OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 8 — Apr. 22, 2002
  • pp: 376–381

Formation of Schrödinger-cat states in the Morse potential: Wigner function picture

Péter Földi, Attila Czirják, Balázs Molnár, and Mihály G. Benedict  »View Author Affiliations


Optics Express, Vol. 10, Issue 8, pp. 376-381 (2002)
http://dx.doi.org/10.1364/OE.10.000376


View Full Text Article

Enhanced HTML    Acrobat PDF (718 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate the time evolution of Morse coherent states in the potential of the NO molecule. We present animated wave functions and Wigner functions of the system exhibiting spontaneous formation of Schrödinger-cat states at certain stages of the time evolution. These nonclassical states are coherent superpositions of two localized states corresponding to two different positions of the center of mass. We analyze the degree of nonclassicality as the function of the expectation value of the position in the initial state. Our numerical calculations are based on a novel, essentially algebraic treatment of the Morse potential.

© 2002 Optical Society of America

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(030.1640) Coherence and statistical optics : Coherence
(270.0270) Quantum optics : Quantum optics

ToC Category:
Research Papers

History
Original Manuscript: March 15, 2002
Revised Manuscript: April 17, 2002
Published: April 22, 2002

Citation
Peter Foldi, Attila Czirjak, Balazs Molnar, and Mihaly Benedict, "Formation of Schr�dinger-cat states in the Morse potential: Wigner function picture," Opt. Express 10, 376-381 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-8-376


Sort:  Journal  |  Reset  

References

  1. J. Parker and C. R. Stroud, Jr., �Coherence and decay of Rydberg Wave packets,� Phys. Rev. Lett. 56, 716-719 (1986). [CrossRef] [PubMed]
  2. D. L. Aronstein and C. R. Stroud, Jr., �Analytical investigation of revival phenomena in the finite square-well potential,� Phys. Rev. A 62, 022102-1�022102-9 (2000). [CrossRef]
  3. S. I. Vetchinkin and V. V. Eryomin, �The structure of wavepacket fractional revivals in a Morselike anharmonic system,� Chem. Phys. Lett. 222, 394-398 (1994). [CrossRef]
  4. K. P. Huber and G. Herzberg, Molecular spectra and molecular structure IV. Constants of diatomic molecules, (van Nostrand Reinhold, 1979).
  5. M. G. Benedict and B. Molnar, �Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics,� Phys. Rev. A 60 R1737-R1740 (1999). [CrossRef]
  6. B. Molnar, P. Foldi, M. G. Benedict and F. Bartha, �Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule,� quant-ph/0202069.
  7. J. Banerji and G. S. Agarwal, �Non-linear wave packet dynamics of coherent states of various symmetry groups,� Opt. Express 5, 220-229 (1999), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-10-220">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-5-10-220</a>. [CrossRef] [PubMed]
  8. J. Bertrand and M. Irac-Astaud, �The SU(1,1) coherent states related to the affine group wavelets,� Czech J. Phys. 51 (12), 1272-1278 (2001). [CrossRef]
  9. B. Molnar, M. G. Benedict and P. Foldi, �State evolution in the anharmonic Morse potential subjected to an external sinusoidal field,� Fortschr. Phys. 49, 1053-1057 (2001) [CrossRef]
  10. E. T. Jaynes and F. W. Cummings, �Comparison of quantum semiclassical radiation theories with application to the beam maser,� Proc. Inst. Elect. Eng. 51, 89-109 (1963).
  11. J. H. Eberly, N. B. Narozhny, J. J. Sanchez-Mondragon �Periodic spontaneous collapse and revival in a simple quantum model,� Phys. Rev. Lett 44, 1323-1327 (1980). [CrossRef]
  12. I. Sh. Averbukh and N. F. Perelman, �Fractional revivals: Universality in the long term evolution of quantum wave packets beyond the correspondence principle dynamics,� Phys. Lett. A 139, 449-453 (1989).
  13. C. Leichtle, I. Sh. Averbukh and W. P. Schleich, �Multilevel quantum beats: An analytical approach,� Phys. Rev. A. 54, 5299-5312 (1996). [CrossRef] [PubMed]
  14. P. Domokos, T. Kiss, J. Janszky, A. Zucchetti, Z. Kis and W. Vogel, �Collapse and revival in the vibronic dynamics of laser-driven diatomic molecules,� Chem. Phys. Lett. 322 3-4, 255-262 (2000). [CrossRef]
  15. Ch. Warmuth, A. Tortschano., F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz and H. F. Kau.mann, �Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,� J. Chem. Phys. 112, 5060-5069 (2000). [CrossRef]
  16. Y. S. Kim and M. E. Noz, Phase space picture of quantum mechanics, (World Scientific, 1991).
  17. J. Janszky, An. V. Vinogradov, T. Kobayashi and Z. Kis, �Vibrational Schroedinger-cat states,� Phys. Rev. A 50, 1777-1784 (1994 ), and see also references therein. [CrossRef] [PubMed]
  18. J. Eiselt and H. Risken, �Quasiprobability distributions for the Jaynes-Cummings model with cavity damping,� Phys. Rev. A 43, 346-360 (1991). [CrossRef] [PubMed]
  19. M. G. Benedict, A. Czirjak, �Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,� Phys. Rev. A 60, 4034-4044 (1999). [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.

Figures

Fig. 1. Fig. 2. Fig. 3.
 
Fig. 4.
 

Supplementary Material


» Media 1: MOV (2071 KB)     
» Media 2: MOV (2181 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited