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

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  1. J. Parker and C. R. Stroud, “Coherence and decay of Rydberg Wave packets,” Phys. Rev. Lett. 56, 716–719 (1986).
    [Crossref] [PubMed]
  2. D. L. Aronstein and C. R. Stroud, “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. Molnár, “Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics,” Phys. Rev. A 60R1737–R1740 (1999).B. Molnár, M. G. Benedict, and J. Bertrand, “Coherent states and the role of the affine group in the quantum mechanics of the Morse potential” J. Phys A:Math. Gen. 34, 3139–3151 (2001).
    [Crossref]
  6. B. Molnár, P. Földi, 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), http: //www. opticsexpress.org/abstract.cfm?URI=OPEX-5-10-220.
    [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. Molnár, M. G. Benedict, and P. Földi, “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, and 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. A139, 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. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “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 Schrödinger-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 and A. Czirják, “Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,” Phys. Rev. A 60, 4034–4044 (1999).
    [Crossref]

2001 (2)

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]

B. Molnár, M. G. Benedict, and P. Földi, “State evolution in the anharmonic Morse potential subjected to an external sinusoidal field,” Fortschr. Phys. 49, 1053–1057 (2001).
[Crossref]

2000 (3)

D. L. Aronstein and C. R. Stroud, “Analytical investigation of revival phenomena in the finite square-well potential,” Phys. Rev. A 62, 022102-1–022102-9 (2000).
[Crossref]

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]

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

1999 (3)

M. G. Benedict and A. Czirják, “Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,” Phys. Rev. A 60, 4034–4044 (1999).
[Crossref]

M. G. Benedict and B. Molnár, “Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics,” Phys. Rev. A 60R1737–R1740 (1999).B. Molnár, M. G. Benedict, and J. Bertrand, “Coherent states and the role of the affine group in the quantum mechanics of the Morse potential” J. Phys A:Math. Gen. 34, 3139–3151 (2001).
[Crossref]

J. Banerji and G. S. Agarwal, “Non-linear wave packet dynamics of coherent states of various symmetry groups,” Opt. Express 5, 220–229 (1999), http: //www. opticsexpress.org/abstract.cfm?URI=OPEX-5-10-220.
[Crossref] [PubMed]

1996 (1)

C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: An analytical approach,” Phys. Rev. A. 54, 5299–5312 (1996).
[Crossref] [PubMed]

1994 (2)

J. Janszky, An. V. Vinogradov, T. Kobayashi, and Z. Kis, “Vibrational Schrödinger-cat states,” Phys. Rev. A 50, 1777–1784(1994), and see also references therein.
[Crossref] [PubMed]

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]

1991 (1)

J. Eiselt and H. Risken, “Quasiprobability distributions for the Jaynes-Cummings model with cavity damping,” Phys. Rev. A 43, 346–360 (1991).
[Crossref] [PubMed]

1989 (1)

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. A139, 449–453 (1989).

1986 (1)

J. Parker and C. R. Stroud, “Coherence and decay of Rydberg Wave packets,” Phys. Rev. Lett. 56, 716–719 (1986).
[Crossref] [PubMed]

1980 (1)

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, 1323–1327 (1980).
[Crossref]

1963 (1)

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).

Agarwal, G. S.

Aronstein, D. L.

D. L. Aronstein and C. R. Stroud, “Analytical investigation of revival phenomena in the finite square-well potential,” Phys. Rev. A 62, 022102-1–022102-9 (2000).
[Crossref]

Averbukh, I. Sh.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: An analytical approach,” Phys. Rev. A. 54, 5299–5312 (1996).
[Crossref] [PubMed]

Averbukh, I.Sh.

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. A139, 449–453 (1989).

Banerji, J.

Bartha, F.

B. Molnár, P. Földi, M. G. Benedict, and F. Bartha, “Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule,” quant-ph/0202069.

Benedict, M. G.

