## Squeezed number state and squeezed thermal state: decoherence analysis and nonclassical properties in the laser process |

JOSA B, Vol. 29, Issue 7, pp. 1835-1843 (2012)

http://dx.doi.org/10.1364/JOSAB.29.001835

Enhanced HTML Acrobat PDF (499 KB)

### Abstract

We investigate how the squeezed thermal state (STS) and squeezed number state (SNS) evolve undergoing decoherence in the laser process. Remarkably, the initial SNS, an example of a pure state, evolves into a mixed state, which turns out to be a Laguerre polynomial of combination of creation and annihilation operators within normal ordering; however, the STS, a mixed state, still keeps squeezed and thermal. At long times, these fields lose their nonclassical nature and decay to a highly classical thermal field. The normally ordered density operators of such states in the laser channel lead to deriving the analytical time-evolution expressions of the Wigner functions (WFs). Their nonclassicality is investigated in reference to the time-evolution WFs, which indicates that both of the WFs decay to the same thermal WF as a result of decoherence when the decay time

© 2012 Optical Society of America

**OCIS Codes**

(000.5490) General : Probability theory, stochastic processes, and statistics

(270.0270) Quantum optics : Quantum optics

(270.2500) Quantum optics : Fluctuations, relaxations, and noise

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: February 22, 2012

Revised Manuscript: April 23, 2012

Manuscript Accepted: April 26, 2012

Published: June 29, 2012

**Citation**

Xiang-guo Meng, Zhen Wang, Hong-yi Fan, and Ji-suo Wang, "Squeezed number state and squeezed thermal state: decoherence analysis and nonclassical properties in the laser process," J. Opt. Soc. Am. B **29**, 1835-1843 (2012)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-7-1835

Sort: Year | Journal | Reset

### References

- A. Vourdas and R. M. Weiner, “Photon-counting distribution in squeezed states,” Phys. Rev. A 36, 5866–5869 (1987). [CrossRef]
- V. V. Dodonov, O. V. Man’ko, V. I. Man’ko, and L. Rosa, “Thermal noise and oscillations of the photon distribution for squeezed and correlated light,” Phys. Lett. A 185, 231–237 (1994). [CrossRef]
- Z. H. Musslimani, S. L. Braunstein, A. Mann, and M. Revzen, “Destruction of photocount oscillations by thermal noise,” Phys. Rev. A 51, 4967–4973 (1995). [CrossRef]
- P. Marian and T. A. Marian, “Squeezed states with thermal noise. I. Photon-number statistics,” Phys. Rev. A 47, 4474–4486 (1993). [CrossRef]
- P. Marian and T. A. Marian, “Squeezed states with thermal noise. II. Damping and photon counting,” Phys. Rev. A 47, 4487–4495 (1993). [CrossRef]
- P. Marian, T. A. Marian, and H. Scutaru, “Quantifying nonclassicality of one-mode Gaussian states of the radiation field,” Phys. Rev. Lett. 88, 153601 (2002). [CrossRef]
- M. S. Kim and V. Bužek, “Schrödinger-cat states at finite temperature: influence of a finite-temperature heat bath on quantum interferences,” Phys. Rev. A 46, 4239–4251 (1992). [CrossRef]
- A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (2007). [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]
- T. Hiroshima, “Decoherence and entanglement in two-mode squeezed vacuum states,” Phys. Rev. A 63, 022305 (2001). [CrossRef]
- H. Jeong, J. Lee, and M. S. Kim, “Dynamics of nonlocality for a two-mode squeezed state in a thermal environment,” Phys. Rev. A 61, 052101 (2000). [CrossRef]
- J. S. Prauzner-Bechcicki, “Two-mode squeezed vacuum state coupled to the common thermal reservoir,” J. Phys. A 37, L173–L181 (2004). [CrossRef]
- C. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
- P. Marian, “Higher-order squeezing properties and correlation functions for squeezed number states,” Phys. Rev. A 44, 3325–3330 (1991). [CrossRef]
- P. Marian, “Higher-order squeezing and photon statistics for squeezed thermal states,” Phys. Rev. A 45, 2044–2051 (1992). [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, 2494–2503 (1989). [CrossRef]
- M. S. Kim and V. Bužek, “Photon statistics of superposition states in phase-sensitive reservoirs,”Phys. Rev. A 47, 610–619 (1993). [CrossRef]
- P. Marian and T. A. Marian, “Destruction of higher-order squeezing by thermal noise,” J. Phys. A 29, 6233–6245 (1996). [CrossRef]
- Z. Cheng, “Quantum effects of thermal radiation in a Kerr nonlinear blackbody,” J. Opt. Soc. Am. B 19, 1692–1705 (2002). [CrossRef]
- Gh.-S. Paraoanu and H. Scutaru, “Fidelity for multimode thermal squeezed states,” Phys. Rev. A 61, 022306 (2000). [CrossRef]
- 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]
- J. Anders, “Thermal state entanglement in harmonic lattices,” Phys. Rev. A 77, 062102 (2008). [CrossRef]
- X. B. Wang, C. H. Oh, and L. C. Kwek, “Bures fidelity of displaced squeezed thermal states,” Phys. Rev. A 58, 4186–4190(1998). [CrossRef]
- M. Aspachs, J. Calsamiglia, R. Munoz-Tapia, and E. Bagan, “Phase estimation for thermal Gaussian states,” Phys. Rev. A 79, 033834 (2009). [CrossRef]
- A. V. Chizhov, T. Gantsogt, and B. K. Murzakhmetovt, “Phase distributions of squeezed number states and squeezed thermal states,” Quantum Opt. 5, 85–93 (1993). [CrossRef]
- H. Y. Fan and L. Y. Hu, “Operator-sum representation of density operators as solution to master equations obtained via the entangled states approach,” Mod. Phys. Lett. B 22, 2435–2468(2008). [CrossRef]
- H. Y. Fan, Representation and Transformation Theory in Quantum Mechanics (Shanghai Scientific and Technical, 1997), in Chinese.
- M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 2004).
- R. Glauber, “Coherent and incoherent states of the radiation field,” Phys. Rev. 131, 2766–2788 (1963). [CrossRef]
- J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, 1985).
- T. Kiesel, W. Vogel, M. Bellini, and A. Zavatta, “Nonclassicality quasiprobability of single-photon-added thermal states,” Phys. Rev. A 83, 032116 (2011). [CrossRef]
- H. Y. Fan and G. Ren, “Evolution of number state to density operator of binomial distribution in the amplitude dissipative channel,” Chin. Phys. Lett. 27, 050302 (2010). [CrossRef]
- H. Y. Fan, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987). [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. Weyl, The Classical Groups (Princeton University, 1953).
- W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).
- C. L. Methta, “Diagonal coherent-state representation of quantum operators,” Phys. Rev. Lett. 18, 752–754 (1967). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.