Abstract

We introduce a new (to our best knowledge) type of squeezing-enhanced thermal states (SETS) that is generated by operating a new two-parameter generalized squeezing operator on a thermal (chaotic) field. By using the operator’s Weyl-ordering invariance under the similarity transformation and the Weyl correspondence scheme, we derive the normally ordered form of the density operator of SETS. Based on it, we study the resulting squeezing effects of the SETS and investigate its statistical properties by the second-order correlation function, photon-number distribution, and the Wigner function. Compared with the usual squeezed thermal state, SETS exhibits stronger squeezing and some new statistical properties. We find that the effect of the new type of squeezing operator is rotated squeezing.

© 2011 Optical Society of America

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  35. H. Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics (IV)—integrations within Weyl ordered product of operators and their applications,” Ann. Phys. 323, 500–526 (2008).
    [CrossRef]
  36. H. Y. Fan and Y. Fan, “Weyl ordering for entangled state representation,” Int. J. Mod. Phys. A 17, 701–708 (2002).
    [CrossRef]
  37. R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
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  44. J. Janszky and Y. Yushin, “Many-photon processes with the participation of squeezed light,” Phys. Rev. A 36, 1288–1292 (1987).
    [CrossRef]
  45. H. Y. Fan, L. Y. Hu, and X. X. Xu, “Legendre polynomials as the normalization of photon-subtracted squeezed states,” Mod. Phys. Lett. A 24, 1597–1603 (2009).
    [CrossRef]
  46. 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).
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2011 (1)

2010 (2)

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[CrossRef]

S. Wang, X. Y. Zhang, and H. Q. Li, “Radiation field eigenstates and its unitary equivalence to coordinate eigenstates,” Opt. Commun. 283, 2716–2718 (2010).
[CrossRef]

2009 (3)

M. Aspachs, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009).
[CrossRef]

H. Y. Fan, L. Y. Hu, and X. X. Xu, “Legendre polynomials as the normalization of photon-subtracted squeezed states,” Mod. Phys. Lett. A 24, 1597–1603 (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]

2008 (4)

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]

G. Adesso and G. Chiribella, “Quantum benchmark for teleportation and storage of squeezed states,” Phys. Rev. Lett. 100, 170503 (2008).
[CrossRef]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (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 applications,” Ann. Phys. 323, 500–526 (2008).
[CrossRef]

2007 (1)

P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
[CrossRef]

2006 (1)

H. 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 (2)

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

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

2002 (3)

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

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[CrossRef]

H. Y. Fan and Y. Fan, “Weyl ordering for entangled state representation,” Int. J. Mod. Phys. A 17, 701–708 (2002).
[CrossRef]

2000 (1)

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[CrossRef]

1998 (1)

Z. H. Musslimani and Y. Ben-Ayreh, “Quantum phase distribution of thermal phase-squeezed states,” Phys. Rev. A 57, 1451–1453 (1998).
[CrossRef]

1993 (1)

P. Marian and T. A. Marian, “Squeezed states with thermal noise. I. photon-number statistics,” Phys. Rev. A 47, 4474–4486 (1993).
[CrossRef]

1992 (1)

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992).
[CrossRef]

1991 (1)

H. Ezawa, A. Mann, K. Nakamura, and M. Revzen, “Characterization of thermal coherent and thermal squeezed states,” Ann. Phys. 209, 216–230 (1991).
[CrossRef]

1989 (1)

M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2053 (1989).
[CrossRef]

1988 (2)

H. Fearn and M. J. Collett, “Representations of squeezed states with thermal noise,” J. Mod. Opt. 35, 553–564 (1988).
[CrossRef]

A. Ekert and K. Rzażewski, “Second harmonic generation and statistical properties of light,” Opt. Commun. 65, 225–228(1988).
[CrossRef]

1987 (2)

J. Janszky and Y. Yushin, “Many-photon processes with the participation of squeezed light,” Phys. Rev. A 36, 1288–1292 (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]

1986 (2)

B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13–16 (1986).
[CrossRef]

G. J. Milburn, “Quantum and classical Liouville dynamics of the anharmonic oscillator,” Phys. Rev. A 33, 674–685 (1986).
[CrossRef]

1985 (1)

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

1976 (1)

H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226–2243 (1976).
[CrossRef]

1970 (1)

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

1963 (2)

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

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

1932 (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
[CrossRef]

Adesso, G.

G. Adesso and G. Chiribella, “Quantum benchmark for teleportation and storage of squeezed states,” Phys. Rev. Lett. 100, 170503 (2008).
[CrossRef]

Aoki, T.

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

Aspachs, M.

M. Aspachs, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009).
[CrossRef]

Bagan, E.

M. Aspachs, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009).
[CrossRef]

Ban, M.

