Abstract

Using the thermal field dynamics theory to convert the thermal state into a "pure" state in doubled Fock space, we find that the average value of <i>e<sup>fa†a</sup></i> under squeezed thermal state (STS) is just the generating function of Legendre polynomials. Based on this remarkable result, the normalization and photon-number distributions of m-photon added (or subtracted) STSs are conviently obtained as the Legendre polynomials. This new concise method can be expanded to the entangled case.

© 2012 Chinese Optics Letters

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  3. J. Zhang and A. Chen, Chin. Opt. Lett. 9, 042701 (2011).
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  6. A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).
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  10. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).
  11. A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).
  12. P. Marek, H. Jeong, and M. Kim, Phys. Rev. A 78, 063811 (2008).
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  18. A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).
  19. Y. Yang and F. Li, J. Opt. Soc. Am. B 26, 830 (2009).
  20. A. Biswas and G. Agarwal, Phys. Rev. A 75, 032104 (2007).
  21. S. Lee and H. Nha, Phys. Rev. A 82, 053812 (2010).
  22. H. Fan and N. Jiang, Chin. Phys. Lett. 27, 044206 (2010).
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  26. L. Hu and H. Fan, Chin. Phys. Lett. 26, 090307 (2009).
  27. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, Berlin, 2001).
  28. G. Arfken and H. Weber, Mathematical Methods for Physicists (Elsevier Academic Press, 2005).
  29. H. Fan, Representation and Transformation Theory in Quantum Mechanics-Progress of Dirac's symbolic method (Shanghai Scientific and Technical Press, Shanghai, 1997).
  30. L. Hu and Z. Zhang, [quant-ph] arXiv: 1110.6587.
  31. L. Hu and H. Fan, Mod. Phys. Lett. A 24, 2263 (2009).
  32. L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

2011 (1)

2010 (5)

F. Han and Y. Xia, Chin. Opt. Lett. 8, 524 (2010).

L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

S. Zhang and P. van Loock, Phys. Rev. A 82, 06216 (2010).

S. Lee and H. Nha, Phys. Rev. A 82, 053812 (2010).

H. Fan and N. Jiang, Chin. Phys. Lett. 27, 044206 (2010).

2009 (4)

L. Hu and H. Fan, Chin. Phys. Lett. 26, 090307 (2009).

L. Hu and H. Fan, Mod. Phys. Lett. A 24, 2263 (2009).

L. Hu and H. Fan, Chin. Phys. B 18, 4657 (2009).

Y. Yang and F. Li, J. Opt. Soc. Am. B 26, 830 (2009).

2008 (2)

L. Hu and H. Fan, J. Opt. Soc. Am. B 25, 1955 (2008).

P. Marek, H. Jeong, and M. Kim, Phys. Rev. A 78, 063811 (2008).

2007 (4)

A. Biswas and G. Agarwal, Phys. Rev. A 75, 032104 (2007).

A. Zavatta, V. Parigi, and M. Bellini, Phys. Rev. A 75, 052106 (2007).

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).

2006 (2)

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).

2005 (2)

S. Olivares and M. Paris, J. Opt. B: Quantum Semiclassical Opt. 7, S392 (2005).

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 72, 023820 (2005).

2004 (1)

A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).

2000 (1)

T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000).

1996 (1)

Memorial Issue for H. Umezawa, Int. J. Mod. Phys. B 10, 1695 (1996).

1992 (1)

Z. Zhang and H. Fan, Phys. Lett. A 165, 14 (1992).

1991 (1)

G. Agarwal and K. Tara, Phys. Rev. A 43, 492 (1991).

1975 (1)

Y. Takahashi and H. Umezawa, Collective Phenomena 2, 55 (1975).

Agarwal, G.

A. Biswas and G. Agarwal, Phys. Rev. A 75, 032104 (2007).

G. Agarwal and K. Tara, Phys. Rev. A 43, 492 (1991).

Bellini, M.

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).

A. Zavatta, V. Parigi, and M. Bellini, Phys. Rev. A 75, 052106 (2007).

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 72, 023820 (2005).

A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).

Biswas, A.

A. Biswas and G. Agarwal, Phys. Rev. A 75, 032104 (2007).

Chefles, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).

Chen, A.

Dantan, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).

Fan, H.

H. Fan and N. Jiang, Chin. Phys. Lett. 27, 044206 (2010).

L. Hu and H. Fan, Mod. Phys. Lett. A 24, 2263 (2009).

L. Hu and H. Fan, Chin. Phys. B 18, 4657 (2009).

L. Hu and H. Fan, Chin. Phys. Lett. 26, 090307 (2009).

L. Hu and H. Fan, J. Opt. Soc. Am. B 25, 1955 (2008).

Z. Zhang and H. Fan, Phys. Lett. A 165, 14 (1992).

Grangier, Ph.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).

Han, F.

Hu, L.

L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

L. Hu and H. Fan, Mod. Phys. Lett. A 24, 2263 (2009).

L. Hu and H. Fan, Chin. Phys. B 18, 4657 (2009).

L. Hu and H. Fan, Chin. Phys. Lett. 26, 090307 (2009).

L. Hu and H. Fan, J. Opt. Soc. Am. B 25, 1955 (2008).

Jeong, H.

P. Marek, H. Jeong, and M. Kim, Phys. Rev. A 78, 063811 (2008).

Jiang, N.

H. Fan and N. Jiang, Chin. Phys. Lett. 27, 044206 (2010).

Kim, M.

