Abstract

We investigate the properties of phase transitions in a weakly coupled ultracold atom-molecule boson system based on the phase space analysis approach. We identify the pure molecular and mixed atom-molecule phases of the system by different values of the time average of molecular population. When applying a periodic modulation on the energy detuning, we find that the atom-molecule mixing dynamics can be well controlled. For both high- and low-frequency modulations, it is shown that the transition points can be shifted effectively by choosing parameters of the periodic modulation appropriately. The analytical expressions for the dependence of the transition parameters on the modulation parameters are also obtained for the two cases. In particular, when the modulation with a frequency near the atom-molecule transition frequency is applied, the resonance between the periodic modulation and atom-molecule Rabi oscillation will emerge, which can affect the atom-molecule mixing dynamics dramatically and lead to the complex chaos phenomenon.

© 2014 Optical Society of America

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  1. E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
    [CrossRef]
  2. J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416, 211–218 (2002).
    [CrossRef]
  3. K. Góral, L. Santos, and M. Lewenstein, “Quantum phases of dipolar bosons in optical lattices,” Phys. Rev. Lett. 88, 170406 (2002).
    [CrossRef]
  4. J. T. Bahns, W. C. Stwalley, and P. L. Gould, “Laser cooling of molecules: a sequential scheme for rotation, translation, and vibration,” J. Chem. Phys. 104, 9689–9697 (1996).
    [CrossRef]
  5. D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
    [CrossRef]
  6. N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
    [CrossRef]
  7. R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
    [CrossRef]
  8. E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
    [CrossRef]
  9. T. Köhler, K. Góral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
    [CrossRef]
  10. C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
    [CrossRef]
  11. S. T. Thompson, E. Hodby, and C. E. Wieman, “Ultracold molecule production via a resonant oscillating magnetic field,” Phys. Rev. Lett. 95, 190404 (2005).
    [CrossRef]
  12. N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
    [CrossRef]
  13. K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
    [CrossRef]
  14. M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
    [CrossRef]
  15. G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
    [CrossRef]
  16. G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
    [CrossRef]
  17. S. C. Li and L. B. Fu, “Quantum phase transition from mixed atom-molecule phase to pure molecule phase: characteristic scaling laws and Berry-curvature signature,” Phys. Rev. A 84, 023605 (2011).
    [CrossRef]
  18. S. C. Li, L. B. Fu, and F. L. Li, “Quantum phase transition in a three-level atom-molecule system,” Phys. Rev. A 88, 013602 (2013).
    [CrossRef]
  19. B. Liu, L. B. Fu, and J. Liu, “Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field,” Phys. Rev. A 81, 013602 (2010).
    [CrossRef]
  20. G. F. Wang, L. B. Fu, and J. Liu, “Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates,” Phys. Rev. A 73, 013619 (2006).
    [CrossRef]
  21. J. Cheng, “Chaotic dynamics in a periodically driven spin-1 condensate,” Phys. Rev. A 81, 023619 (2010).
    [CrossRef]
  22. L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
    [CrossRef]
  23. S. B. Papp and C. E. Wieman, “Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas,” Phys. Rev. Lett. 97, 180404 (2006).
    [CrossRef]
  24. Y. Kayanuma, “Role of phase coherence in the transition dynamics of a periodically driven two-level system,” Phys. Rev. A 50, 843–845 (1994).
    [CrossRef]
  25. Y. Kayanuma and Y. Mizumoto, “Landau-Zener transitions in a level-crossing system with periodic modulations of the diagonal energy,” Phys. Rev. A 62, 061401(R) (2000).
    [CrossRef]

2013 (2)

M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

S. C. Li, L. B. Fu, and F. L. Li, “Quantum phase transition in a three-level atom-molecule system,” Phys. Rev. A 88, 013602 (2013).
[CrossRef]

2011 (1)

S. C. Li and L. B. Fu, “Quantum phase transition from mixed atom-molecule phase to pure molecule phase: characteristic scaling laws and Berry-curvature signature,” Phys. Rev. A 84, 023605 (2011).
[CrossRef]

