1987).
[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]

W. Schleich and J. A. Wheeler, “Oscillations in photon distribution of squeezed states,” J. Opt. Soc. Am. B 4, 1715–1722 (1987).
[CrossRef]

1982 (1)

L. Mandel, “Squeezed states and sub-Poissonian photon statistics,” Phys. Rev. Lett. 49, 136–138 (1982).
[CrossRef]

1975 (1)

Y. Takahashi and H. Umezawa, “Collective phenomena,” Int. J. Mod. Phys. 2, 55–80 (1975).

1963 (1)

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

1927 (1)

H. Weyl, “Quantenmechanik und Gruppentheorie,” Z. Phys. 46, 1–46 (1927).
[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 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]

Anhut, T.

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

Ban, M.

M. Ban, “Photon statistics of conditional output states of lossless beam splitter,” J. Mod. Opt. 43, 1281–1303 (1996).
[CrossRef]

Banaszek, K.

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Quantifying the non-Gaussian character of a quantum state by quantum relative entropy,” Phys. Rev. A 78, 060303 (2008).
[CrossRef]

M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Measure of the non-Gaussian character of a quantum state,” Phys. Rev. A 76, 042327 (2007).
[CrossRef]

Barbieri, M.

M. Barbieri, N. Spagnolo, M. G. Genoni, F. Ferreyrol, R. Blandino, M. G. A. Paris, P. Grangier, and R. Tualle-Brouri, “Non-Gaussianity of quantum states: an experimental test on single-photon added coherent states,” Phys. Rev. A 82, 063833 (2010).
[CrossRef]

Bellini, M.

T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011).
[CrossRef]

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[CrossRef]

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J. Mod. Opt. (1)

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J. Phys. B At. Mol. Opt. Phys. (2)

X.-B. Wang, L. C. Kwek, Y. Liu, and C. H. Oh, “Non-classical effects of two-mode photon-added displaced squeezed states,” J. Phys. B At. Mol. Opt. Phys. 34, 1059–1078 (2001).
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Nat. Photon. (1)

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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).
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Z. Phys. (1)

H. Weyl, “Quantenmechanik und Gruppentheorie,” Z. Phys. 46, 1–46 (1927).
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Other (5)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 2004).

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).

J. R. Klauder and B.-S. Skagerstam, Coherent States (World Scientific, 1985).

C. W. Gardner and P. Zoller, Quantum Noise (Springer, 2000).

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, 1996).

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