Abstract

The Dicke model is a paradigm of collective behavior in quantum mechanics describing an ensemble of N two-level atoms interacting with a single mode of the electromagnetic field. Here we simulate a spin-1 Dicke model using magnetic sublevels of the lowest F=1 hyperfine level of Rb87 atoms confined to a high finesse cavity. Our implementation enables simple tuning of the model parameters over a large parameter space. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. Exploring the system over a wide range of parameters, we obtain boundaries between normal, super-radiant, and oscillatory phases, and compare with a simple theoretical model. This study provides further understanding of the fundamental nature of the model and has technological applications such as superradiant lasers and storage of quantum information in collective atomic states.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Directly probing the Chern number of the Haldane model in optical lattices

Rui-Bin Liu, Dong-Ling Deng, Dan-Wei Zhang, and Shi-Liang Zhu
J. Opt. Soc. Am. B 32(12) 2500-2506 (2015)

Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian

B. M. Rodríguez-Lara and Ray-Kuang Lee
J. Opt. Soc. Am. B 27(11) 2443-2450 (2010)

Quantum phase transition of light in a finite size Dicke model with Kerr-type nonlinearity

Xiaoyong Guo, Zhongzhou Ren, and Zimeng Chi
J. Opt. Soc. Am. B 28(5) 1245-1251 (2011)

References

  • View by:
  • |
  • |
  • |

  1. H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002).
    [Crossref]
  2. H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
    [Crossref]
  3. Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
    [Crossref]
  4. J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
    [Crossref]
  5. J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
    [Crossref]
  6. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
    [Crossref]
  7. A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
    [Crossref]
  8. A. T. Black, H. W. Chan, and V. Vuletic, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
    [Crossref]
  9. T. Elsasser, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69, 033403 (2004).
    [Crossref]
  10. S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
    [Crossref]
  11. K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
    [Crossref]
  12. K. J. Arnold, M. P. Baden, and M. D. Barrett, “Collective cavity quantum electrodynamics with multiple atomic levels,” Phys. Rev. A 84, 033843 (2011).
    [Crossref]
  13. K. J. Arnold, M. P. Baden, and M. D. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
    [Crossref]
  14. C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett. 90, 044101 (2003).
    [Crossref]
  15. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
    [Crossref]
  16. B. M. Garraway, “The Dicke model in quantum optics: Dicke model revisited,” Philos. Trans. R. Soc. London A 369, 1137–1155 (2011).
    [Crossref]
  17. M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
    [Crossref]
  18. M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
    [Crossref]
  19. J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
    [Crossref]
  20. F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
    [Crossref]
  21. S. J. Masson, M. D. Barrett, and A. S. Parkins are preparing a manuscript to be called “Quantum spin-nematic squeezing via cavity-mediated spin-mixing dynamics in a spinor gas.”
  22. E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
    [Crossref]
  23. J. Gelhausen, M. Buchhold, and P. Strack, “Many-body quantum optics with decaying atomic spin states:(γ, κ) Dicke model,” arXiv:1605.07637 (2016).
  24. J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
    [Crossref]

2016 (1)

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

2015 (2)

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

2014 (1)

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

2012 (4)

M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

2011 (3)

B. M. Garraway, “The Dicke model in quantum optics: Dicke model revisited,” Philos. Trans. R. Soc. London A 369, 1137–1155 (2011).
[Crossref]

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Collective cavity quantum electrodynamics with multiple atomic levels,” Phys. Rev. A 84, 033843 (2011).
[Crossref]

2010 (1)

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

2008 (1)

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref]

2007 (3)

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[Crossref]

2004 (1)

T. Elsasser, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69, 033403 (2004).
[Crossref]

2003 (2)

C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett. 90, 044101 (2003).
[Crossref]

A. T. Black, H. W. Chan, and V. Vuletic, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

2002 (1)

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002).
[Crossref]

1999 (1)

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

Arnold, K. J.

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Collective cavity quantum electrodynamics with multiple atomic levels,” Phys. Rev. A 84, 033843 (2011).
[Crossref]

Baden, M. P.

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Collective cavity quantum electrodynamics with multiple atomic levels,” Phys. Rev. A 84, 033843 (2011).
[Crossref]

Barrett, M. D.

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Collective cavity quantum electrodynamics with multiple atomic levels,” Phys. Rev. A 84, 033843 (2011).
[Crossref]

S. J. Masson, M. D. Barrett, and A. S. Parkins are preparing a manuscript to be called “Quantum spin-nematic squeezing via cavity-mediated spin-mixing dynamics in a spinor gas.”

Baumann, K.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Bhaseen, M. J.

M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
[Crossref]

Black, A. T.

A. T. Black, H. W. Chan, and V. Vuletic, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

Bohnet, J. G.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

Brandes, T.

C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett. 90, 044101 (2003).
[Crossref]

Brennecke, F.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Buchhold, M.

J. Gelhausen, M. Buchhold, and P. Strack, “Many-body quantum optics with decaying atomic spin states:(γ, κ) Dicke model,” arXiv:1605.07637 (2016).

Bux, S.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

Carmichael, H. J.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[Crossref]

Chan, H. W.

A. T. Black, H. W. Chan, and V. Vuletic, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

Chen, Z.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

Colombe, Y.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

Courteille, P.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

Cox, K. C.

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

Demler, E.

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

Dimer, F.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[Crossref]

Doherty, A. C.

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002).
[Crossref]

Dubois, G.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

Elsasser, T.

T. Elsasser, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69, 033403 (2004).
[Crossref]

Emary, C.