2010 (3)

B. Liu, L. B. Fu, and J. Liu, “Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field,” Phys. Rev. A 81, 013602 (2010).
[CrossRef]

J. Cheng, “Chaotic dynamics in a periodically driven spin-1 condensate,” Phys. Rev. A 81, 023619 (2010).
[CrossRef]

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
[CrossRef]

2007 (2)

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
[CrossRef]

2006 (4)

S. B. Papp and C. E. Wieman, “Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas,” Phys. Rev. Lett. 97, 180404 (2006).
[CrossRef]

G. F. Wang, L. B. Fu, and J. Liu, “Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates,” Phys. Rev. A 73, 013619 (2006).
[CrossRef]

T. Köhler, K. Góral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
[CrossRef]

2005 (2)

S. T. Thompson, E. Hodby, and C. E. Wieman, “Ultracold molecule production via a resonant oscillating magnetic field,” Phys. Rev. Lett. 95, 190404 (2005).
[CrossRef]

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

2003 (1)

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
[CrossRef]

2002 (5)

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416, 211–218 (2002).
[CrossRef]

K. Góral, L. Santos, and M. Lewenstein, “Quantum phases of dipolar bosons in optical lattices,” Phys. Rev. Lett. 88, 170406 (2002).
[CrossRef]

N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef]

2000 (3)

D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
[CrossRef]

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

Y. Kayanuma and Y. Mizumoto, “Landau-Zener transitions in a level-crossing system with periodic modulations of the diagonal energy,” Phys. Rev. A 62, 061401(R) (2000).
[CrossRef]

1996 (1)

J. T. Bahns, W. C. Stwalley, and P. L. Gould, “Laser cooling of molecules: a sequential scheme for rotation, translation, and vibration,” J. Chem. Phys. 104, 9689–9697 (1996).
[CrossRef]

1994 (1)

Y. Kayanuma, “Role of phase coherence in the transition dynamics of a periodically driven two-level system,” Phys. Rev. A 50, 843–845 (1994).
[CrossRef]

Anglin, J. R.

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416, 211–218 (2002).
[CrossRef]

Bahns, J. T.

J. T. Bahns, W. C. Stwalley, and P. L. Gould, “Laser cooling of molecules: a sequential scheme for rotation, translation, and vibration,” J. Chem. Phys. 104, 9689–9697 (1996).
[CrossRef]

Bauer, D. M.

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Bohn, J. L.

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
[CrossRef]

Cheng, J.

J. Cheng, “Chaotic dynamics in a periodically driven spin-1 condensate,” Phys. Rev. A 81, 023619 (2010).
[CrossRef]

Claussen, N. R.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef]

Comparat, D.

N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

Cornell, E. A.

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

Dahmen, S. R.

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
[CrossRef]

de Souza Melo, W.

N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

Denschlag, J. H.

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

DeSalvo, B. J.

M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

Dietze, D.

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Donley, E. A.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef]

Drummond, P. D.

D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
[CrossRef]

Durr, S.

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Foerster, A.

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
[CrossRef]

G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
[CrossRef]

Freeland, R. S.

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

Fu, L. B.

S. C. Li, L. B. Fu, and F. L. Li, “Quantum phase transition in a three-level atom-molecule system,” Phys. Rev. A 88, 013602 (2013).
[CrossRef]

S. C. Li and L. B. Fu, “Quantum phase transition from mixed atom-molecule phase to pure molecule phase: characteristic scaling laws and Berry-curvature signature,” Phys. Rev. A 84, 023605 (2011).
[CrossRef]

B. Liu, L. B. Fu, and J. Liu, “Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field,” Phys. Rev. A 81, 013602 (2010).
[CrossRef]

G. F. Wang, L. B. Fu, and J. Liu, “Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates,” Phys. Rev. A 73, 013619 (2006).
[CrossRef]

Góral, K.

T. Köhler, K. Góral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

K. Góral, L. Santos, and M. Lewenstein, “Quantum phases of dipolar bosons in optical lattices,” Phys. Rev. Lett. 88, 170406 (2002).
[CrossRef]

Gould, P. L.

