OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 3 — Mar. 1, 2012
  • pp: 397–406

Photon-subtracted squeezed coherent state: nonclassicality and decoherence in thermal environment

Zhen Wang, Xiang-guo Meng, and Hong-yi Fan  »View Author Affiliations

JOSA B, Vol. 29, Issue 3, pp. 397-406 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (798 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.6570) Quantum optics : Squeezed states

ToC Category:
Quantum Optics

Original Manuscript: September 30, 2011
Revised Manuscript: November 14, 2011
Manuscript Accepted: November 14, 2011
Published: February 22, 2012

Zhen Wang, Xiang-guo Meng, and Hong-yi Fan, "Photon-subtracted squeezed coherent state: nonclassicality and decoherence in thermal environment," J. Opt. Soc. Am. B 29, 397-406 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. L. Braunstein and P. Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005). [CrossRef]
  2. 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]
  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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004). [CrossRef]
  13. 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]
  14. 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]
  15. 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]
  16. H. Y. Fan, “Squeezed states: Operators for two types of one- and two-mode squeezing transformations,” Phys. Rev. A 41, 1526–1532 (1990).
  17. 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]
  18. V. V. Dodonov, “Nonclassical states in quantum optics: a squeezed review of the first 75 years,” J. Opt. B 4, R1–R33 (2002). [CrossRef]
  19. 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]
  20. 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]
  21. A. Biswas and G. S. Agarwal, “Nonclassicality and decoherence of photon-subtracted squeezed states,” Phys. Rev. A 75, 032104 (2007). [CrossRef]
  22. 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]
  23. 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]
  24. D. Stoler, “ Equivalence classes of minimum uncertainty packets,” Phys. Rev. D 1, 3217–3219 (1970). [CrossRef]
  25. H. P. Yuen and J. H. Shapiro, “Generation and detection of two-photon coherent states in degenerate four-wave mixing,” Opt. Lett. 4, 334–336 (1979). [CrossRef]
  26. B. Yurke, “Squeezed-coherent-state generation via four-wave mixers and detection via homodyne detectors,” Phys. Rev. A 32, 300–310 (1985). [CrossRef]
  27. 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]
  28. M. Matsuoka and T. Hirano, “Quantum key distribution with a single photon from a squeezed coherent state,” Phys. Rev. A 67, 042307 (2003). [CrossRef]
  29. A. Luis, “Squeezed coherent states as feasible approximations to phase-optimized states,” Phys. Lett. A 354, 71–78 (2006). [CrossRef]
  30. H. Y. Fan and M. Xiao, “A spacial type of squeezed coherent state,” Phys. Lett. A 220, 81–86 (1996). [CrossRef]
  31. 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]
  32. 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]
  33. 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]
  34. A. Kenfack and K. Zyczkowski, “Negativity of the Wigner function as an indicator of nonclassicality,” J. Opt. B 6, 396–404 (2004). [CrossRef]
  35. 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]
  36. W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, 2001).
  37. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
  38. H. Paul, “Photon antibunching,” Rev. Mod. Phys. 54, 1061–1102 (1982). [CrossRef]
  39. R. Short and L. Mandel, “Observation of sub-Poissonian photon statistics,” Phys. Rev. Lett. 51, 384–387 (1983). [CrossRef]
  40. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979). [CrossRef]
  41. 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]
  42. R. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, 2001).
  43. 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]
  44. 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]
  45. H. Y. Fan and V. J. Linde, “Similarity transformations in one- and two-mode Fock space,” J. Phys. A 24, 2529–2538(1991).
  46. 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]
  47. 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]

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.

CrossCheck Deposited