OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 12 — Dec. 1, 2012
  • pp: 3412–3418

Nonclassical properties of Hermite polynomial’s coherent state

Gang Ren, Jian-ming Du, Hai-jun Yu, and Ye-jun Xu  »View Author Affiliations


JOSA B, Vol. 29, Issue 12, pp. 3412-3418 (2012)
http://dx.doi.org/10.1364/JOSAB.29.003412


View Full Text Article

Enhanced HTML    Acrobat PDF (534 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper, we introduce the Hermite polynomial’s coherent state (HPCS) |αH, which is defined as Hn(X)|α up to a normalization constant and where Hn(X) is the coordinate operator’s Hermite polynomial of order n and |α=exp((1/2)|α|2+αa)|0. This state may be produced by the superposition of some different photon added coherent states when n=2. The mathematical and physical properties of HPCS are also studied. It is shown that HPCS has remarkable nonclassical state features such as sub-Poissonian and squeezing properties.

© 2012 Optical Society of America

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

ToC Category:
Quantum Optics

History
Original Manuscript: September 6, 2012
Revised Manuscript: October 5, 2012
Manuscript Accepted: October 8, 2012
Published: November 28, 2012

Citation
Gang Ren, Jian-ming Du, Hai-jun Yu, and Ye-jun Xu, "Nonclassical properties of Hermite polynomial’s coherent state," J. Opt. Soc. Am. B 29, 3412-3418 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-12-3412


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer-Verlag, 2000).
  2. X.-X. Xu, L.-Y. Hu, and H.-Y. Fan, “Photon-added squeezed thermal states: statistical properties and its decoherence in a photon-loss channel,” Opt. Commun. 283, 1801–1809 (2010). [CrossRef]
  3. L.-Y. Hu, X.-X. Xu, Z.-S. Wang, and X.-F. Xu, “Photon-subtracted squeezed thermal state: nonclassicality and decoherence,” Phys. Rev. A 82, 043842 (2010). [CrossRef]
  4. Roy J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963). [CrossRef]
  5. E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Phys. Rev. Lett. 10, 277–279 (1963). [CrossRef]
  6. J. R. Klauder, “Continuous-representation theory. III. On functional quantization of classical systems,” J. Math. Phys. 5, 177–186 (1964). [CrossRef]
  7. C. C. Gerry, “Proposal for generating even and odd coherent states,” Opt. Commun. 91, 247–251 (1992). [CrossRef]
  8. R. Blandino, F. Ferreyrol, M. Barbieri, P. Grangier, and R. Tualle-Brouri, “Characterization of a π-phase shift quantum gate for coherent-state qubits,” New J. Phys. 14, 013017 (2012). [CrossRef]
  9. V. Parigi, A. Zavatta, M. S. 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]
  10. 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]
  11. 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]
  12. H. Nha and H. J. Carmichael, “Proposed test of quantum nonlocality for continuous variables,” Phys. Rev. Lett. 93, 020401 (2004). [CrossRef]
  13. S. D. Bartlett and B. C. Sanders, “Universal continuous-variable quantum computation: requirement of optical nonlinearity for photon counting,” Phys. Rev. A 65, 042304 (2002). [CrossRef]
  14. 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]
  15. 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]
  16. F. Dell’Anno, S. De Siena, L. Albano, and F. Illuminati, “Continuous-variable quantum teleportation with non-Gaussian resources,” Phys. Rev. A 76, 022301 (2007). [CrossRef]
  17. 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]
  18. M. S. Kim, “Recent developments in photon-level operations on travelling light fields,” J. Phys. B 41, 133001 (2008). [CrossRef]
  19. 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]
  20. 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]
  21. H.-C. Yuan, X.-X. Xu, and H.-Y. Fan, “Generalized photon-added coherent state and its quantum statistical properties,” Chin. Phys. B 19, 10425 (2010). [CrossRef]
  22. 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]
  23. J. R. Klauder and B. S. Skargerstam, Coherent States (World Scientific, Singapore, 1985).
  24. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, 1984), p. 12.
  25. V. V. Dodonov, Y. A. Korennoy, V. I. Manko, and Y. A. Moukhin, “Nonclassical properties of states generated by the excitations of even/odd coherent states of light,” J. Opt. B 8413–427(1996). [CrossRef]
  26. V. V. Dodonov, V. I. Manko, and P. G. Polynkin, “Geometrical squeezed states of a charged-particle in a time-dependent magnetic-field,” Phys. Lett. A 188, 232–238 (1994). [CrossRef]
  27. V. V. Dodonov and V. I. Manko, Invariants and Evolution of Nonstationary Quantum Systems, M. A. Markov, ed. (Nova Science,1989).
  28. C. K. Hong and L. Mandel, “Generation of higher-order squeezing of quantum electromagnetic field,” Phys. Rev. A 32, 974–982 (1985). [CrossRef]
  29. 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]
  30. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205–207 (1979). [CrossRef]
  31. H. Y. Fan and H. R. Zaidi, “Application of IWOP technique to the generalized Weyl correspondence,” Phys. Lett. A 124, 303–307 (1987). [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