J. T. Bahns, W. C. Stwalley, and P. L. Gould, “Laser cooling of molecules: a sequential scheme for rotation, translation, and vibration,” J. Chem. Phys. 104, 9689–9697 (1996).
[CrossRef]

Grimm, R.

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

Han, D. J.

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

Heinzen, D. J.

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
[CrossRef]

Hodby, E.

S. T. Thompson, E. Hodby, and C. E. Wieman, “Ultracold molecule production via a resonant oscillating magnetic field,” Phys. Rev. Lett. 95, 190404 (2005).
[CrossRef]

Huang, Y.

M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

Jiang, L.

L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
[CrossRef]

Jin, D. S.

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
[CrossRef]

Julienne, P. S.

T. Köhler, K. Góral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

Kayanuma, Y.

Y. Kayanuma and Y. Mizumoto, “Landau-Zener transitions in a level-crossing system with periodic modulations of the diagonal energy,” Phys. Rev. A 62, 061401(R) (2000).
[CrossRef]

Y. Kayanuma, “Role of phase coherence in the transition dynamics of a periodically driven two-level system,” Phys. Rev. A 50, 843–845 (1994).
[CrossRef]

Ketterle, W.

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416, 211–218 (2002).
[CrossRef]

Kheruntsyan, K. V.

D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
[CrossRef]

Killian, T. C.

M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

Köhler, T.

T. Köhler, K. Góral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

Lettner, M.

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Lewenstein, M.

K. Góral, L. Santos, and M. Lewenstein, “Quantum phases of dipolar bosons in optical lattices,” Phys. Rev. Lett. 88, 170406 (2002).
[CrossRef]

Li, F. L.

S. C. Li, L. B. Fu, and F. L. Li, “Quantum phase transition in a three-level atom-molecule system,” Phys. Rev. A 88, 013602 (2013).
[CrossRef]

Li, S. C.

S. C. Li, L. B. Fu, and F. L. Li, “Quantum phase transition in a three-level atom-molecule system,” Phys. Rev. A 88, 013602 (2013).
[CrossRef]

S. C. Li and L. B. Fu, “Quantum phase transition from mixed atom-molecule phase to pure molecule phase: characteristic scaling laws and Berry-curvature signature,” Phys. Rev. A 84, 023605 (2011).
[CrossRef]

Ling, H. Y.

L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
[CrossRef]

Links, J.

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
[CrossRef]

G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
[CrossRef]

Liu, B.

B. Liu, L. B. Fu, and J. Liu, “Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field,” Phys. Rev. A 81, 013602 (2010).
[CrossRef]

Liu, J.

B. Liu, L. B. Fu, and J. Liu, “Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field,” Phys. Rev. A 81, 013602 (2010).
[CrossRef]

G. F. Wang, L. B. Fu, and J. Liu, “Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates,” Phys. Rev. A 73, 013619 (2006).
[CrossRef]

Mattei, E.

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
[CrossRef]

Mizumoto, Y.

Y. Kayanuma and Y. Mizumoto, “Landau-Zener transitions in a level-crossing system with periodic modulations of the diagonal energy,” Phys. Rev. A 62, 061401(R) (2000).
[CrossRef]

Naidon, P.

M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

Papp, S. B.

S. B. Papp and C. E. Wieman, “Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas,” Phys. Rev. Lett. 97, 180404 (2006).
[CrossRef]

Pillet, P.

N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

Pu, H.

L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
[CrossRef]

Regal, C. A.

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
[CrossRef]

Rempe, G.

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Ritsch, H.

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

Ryu, C.

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

Santos, G.

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
[CrossRef]

G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
[CrossRef]

Santos, L.

K. Góral, L. Santos, and M. Lewenstein, “Quantum phases of dipolar bosons in optical lattices,” Phys. Rev. Lett. 88, 170406 (2002).
[CrossRef]

Stwalley, W. C.

J. T. Bahns, W. C. Stwalley, and P. L. Gould, “Laser cooling of molecules: a sequential scheme for rotation, translation, and vibration,” J. Chem. Phys. 104, 9689–9697 (1996).
[CrossRef]

Syassen, N.