B. Molnár, M. G. Benedict, and P. Földi, “State evolution in the anharmonic Morse potential subjected to an external sinusoidal field,” Fortschr. Phys. 49, 1053–1057 (2001).
[Crossref]

M. G. Benedict and A. Czirják, “Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,” Phys. Rev. A 60, 4034–4044 (1999).
[Crossref]

M. G. Benedict and B. Molnár, “Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics,” Phys. Rev. A 60R1737–R1740 (1999).B. Molnár, M. G. Benedict, and J. Bertrand, “Coherent states and the role of the affine group in the quantum mechanics of the Morse potential” J. Phys A:Math. Gen. 34, 3139–3151 (2001).
[Crossref]

B. Molnár, P. Földi, M. G. Benedict, and F. Bartha, “Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule,” quant-ph/0202069.

Bertrand, J.

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]

Cummings, F. W.

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).

Czirják, A.

M. G. Benedict and A. Czirják, “Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,” Phys. Rev. A 60, 4034–4044 (1999).
[Crossref]

Domokos, P.

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]

Eberly, J. H.

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, 1323–1327 (1980).
[Crossref]

Eiselt, J.

J. Eiselt and H. Risken, “Quasiprobability distributions for the Jaynes-Cummings model with cavity damping,” Phys. Rev. A 43, 346–360 (1991).
[Crossref] [PubMed]

Eryomin, V. V.

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]

Földi, P.

B. Molnár, M. G. Benedict, and P. Földi, “State evolution in the anharmonic Morse potential subjected to an external sinusoidal field,” Fortschr. Phys. 49, 1053–1057 (2001).
[Crossref]

B. Molnár, P. Földi, M. G. Benedict, and F. Bartha, “Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule,” quant-ph/0202069.

Herzberg, G.

K. P. Huber and G. Herzberg, Molecular spectra and molecular structure IV. Constants of diatomic molecules, (van Nostrand Reinhold, 1979).

Huber, K. P.

K. P. Huber and G. Herzberg, Molecular spectra and molecular structure IV. Constants of diatomic molecules, (van Nostrand Reinhold, 1979).

Irac-Astaud, M.

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]

Jakubetz, W.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Janszky, J.

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]

J. Janszky, An. V. Vinogradov, T. Kobayashi, and Z. Kis, “Vibrational Schrödinger-cat states,” Phys. Rev. A 50, 1777–1784(1994), and see also references therein.
[Crossref] [PubMed]

Jaynes, E. T.

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).

Kauffmann, H. F.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Kim, Y. S.

Y. S. Kim and M. E. Noz, Phase space picture of quantum mechanics, (World Scientific, 1991).

Kis, Z.

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]

J. Janszky, An. V. Vinogradov, T. Kobayashi, and Z. Kis, “Vibrational Schrödinger-cat states,” Phys. Rev. A 50, 1777–1784(1994), and see also references therein.
[Crossref] [PubMed]

Kiss, T.

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]

Kobayashi, T.

J. Janszky, An. V. Vinogradov, T. Kobayashi, and Z. Kis, “Vibrational Schrödinger-cat states,” Phys. Rev. A 50, 1777–1784(1994), and see also references therein.
[Crossref] [PubMed]

Leichtle, C.

C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: An analytical approach,” Phys. Rev. A. 54, 5299–5312 (1996).
[Crossref] [PubMed]

Milota, F.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Molnár, B.

B. Molnár, M. G. Benedict, and P. Földi, “State evolution in the anharmonic Morse potential subjected to an external sinusoidal field,” Fortschr. Phys. 49, 1053–1057 (2001).
[Crossref]

M. G. Benedict and B. Molnár, “Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics,” Phys. Rev. A 60R1737–R1740 (1999).B. Molnár, M. G. Benedict, and J. Bertrand, “Coherent states and the role of the affine group in the quantum mechanics of the Morse potential” J. Phys A:Math. Gen. 34, 3139–3151 (2001).
[Crossref]

B. Molnár, P. Földi, M. G. Benedict, and F. Bartha, “Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule,” quant-ph/0202069.