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

Ben-Ayreh, Y.

Z. H. Musslimani and Y. Ben-Ayreh, “Quantum phase distribution of thermal phase-squeezed states,” Phys. Rev. A 57, 1451–1453 (1998).
[CrossRef]

Blasiak, P.

P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
[CrossRef]

Braunstein, S. L.

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

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[CrossRef]

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic, 2003).

Buzek, V.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Calsamiglia, J.

M. Aspachs, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009).
[CrossRef]

Chelkowski, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Chiribella, G.

G. Adesso and G. Chiribella, “Quantum benchmark for teleportation and storage of squeezed states,” Phys. Rev. Lett. 100, 170503 (2008).
[CrossRef]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Collett, M. J.

H. Fearn and M. J. Collett, “Representations of squeezed states with thermal noise,” J. Mod. Opt. 35, 553–564 (1988).
[CrossRef]

Danzmann, K.

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[CrossRef]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

de Oliveira, F. A. M.

M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2053 (1989).
[CrossRef]

Dodonov, V. V.

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

Duchamp, G. H. E.

P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
[CrossRef]

Ekert, A.

A. Ekert and K. Rzażewski, “Second harmonic generation and statistical properties of light,” Opt. Commun. 65, 225–228(1988).
[CrossRef]

Ezawa, H.

H. Ezawa, A. Mann, K. Nakamura, and M. Revzen, “Characterization of thermal coherent and thermal squeezed states,” Ann. Phys. 209, 216–230 (1991).
[CrossRef]

Fan, H. 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]

H. Y. Fan, L. Y. Hu, and X. X. Xu, “Legendre polynomials as the normalization of photon-subtracted squeezed states,” Mod. Phys. Lett. A 24, 1597–1603 (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]

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

H. 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 Y. Fan, “Weyl ordering for entangled state representation,” Int. J. Mod. Phys. A 17, 701–708 (2002).
[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, Y.

H. Y. Fan and Y. Fan, “Weyl ordering for entangled state representation,” Int. J. Mod. Phys. A 17, 701–708 (2002).
[CrossRef]

Fearn, H.

H. Fearn and M. J. Collett, “Representations of squeezed states with thermal noise,” J. Mod. Opt. 35, 553–564 (1988).
[CrossRef]

Franzen, A.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Furusawa, A.

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

Gerry, C. C.

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004).

Glauber, R. J.

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

R. J. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963).
[CrossRef]

Gobler, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Hage, B.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Hiraoka, T.

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

Hong, C. K.

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

Horzela, A.

P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
[CrossRef]

Hu, L. Y.

Janszky, J.

J. Janszky and Y. Yushin, “Many-photon processes with the participation of squeezed light,” Phys. Rev. A 36, 1288–1292 (1987).
[CrossRef]

Kim, J.

Kim, M. S.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[CrossRef]

M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2053 (1989).
[CrossRef]

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
[CrossRef]

Knight, P. L.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[CrossRef]

M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2053 (1989).
[CrossRef]

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004).

Koike, S.

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

Lambropoulos, P.

P. Lambropoulos and D. Petrosyan, Fundamentals of Quantum Optics and Quantum Information (Springer-Verlag, 2007).

Lastzka, N.

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[CrossRef]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

Lee, J.

Leonhardt, U.

U. Leonhardt, “Quantum theory of light” in Measuring the Quantum State of Light (Cambridge University, 1997), Chap. 2.

Li, H. Q.

S. Wang, X. Y. Zhang, and H. Q. Li, “Radiation field eigenstates and its unitary equivalence to coordinate eigenstates,” Opt. Commun. 283, 2716–2718 (2010).
[CrossRef]

Louisell, W. H.

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

Mandel, L.

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Mann, A.

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P. Marian and T. A. Marian, “Squeezed states with thermal noise. I. photon-number statistics,” Phys. Rev. A 47, 4474–4486 (1993).
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M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
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M. Aspachs, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009).
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Z. H. Musslimani and Y. Ben-Ayreh, “Quantum phase distribution of thermal phase-squeezed states,” Phys. Rev. A 57, 1451–1453 (1998).
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H. Ezawa, A. Mann, K. Nakamura, and M. Revzen, “Characterization of thermal coherent and thermal squeezed states,” Ann. Phys. 209, 216–230 (1991).
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P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
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R. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, 2001).

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H. Ezawa, A. Mann, K. Nakamura, and M. Revzen, “Characterization of thermal coherent and thermal squeezed states,” Ann. Phys. 209, 216–230 (1991).
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W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, 2001).

Schnabel, R.

M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
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H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
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M. O. Scully and M. S. Zubairy, “Squeezing via nonlinear optical processes,” in Quantum Optics (Cambridge University, 1997), Chap. 16.