P. Marek, H. Jeong, and M. Kim, Phys. Rev. A 78, 063811 (2008).

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).

Kitagawa, A.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).

Kurizki, G.

T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000).

Laurat, J.

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).

Lee, S.

S. Lee and H. Nha, Phys. Rev. A 82, 053812 (2010).

Li, F.

Loock, P. van

S. Zhang and P. van Loock, Phys. Rev. A 82, 06216 (2010).

Marek, P.

P. Marek, H. Jeong, and M. Kim, Phys. Rev. A 78, 063811 (2008).

Nha, H.

S. Lee and H. Nha, Phys. Rev. A 82, 053812 (2010).

Olivares, S.

S. Olivares and M. Paris, J. Opt. B: Quantum Semiclassical Opt. 7, S392 (2005).

Opatrny, T.

T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000).

Ourjoumtsev, A.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).

Parigi, V.

A. Zavatta, V. Parigi, and M. Bellini, Phys. Rev. A 75, 052106 (2007).

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).

Paris, M.

S. Olivares and M. Paris, J. Opt. B: Quantum Semiclassical Opt. 7, S392 (2005).

Sasaki, M.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).

Takahashi, Y.

Y. Takahashi and H. Umezawa, Collective Phenomena 2, 55 (1975).

Takeoka, M.

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).

Tara, K.

G. Agarwal and K. Tara, Phys. Rev. A 43, 492 (1991).

Tualle-Brouri, R.

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).

Umezawa, H.

Y. Takahashi and H. Umezawa, Collective Phenomena 2, 55 (1975).

Umezawa, Memorial Issue for H.

Memorial Issue for H. Umezawa, Int. J. Mod. Phys. B 10, 1695 (1996).

Viciani, S.

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 72, 023820 (2005).

A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).

Wang, Z.

L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

Welsch, D.-G.

T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000).

Xia, Y.

Xu, X.

L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

Yang, Y.

Zavatta, A.

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).

A. Zavatta, V. Parigi, and M. Bellini, Phys. Rev. A 75, 052106 (2007).

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 72, 023820 (2005).

A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).

Zhang, J.

Zhang, S.

S. Zhang and P. van Loock, Phys. Rev. A 82, 06216 (2010).

Zhang, Z.

Z. Zhang and H. Fan, Phys. Lett. A 165, 14 (1992).

Chin. Opt. Lett. (2)

Chin. Phys. B (1)

L. Hu and H. Fan, Chin. Phys. B 18, 4657 (2009).

Chin. Phys. Lett. (2)

L. Hu and H. Fan, Chin. Phys. Lett. 26, 090307 (2009).

H. Fan and N. Jiang, Chin. Phys. Lett. 27, 044206 (2010).

Collective Phenomena (1)

Y. Takahashi and H. Umezawa, Collective Phenomena 2, 55 (1975).

Int. J. Mod. Phys. B (1)

Memorial Issue for H. Umezawa, Int. J. Mod. Phys. B 10, 1695 (1996).

J. Opt. B: Quantum Semiclassical Opt. (1)

S. Olivares and M. Paris, J. Opt. B: Quantum Semiclassical Opt. 7, S392 (2005).

J. Opt. Soc. Am. B (2)

Mod. Phys. Lett. A (1)

L. Hu and H. Fan, Mod. Phys. Lett. A 24, 2263 (2009).

Phys. Lett. A (1)

Z. Zhang and H. Fan, Phys. Lett. A 165, 14 (1992).

Phys. Rev. A (10)

G. Agarwal and K. Tara, Phys. Rev. A 43, 492 (1991).

A. Zavatta, V. Parigi, and M. Bellini, Phys. Rev. A 75, 052106 (2007).

A. Zavatta, S. Viciani, and M. Bellini, Phys. Rev. A 72, 023820 (2005).

P. Marek, H. Jeong, and M. Kim, Phys. Rev. A 78, 063811 (2008).

S. Zhang and P. van Loock, Phys. Rev. A 82, 06216 (2010).

A. Biswas and G. Agarwal, Phys. Rev. A 75, 032104 (2007).

S. Lee and H. Nha, Phys. Rev. A 82, 053812 (2010).

L. Hu, X. Xu, Z. Wang, and X. Xu, Phys. Rev. A 82, 043842 (2010).

T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000).

A. Kitagawa, M. Takeoka, M. Sasaki, and A. Chefles, Phys. Rev. A 73, 042310 (2006).

Phys. Rev. Lett. (1)

A. Ourjoumtsev, A. Dantan, R. Tualle-Brouri, and Ph. Grangier, Phys. Rev. Lett. 98, 030502 (2007).

Science (3)

A. Zavatta, S. Viciani, and M. Bellini, Science 306, 660 (2004).

V. Parigi, A. Zavatta, M. Kim, and M. Bellini, Science 317, 1890 (2007).

A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and Ph. Grangier, Science 312, 83 (2006).

Other (6)

H. Umezawa, Advanced Field Theory-Micro; Macro; and Thermal Physics (AIP, 1993).

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

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

G. Arfken and H. Weber, Mathematical Methods for Physicists (Elsevier Academic Press, 2005).

H. Fan, Representation and Transformation Theory in Quantum Mechanics-Progress of Dirac's symbolic method (Shanghai Scientific and Technical Press, Shanghai, 1997).

L. Hu and Z. Zhang, [quant-ph] arXiv: 1110.6587.

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