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Thalhammer, G.

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

Theis, M.

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

Thompson, S. T.

S. T. Thompson, E. Hodby, and C. E. Wieman, “Ultracold molecule production via a resonant oscillating magnetic field,” Phys. Rev. Lett. 95, 190404 (2005).
[CrossRef]

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef]

Ticknor, C.

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
[CrossRef]

Tolra, B. L.

N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

Tonel, A.

G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
[CrossRef]

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N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

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N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

Wang, G. F.

G. F. Wang, L. B. Fu, and J. Liu, “Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates,” Phys. Rev. A 73, 013619 (2006).
[CrossRef]

Wieman, C. E.

S. B. Papp and C. E. Wieman, “Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas,” Phys. Rev. Lett. 97, 180404 (2006).
[CrossRef]

S. T. Thompson, E. Hodby, and C. E. Wieman, “Ultracold molecule production via a resonant oscillating magnetic field,” Phys. Rev. Lett. 95, 190404 (2005).
[CrossRef]

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef]

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

Winkler, K.

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

Wynar, R.

D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
[CrossRef]

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

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M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

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L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
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L. Zhou, W. Zhang, H. Y. Ling, L. Jiang, and H. Pu, “Properties of a coupled two-species atom-heteronuclear-molecule condensate,” Phys. Rev. A 75, 043603 (2007).
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J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416, 211–218 (2002).
[CrossRef]

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom-molecule coherence in a Bose-Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef]

C. A. Regal, C. Ticknor, J. L. Bohn, and D. S. Jin, “Creation of ultracold molecules from a Fermi gas of atoms,” Nature 424, 47–50 (2003).
[CrossRef]

Phys. Rev. A (10)

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G. Santos, A. Tonel, A. Foerster, and J. Links, “Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates,” Phys. Rev. A 73, 023609 (2006).
[CrossRef]

G. Santos, A. Foerster, J. Links, E. Mattei, and S. R. Dahmen, “Quantum phase transitions in an interacting atom-molecule boson model,” Phys. Rev. A 81, 063621 (2010).
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S. C. Li and L. B. Fu, “Quantum phase transition from mixed atom-molecule phase to pure molecule phase: characteristic scaling laws and Berry-curvature signature,” Phys. Rev. A 84, 023605 (2011).
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S. C. Li, L. B. Fu, and F. L. Li, “Quantum phase transition in a three-level atom-molecule system,” Phys. Rev. A 88, 013602 (2013).
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B. Liu, L. B. Fu, and J. Liu, “Shapiro-like resonance in ultracold molecule production via an oscillating magnetic field,” Phys. Rev. A 81, 013602 (2010).
[CrossRef]

G. F. Wang, L. B. Fu, and J. Liu, “Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates,” Phys. Rev. A 73, 013619 (2006).
[CrossRef]

J. Cheng, “Chaotic dynamics in a periodically driven spin-1 condensate,” Phys. Rev. A 81, 023619 (2010).
[CrossRef]

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[CrossRef]

Phys. Rev. Lett. (8)

S. B. Papp and C. E. Wieman, “Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas,” Phys. Rev. Lett. 97, 180404 (2006).
[CrossRef]

K. Góral, L. Santos, and M. Lewenstein, “Quantum phases of dipolar bosons in optical lattices,” Phys. Rev. Lett. 88, 170406 (2002).
[CrossRef]

D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000).
[CrossRef]

N. Vanhaecke, W. de Souza Melo, B. L. Tolra, D. Comparat, and P. Pillet, “Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap,” Phys. Rev. Lett. 89, 063001 (2002).
[CrossRef]

S. T. Thompson, E. Hodby, and C. E. Wieman, “Ultracold molecule production via a resonant oscillating magnetic field,” Phys. Rev. Lett. 95, 190404 (2005).
[CrossRef]