Narozhny, N. B.

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, 1323–1327 (1980).
[Crossref]

Noz, M. E.

Y. S. Kim and M. E. Noz, Phase space picture of quantum mechanics, (World Scientific, 1991).

Parker, J.

J. Parker and C. R. Stroud, “Coherence and decay of Rydberg Wave packets,” Phys. Rev. Lett. 56, 716–719 (1986).
[Crossref] [PubMed]

Perelman, N. F.

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. A139, 449–453 (1989).

Prior, Y.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Risken, H.

J. Eiselt and H. Risken, “Quasiprobability distributions for the Jaynes-Cummings model with cavity damping,” Phys. Rev. A 43, 346–360 (1991).
[Crossref] [PubMed]

Sanchez-Mondragon, J. J.

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, 1323–1327 (1980).
[Crossref]

Schleich, W.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Schleich, W. P.

C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: An analytical approach,” Phys. Rev. A. 54, 5299–5312 (1996).
[Crossref] [PubMed]

Shapiro, M.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Stroud, C. R.

D. L. Aronstein and C. R. Stroud, “Analytical investigation of revival phenomena in the finite square-well potential,” Phys. Rev. A 62, 022102-1–022102-9 (2000).
[Crossref]

J. Parker and C. R. Stroud, “Coherence and decay of Rydberg Wave packets,” Phys. Rev. Lett. 56, 716–719 (1986).
[Crossref] [PubMed]

Tortschanoff, A.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Vetchinkin, S. I.

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]

Vinogradov, An. V.

J. Janszky, An. V. Vinogradov, T. Kobayashi, and Z. Kis, “Vibrational Schrödinger-cat states,” Phys. Rev. A 50, 1777–1784(1994), and see also references therein.
[Crossref] [PubMed]

Vogel, W.

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]

Warmuth, Ch.

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Zucchetti, A.

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]

Chem. Phys. Lett. (2)

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]

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]

Czech J. Phys. (1)

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]

Fortschr. Phys. (1)

B. Molnár, M. G. Benedict, and P. Földi, “State evolution in the anharmonic Morse potential subjected to an external sinusoidal field,” Fortschr. Phys. 49, 1053–1057 (2001).
[Crossref]

J. Chem. Phys. (1)

Ch. Warmuth, A. Tortschanoff, F. Milota, M. Shapiro, Y. Prior, I. Sh. Averbukh, W. Schleich, W. Jakubetz, and H. F. Kauffmann, “Studying vibrational wavepacket dynamics by measuring fluorescence interference fluctuations,” J. Chem. Phys. 112, 5060–5069 (2000).
[Crossref]

Opt. Express (1)

Phys. Lett. (1)

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. A139, 449–453 (1989).

Phys. Rev. A (5)

J. Janszky, An. V. Vinogradov, T. Kobayashi, and Z. Kis, “Vibrational Schrödinger-cat states,” Phys. Rev. A 50, 1777–1784(1994), and see also references therein.
[Crossref] [PubMed]

J. Eiselt and H. Risken, “Quasiprobability distributions for the Jaynes-Cummings model with cavity damping,” Phys. Rev. A 43, 346–360 (1991).
[Crossref] [PubMed]

M. G. Benedict and A. Czirják, “Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms,” Phys. Rev. A 60, 4034–4044 (1999).
[Crossref]

M. G. Benedict and B. Molnár, “Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics,” Phys. Rev. A 60R1737–R1740 (1999).B. Molnár, M. G. Benedict, and J. Bertrand, “Coherent states and the role of the affine group in the quantum mechanics of the Morse potential” J. Phys A:Math. Gen. 34, 3139–3151 (2001).
[Crossref]

