Non-linear wave packet dynamics of coherent states of various symmetry groups
Optics Express, Vol. 5, Issue 10, pp. 220-229 (1999)
http://dx.doi.org/10.1364/OE.5.000220
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Abstract
We present a comparative study of the non-linear wave packet dynamics of two-mode coherent states of the Heisenberg-Weyl group, the SU(1,1) group and the SU(2) group under the action of a model anharmonic Hamiltonian. In each case, we find certain generic signatures of non-linear evolution such as quick onset of decoherence followed by Schrödinger cat formation and revival. We also report important differences in the evolution of coherent states belonging to different symmetry groups.
© Optical Society of America
1 Introduction
1. I. Sh. Averbukh and N. F. Perelman, “Fractional revival: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics,” Phys. Lett. A 139, 449 (1989). [CrossRef]
2. Z. D. Gaeta and C. R. Stroud Jr., “Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom,” Phys. Rev. A 42, 6308 (1990). [CrossRef] [PubMed]
3. X. Chen and J. A. Yeazell, “Phase-conjugate picture of a wave-packet interference design for arbitrary target states,” Phys. Rev. A 59, 3782 (1999). [CrossRef]
4. J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323 (1980). [CrossRef]
5. B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986). [CrossRef] [PubMed]
6. K. Tara, G. S. Agarwal, and S. Chaturvedi, “Production of Schrödinger macroscopic quantum-superposition states in a Kerr medium,” Phys. Rev. A 47, 5024 (1993). [CrossRef] [PubMed]
7. C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: an analytical approach,” Phys. Rev. A 54, 5299 (1996). [CrossRef] [PubMed]
8. R. Bluhm, V. A. Kostelecký, and B. Tudose, “Wave-packet revivals for quantum systems with nondegenerate energies,” Phys. Lett. A 222, 220 (1996). [CrossRef]
9. G. S. Agarwal and J. Banerji, “Fractional revivals in systems with two time scales,” Phys. Rev. A 57, 3880 (1998). [CrossRef]
10. J. Banerji and G. S. Agarwal, “Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states,” Phys. Rev. A 59, 4777 (1999). [CrossRef]
11. G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states,” J. Opt. Soc. Am. B 5, 1940 (1988). [CrossRef]
12. A. M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin1986). [CrossRef]
14. C. M. Caves and B. L. Shumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068 (1985). [CrossRef] [PubMed]
10. J. Banerji and G. S. Agarwal, “Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states,” Phys. Rev. A 59, 4777 (1999). [CrossRef]
15. F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972). [CrossRef]
16. K. Wódkiewicz and J. H. Eberly, “Coherent states, squeezed fluctuations, and the SU(2) and SU(1,1,) groups in quantum-optics applications,” J. Opt. Soc. Am B 2, 458 (1985). [CrossRef]
17. V. Bužek and T. Quang, “Generalized coherent state for bosonic realization of SU(2) Lie algebra,” J. Opt. Soc. Am B 6, 2447 (1989). [CrossRef]
18. G. S. Agarwal, R. R. Puri, and R. P. Singh, “Atomic Schrödinger cat states,” Phys. Rev. A 56, 2249 (1997). [CrossRef]
2 Coherent states
17. V. Bužek and T. Quang, “Generalized coherent state for bosonic realization of SU(2) Lie algebra,” J. Opt. Soc. Am B 6, 2447 (1989). [CrossRef]
3 Wave packet dynamics
9. G. S. Agarwal and J. Banerji, “Fractional revivals in systems with two time scales,” Phys. Rev. A 57, 3880 (1998). [CrossRef]
10. J. Banerji and G. S. Agarwal, “Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states,” Phys. Rev. A 59, 4777 (1999). [CrossRef]
3.1 H. O. Coherent States
3.2 SU(1,1) Coherent States
19. G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207 (1997). [CrossRef]
10. J. Banerji and G. S. Agarwal, “Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states,” Phys. Rev. A 59, 4777 (1999). [CrossRef]
3.3 SU(2) Coherent States
19. G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207 (1997). [CrossRef]
10. J. Banerji and G. S. Agarwal, “Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states,” Phys. Rev. A 59, 4777 (1999). [CrossRef]
4 Conclusion
References and links
1. | I. Sh. Averbukh and N. F. Perelman, “Fractional revival: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics,” Phys. Lett. A 139, 449 (1989). [CrossRef] |
2. | Z. D. Gaeta and C. R. Stroud Jr., “Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom,” Phys. Rev. A 42, 6308 (1990). [CrossRef] [PubMed] |
3. | X. Chen and J. A. Yeazell, “Phase-conjugate picture of a wave-packet interference design for arbitrary target states,” Phys. Rev. A 59, 3782 (1999). [CrossRef] |
4. | J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, “Periodic spontaneous collapse and revival in a simple quantum model,” Phys. Rev. Lett. 44, 1323 (1980). [CrossRef] |
5. | B. Yurke and D. Stoler, “Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion,” Phys. Rev. Lett. 57, 13 (1986). [CrossRef] [PubMed] |
6. | K. Tara, G. S. Agarwal, and S. Chaturvedi, “Production of Schrödinger macroscopic quantum-superposition states in a Kerr medium,” Phys. Rev. A 47, 5024 (1993). [CrossRef] [PubMed] |
7. | C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: an analytical approach,” Phys. Rev. A 54, 5299 (1996). [CrossRef] [PubMed] |