N. Syassen, D. M. Bauer, M. Lettner, D. Dietze, T. Volz, S. Durr, and G. Rempe, “Atom-molecule Rabi oscillations in a Mott insulator,” Phys. Rev. Lett. 99, 033201 (2007).
[CrossRef]

K. Winkler, G. Thalhammer, M. Theis, H. Ritsch, R. Grimm, and J. H. Denschlag, “Atom-molecule dark states in a Bose-Einstein condensate,” Phys. Rev. Lett. 95, 063202 (2005).
[CrossRef]

M. Yan, B. J. DeSalvo, Y. Huang, P. Naidon, and T. C. Killian, “Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation,” Phys. Rev. Lett. 111, 150402 (2013).
[CrossRef]

Rev. Mod. Phys. (2)

E. A. Cornell and C. E. Wieman, “Nobel lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments,” Rev. Mod. Phys. 74, 875–893 (2002).
[CrossRef]

T. Köhler, K. Góral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

Science (1)

R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, “Molecules in a Bose-Einstein condensate,” Science 287, 1016–1019 (2000).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Trajectories in the phase space of the Hamiltonian system (5) with δ=0 (left column). The right column illustrates the corresponding energy curves (solid lines) for q=0 (upper branch) and for q=π (lower branch). The dashed line denotes the energy value u/4.

Fig. 2.
Fig. 2.

Average of molecular population probability with δ=0 versus the scaled parameter u/g when the trajectory (p,q)=(1/2,0) evolves with time. The arrow denotes the critical point.

Fig. 3.
Fig. 3.

Phase space of the Hamiltonian system (5) with δ=Asinωt for ω=100 and A=150, obtained by stroboscopic plotting of the trajectories with period 2π/ω.

Fig. 4.
Fig. 4.

(a) Average of molecular population probability versus the scaled parameter u/g when the trajectory (p,q)=(1/2,0) evolves with time for ω=100 and A=150. (b) Transition phase diagram for the occurrence of atom-molecule mixing. The circles give the numerical results for ω=100, while the solid line shows the analytical prediction u/g=2J0(A/ω).

Fig. 5.
Fig. 5.

(a) Average of molecular population probability versus the interaction parameter u when the trajectory (p,q)=(1/2,0) evolves with time for g=A=1 and ω=0.01. (b) Transition phase diagram for the occurrence of atom-molecule mixing. The triangles show the numerical results for ω=0.01, while the solid line gives the analytical prediction u=(A+2g).

Fig. 6.
Fig. 6.

Evolution of the phase space of the Hamiltonian system (5) with u/g=2.3 (upper panels) and u/g=2.5 (lower panels) as δ changes adiabatically. The arrows refer to the moving direction of the fixed points as δ increases.

Fig. 7.
Fig. 7.

Evolution of the energy profiles for the relative phase q=π with u/g=2.3 (left column) and u/g=2.5 (right column) as δ changes adiabatically. The arrows denote the moving direction of the fixed points as δ increases.

Fig. 8.
Fig. 8.

Average of molecular population probability versus the interaction parameter u when the trajectory (p,q)=(1/2,0) evolves with time for g=ω=1 with different amplitudes.

Fig. 9.
Fig. 9.

Phase space of the Hamiltonian system (5) with δ=Asinωt for ω=1 and A=2, obtained by stroboscopic plotting of the trajectories with period 2π/ω. (a) u/g=1.5, (b) u/g=2.0, and (c) u/g=2.5.

Fig. 10.
Fig. 10.

Largest Lyapunov exponents in the phase space for u/g=1.5 corresponding to the region with q[0,0.5] and p[0.2,0.4] in Fig. 9(a).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

H^=ΔNm+l,jUljNlNj+Ω(a^1a^2a^m+h.c.),
H^=δNm+UNm2+Ω(a^1a^2a^m+h.c.),
iddt(a1am)=H(a1am),
H=(0ga1*g2a1δ+2u|am|2),
H=δp+up2+gp(12p)2cosq.
idadt=geiAωcosωta*b,
idbdt=g2eiAωcosωta2+2u|b|2b.
e±iAωcosωt=n=Jn(Aω)(±i)ne±inωt,

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