D. L. Aronstein and C. R. Stroud, “Analytical investigation of revival phenomena in the finite square-well potential,” Phys. Rev. A 62, 022102-1–022102-9 (2000).
[Crossref]

Phys. Rev. A. (1)

C. Leichtle, I. Sh. Averbukh, and W. P. Schleich, “Multilevel quantum beats: An analytical approach,” Phys. Rev. A. 54, 5299–5312 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett (1)

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, 1323–1327 (1980).
[Crossref]

Phys. Rev. Lett. (1)

J. Parker and C. R. Stroud, “Coherence and decay of Rydberg Wave packets,” Phys. Rev. Lett. 56, 716–719 (1986).
[Crossref] [PubMed]

Proc. Inst. Elect. Eng. (1)

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).

Other (3)

B. Molnár, P. Földi, M. G. Benedict, and F. Bartha, “Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule,” quant-ph/0202069.

K. P. Huber and G. Herzberg, Molecular spectra and molecular structure IV. Constants of diatomic molecules, (van Nostrand Reinhold, 1979).

Y. S. Kim and M. E. Noz, Phase space picture of quantum mechanics, (World Scientific, 1991).

Supplementary Material (2)

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Figures (4)

Fig. 1.
Fig. 1.

[2.1 MB] The absolute square of the wave functions corresponding to the Morse coherent states |x 0,0〉, with x 0 = 0.0 (ground state) and x 0 = 0.5. The time evolution of the latter initial wave function is shown in the attached movie file. These plots correspond to the case of the NO molecule, where s = 54.54.

Fig. 2.
Fig. 2.

The expectation value of the dimensionless position operator as a function of time. The initial states were |ϕ(t = 0)〉 = |x 0,0〉, with x 0 = 1.0, x 0 = 0.5 and x 0 = 0.06.

Fig. 3.
Fig. 3.

A) [1.3 MB] and B) [2.2 MB]. Frames of two movie files, showing Wigner functions of the Morse system at the initial stage of the time evolution and the formation of a Schrödinger-cat state. The plots correspond to t/T = 0 and t/T = 30, respectively. The initial state was |ϕ(t = 0)〉 = |x 0,0), with x 0 = 0.5.

Fig. 4.
Fig. 4.

Nonclassicality as a function of time. The initial state was |ϕ(t = 0)〉 = |x 0, 0〉, with x 0 = 1.0, x 0 = 0.5 and x 0 = 0.06.

Equations (9)

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H = P 2 + ( s + 1 2 ) 2 [ exp ( 2 X ) 2 exp ( X ) ] ,
d dt ϕ = i 2 π 2 s + 1 H ϕ ,
y β = ( 1 β 2 ) s Γ ( 2 s ) ( 1 β ) 2 s y s exp ( y 2 1 + β 1 β ) .
β = n = 0 N c n ψ n = n = 0 [ s ] [ ( 2 s 2 n ) Γ ( 2 s n + 1 ) n ! Γ ( 2 s ) Γ ( 2 s n ) Γ ( 2 s 2 n + 1 ) ( 1 β 2 ) s ( 1 β ) n
× 2 F 1 ( n , 2 s n ; 2 s 2 n + 1 ; 1 β ) ψ n ] + n = [ s ] + 1 N c n ψ n ,
X β = ln ( Re 1 + β 1 β ) , P β = s Re [ ( 1 + β ) ( 1 β ) ] Im [ ( 1 + β ) ( 1 β ) ] ,
X ( t ) = n , k = 0 N c n ( x ) c k * ( x ) ψ k X ψ n exp [ it 2 π 2 s + 1 ( E k ( s ) E n ( s ) ) ]
W x p t = 1 2 π ϕ * ( x + u 2 , t ) ϕ ( x u 2 , t ) e iup du .
M nc ( ϕ ) = 1 I + ( ϕ ) I ( ϕ ) I + ( ϕ ) + I ( ϕ ) ,

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