8. | R. Bluhm, V. A. Kostelecký, and B. Tudose, “Wave-packet revivals for quantum systems with nondegenerate energies,” Phys. Lett. A 222, 220 (1996). [CrossRef] |
9. | G. S. Agarwal and J. Banerji, “Fractional revivals in systems with two time scales,” Phys. Rev. A 57, 3880 (1998). [CrossRef] |
10. | J. Banerji and G. S. Agarwal, “Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states,” Phys. Rev. A 59, 4777 (1999). [CrossRef] |
11. | G. S. Agarwal, “Nonclassical statistics of fields in pair coherent states,” J. Opt. Soc. Am. B 5, 1940 (1988). [CrossRef] |
12. | A. M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin1986). [CrossRef] |
13. | Coherent states, edited by J. R. Klauder and B. S. Skagerstam, (World Scientific, Singapore, 1985). |
14. | C. M. Caves and B. L. Shumaker, “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states,” Phys. Rev. A 31, 3068 (1985). [CrossRef] [PubMed] |
15. | F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211 (1972). [CrossRef] |
16. | K. Wódkiewicz and J. H. Eberly, “Coherent states, squeezed fluctuations, and the SU(2) and SU(1,1,) groups in quantum-optics applications,” J. Opt. Soc. Am B 2, 458 (1985). [CrossRef] |
17. | V. Bužek and T. Quang, “Generalized coherent state for bosonic realization of SU(2) Lie algebra,” J. Opt. Soc. Am B 6, 2447 (1989). [CrossRef] |
18. | G. S. Agarwal, R. R. Puri, and R. P. Singh, “Atomic Schrödinger cat states,” Phys. Rev. A 56, 2249 (1997). [CrossRef] |
19. | G. S. Agarwal, R. R. Puri, and R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207 (1997). [CrossRef] |
20. | L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light” in Progress in Optics, edited by E. Wolf, (North Holland, Amsterdam), 39, 294 (1999). |
21. | J. H. Hannay and M. V. Berry, “Quantization of linear maps on a torus-Fresnel diffraction by a periodic grating,” Physica , 1D, 267 (1980). |
OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(190.0190) Nonlinear optics : Nonlinear optics
(270.0270) Quantum optics : Quantum optics
(270.1670) Quantum optics : Coherent optical effects
ToC Category:
Research Papers
History
Original Manuscript: September 21, 1999
Published: November 8, 1999
Citation
J. Banerji and Girish Saran Agarwal, "Non-linear wave packet dynamics of coherent states of various symmetry groups," Opt. Express 5, 220-229 (1999)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-5-10-220
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References
- I. Sh. Averbukh and N. F. Perelman, "Fractional revival: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A 139, 449 (1989). [CrossRef]
- Z. D. Gaeta and C. R. Stroud Jr., "Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom," Phys. Rev. A 42, 6308 (1990). [CrossRef] [PubMed]
- X. Chen and J. A. Yeazell, "Phase-conjugate picture of a wave-packet interference design for arbitrary target states," Phys. Rev. A 59, 3782 (1999). [CrossRef]
- J. H. Eberly, N. B. Narozhny, and J. J. Sanchez-Mondragon, "Periodic spontaneous collapse and revival in a simple quantum model," Phys. Rev. Lett. 44, 1323 (1980). [CrossRef]
- B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13 (1986). [CrossRef] [PubMed]
- K. Tara, G. S. Agarwal, and S. Chaturvedi, "Production of Schrodinger macroscopic quantum- superposition states in a Kerr medium," Phys. Rev. A 47, 5024 (1993). [CrossRef] [PubMed]
- C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, "Multilevel quantum beats: an analytical approach," Phys. Rev. A 54, 5299 (1996). [CrossRef] [PubMed]
- R. Bluhm, V. A. Kostelecky and B. Tudose, "Wave-packet revivals for quantum systems with nondegenerate energies," Phys. Lett. A 222, 220 (1996). [CrossRef]
- G. S. Agarwal and J. Banerji, "Fractional revivals in systems with two time scales," Phys. Rev. A 57, 3880 (1998). [CrossRef]
- J. Banerji and G. S. Agarwal, "Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states," Phys. Rev. A 59, 4777 (1999). [CrossRef]
- G. S. Agarwal, "Nonclassical statistics of fields in pair coherent states," J. Opt. Soc. Am. B 5, 1940 (1988). [CrossRef]
- A. M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin 1986). [CrossRef]
- Coherent states, edited by J. R. Klauder and B. S. Skagerstam, (World Scientific, Singapore, 1985).
- C. M. Caves and B. L. Shumaker, "New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states," Phys. Rev. A 31, 3068 (1985). [CrossRef] [PubMed]
- F. T. Arecchi, E. Courtens, R. Gilmore and H. Thomas, "Atomic coherent states in quantum optics," Phys. Rev. A 6, 2211 (1972). [CrossRef]
- K. Wódkiewicz and J. H. Eberly, "Coherent states, squeezed uctuations, and the SU(2) and SU(1,1,) groups in quantum-optics applications," J. Opt. Soc. Am B 2, 458 (1985). [CrossRef]
- V. Buzek and T. Quang, "Generalized coherent state for bosonic realization of SU(2) Lie algebra," J. Opt. Soc. Am B 6, 2447 (1989). [CrossRef]
- G. S. Agarwal, R. R. Puri and R. P. Singh, "Atomic Schrodinger cat states," Phys. Rev. A 56, 2249 (1997). [CrossRef]
- G. S. Agarwal, R. R. Puri and R. P. Singh, "Vortex states for the quantized radiation field," Phys. Rev. A 56, 4207 (1997). [CrossRef]
- L. Allen, M. J. Padgett and M. Babiker, "The orbital angular momentum of light" in Progress in Optics, edited by E. Wolf, (North Holland, Amsterdam), 39, 294 (1999).
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