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P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
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M. S. Kim, W. Son, V. Buzek, and P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
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B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13–16 (1986).
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N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
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N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
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M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
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H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
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S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
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N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
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N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
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B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13–16 (1986).
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J. Janszky and Y. Yushin, “Many-photon processes with the participation of squeezed light,” Phys. Rev. A 36, 1288–1292 (1987).
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H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307(1987).
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M. O. Scully and M. S. Zubairy, “Squeezing via nonlinear optical processes,” in Quantum Optics (Cambridge University, 1997), Chap. 16.

Am. J. Phys. (1)

P. Blasiak, A. Horzela, K. A. Penson, A. I. Solomon, and G. H. E. Duchamp, “Combinatorics and Boson normal ordering: a gentle introduction,” Am. J. Phys. 75, 639–646 (2007).
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Ann. Phys. (3)

H. Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics and derivation of entangled state representations,” Ann. Phys. 321, 480–494 (2006).
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H. Y. Fan, “Newton–Leibniz integration for ket–bra operators in quantum mechanics (IV)—integrations within Weyl ordered product of operators and their applications,” Ann. Phys. 323, 500–526 (2008).
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H. Ezawa, A. Mann, K. Nakamura, and M. Revzen, “Characterization of thermal coherent and thermal squeezed states,” Ann. Phys. 209, 216–230 (1991).
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J. Opt. Soc. Am. B (3)

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H. Y. Fan, L. Y. Hu, and X. X. Xu, “Legendre polynomials as the normalization of photon-subtracted squeezed states,” Mod. Phys. Lett. A 24, 1597–1603 (2009).
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Opt. Commun. (2)

A. Ekert and K. Rzażewski, “Second harmonic generation and statistical properties of light,” Opt. Commun. 65, 225–228(1988).
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S. Wang, X. Y. Zhang, and H. Q. Li, “Radiation field eigenstates and its unitary equivalence to coordinate eigenstates,” Opt. Commun. 283, 2716–2718 (2010).
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Phys. Lett. A (1)

H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307(1987).
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Phys. Rev. (3)

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Phys. Rev. A (13)

J. Janszky and Y. Yushin, “Many-photon processes with the participation of squeezed light,” Phys. Rev. A 36, 1288–1292 (1987).
[CrossRef]

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

G. J. Milburn, “Quantum and classical Liouville dynamics of the anharmonic oscillator,” Phys. Rev. A 33, 674–685 (1986).
[CrossRef]

M. Aspachs, J. Calsamiglia, R. Muñoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009).
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S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61, 042302 (2000).
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M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, and R. Schnabel, “Observation of squeezed states with strong photon-number oscillations,” Phys. Rev. A 81, 013814 (2010).
[CrossRef]

H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226–2243 (1976).
[CrossRef]

M. S. Kim, F. A. M. de Oliveira, and P. L. Knight, “Properties of squeezed number states and squeezed thermal states,” Phys. Rev. A 40, 2494–2053 (1989).
[CrossRef]

P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992).
[CrossRef]

P. Marian and T. A. Marian, “Squeezed states with thermal noise. I. photon-number statistics,” Phys. Rev. A 47, 4474–4486 (1993).
[CrossRef]

Z. H. Musslimani and Y. Ben-Ayreh, “Quantum phase distribution of thermal phase-squeezed states,” Phys. Rev. A 57, 1451–1453 (1998).
[CrossRef]

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, “Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).
[CrossRef]

N. Takei, T. Aoki, S. Koike, K. I. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304 (2005).
[CrossRef]

Phys. Rev. D (1)

D. Stoler, “Equivalence classes of minimum uncertainty packets,” Phys. Rev. D 1, 3217–3219 (1970).
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Phys. Rev. Lett. (3)

G. Adesso and G. Chiribella, “Quantum benchmark for teleportation and storage of squeezed states,” Phys. Rev. Lett. 100, 170503 (2008).
[CrossRef]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Gobler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10 dB quantum-noise reduction,” Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef]

B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13–16 (1986).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (12)

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

F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, 1994).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004).

S. L. Braunstein and A. K. Pati, Quantum Information with Continuous Variables (Kluwer Academic, 2003).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

H. Weyl, The Classical Groups (Princeton University, 1953).

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

U. Leonhardt, “Quantum theory of light” in Measuring the Quantum State of Light (Cambridge University, 1997), Chap. 2.

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

M. O. Scully and M. S. Zubairy, “Squeezing via nonlinear optical processes,” in Quantum Optics (Cambridge University, 1997), Chap. 16.

P. Lambropoulos and D. Petrosyan, Fundamentals of Quantum Optics and Quantum Information (Springer-Verlag, 2007).

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