C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett. 90, 044101 (2003).
[Crossref]

Esslinger, T.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Estienne, B.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[Crossref]

Fox, R. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Garraway, B. M.

B. M. Garraway, “The Dicke model in quantum optics: Dicke model revisited,” Philos. Trans. R. Soc. London A 369, 1137–1155 (2011).
[Crossref]

Gelhausen, J.

J. Gelhausen, M. Buchhold, and P. Strack, “Many-body quantum optics with decaying atomic spin states:(γ, κ) Dicke model,” arXiv:1605.07637 (2016).

Goban, A.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Grimsmo, A. L.

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

Guerlin, C.

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Hemmerich, A.

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

T. Elsasser, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69, 033403 (2004).
[Crossref]

Holland, M. J.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

Hood, J. D.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Hung, C.-L.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Hunger, D.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

Jiang, Y. Y.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Keeling, J.

M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
[Crossref]

Keßler, H.

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

Kimble, H. J.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[Crossref]

Klinder, J.

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

Krenz, G.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

Lemke, N. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Linke, F.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

Ludlow, A. D.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Lukin, M. D.

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

Ma, L.-S.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Mabuchi, H.

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002).
[Crossref]

Masson, S. J.

S. J. Masson, M. D. Barrett, and A. S. Parkins are preparing a manuscript to be called “Quantum spin-nematic squeezing via cavity-mediated spin-mixing dynamics in a spinor gas.”

Mathey, L.

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

Mayoh, J.

M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
[Crossref]

Meiser, D.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

Muniz, J. A.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Nagorny, B.

T. Elsasser, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69, 033403 (2004).
[Crossref]

Oates, C. W.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Painter, O.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Parkins, A. S.

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[Crossref]

S. J. Masson, M. D. Barrett, and A. S. Parkins are preparing a manuscript to be called “Quantum spin-nematic squeezing via cavity-mediated spin-mixing dynamics in a spinor gas.”

Parkins, S.

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

Reichel, J.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

Shchadilova, Y.

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

Sherman, J. A.

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Simons, B. D.

M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
[Crossref]

Slama, S.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

Steinmetz, T.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

Strack, P.

J. Gelhausen, M. Buchhold, and P. Strack, “Many-body quantum optics with decaying atomic spin states:(γ, κ) Dicke model,” arXiv:1605.07637 (2016).

Thompson, J. K.

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

Torre, E. G. D.

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

Vernooy, D. W.

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[Crossref]

Vuletic, V.

A. T. Black, H. W. Chan, and V. Vuletic, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

Weiner, J. M.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

Wilner, E. Y.

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

Wolke, M.

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

Ye, J.

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[Crossref]

Yu, S.-P.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

Zimmermann, C.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

Nat. Photonics (1)

Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, “Making optical atomic clocks more stable with 10-16-level laser stabilization,” Nat. Photonics 5, 158–161 (2011).
[Crossref]

Nature (4)

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 78–81 (2012).
[Crossref]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[Crossref]

K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity,” Nature 464, 1301–1306 (2010).
[Crossref]

Philos. Trans. R. Soc. London A (1)

B. M. Garraway, “The Dicke model in quantum optics: Dicke model revisited,” Philos. Trans. R. Soc. London A 369, 1137–1155 (2011).
[Crossref]

Phys. Rev. (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99–110 (1954).
[Crossref]

Phys. Rev. A (5)

F. Dimer, B. Estienne, A. S. Parkins, and H. J. Carmichael, “Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system,” Phys. Rev. A 75, 013804 (2007).
[Crossref]

E. G. D. Torre, Y. Shchadilova, E. Y. Wilner, M. D. Lukin, and E. Demler, “Dicke phase transition without total spin conservation,” Phys. Rev. A 94, 061802(R) (2016).
[Crossref]

M. J. Bhaseen, J. Mayoh, B. D. Simons, and J. Keeling, “Dynamics of nonequilibrium Dicke models,” Phys. Rev. A 85, 013817 (2012).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Collective cavity quantum electrodynamics with multiple atomic levels,” Phys. Rev. A 84, 033843 (2011).
[Crossref]

T. Elsasser, B. Nagorny, and A. Hemmerich, “Optical bistability and collective behavior of atoms trapped in a high-Q ring cavity,” Phys. Rev. A 69, 033403 (2004).
[Crossref]

Phys. Rev. Lett. (8)

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and P. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref]

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

A. T. Black, H. W. Chan, and V. Vuletic, “Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering,” Phys. Rev. Lett. 91, 203001 (2003).
[Crossref]

J. Ye, D. W. Vernooy, and H. J. Kimble, “Trapping of single atoms in cavity QED,” Phys. Rev. Lett. 83, 4987–4990 (1999).
[Crossref]

K. J. Arnold, M. P. Baden, and M. D. Barrett, “Self-organization threshold scaling for thermal atoms coupled to a cavity,” Phys. Rev. Lett. 109, 153002 (2012).
[Crossref]

C. Emary and T. Brandes, “Quantum chaos triggered by precursors of a quantum phase transition: the Dicke model,” Phys. Rev. Lett. 90, 044101 (2003).
[Crossref]

M. P. Baden, K. J. Arnold, A. L. Grimsmo, S. Parkins, and M. D. Barrett, “Realization of the Dicke model using cavity-assisted Raman transitions,” Phys. Rev. Lett. 113, 020408 (2014).
[Crossref]

J. G. Bohnet, Z. Chen, J. M. Weiner, K. C. Cox, and J. K. Thompson, “Relaxation oscillations, stability, and cavity feedback in a superradiant Raman laser,” Phys. Rev. Lett. 109, 253602 (2012).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, “Dynamical phase transition in the open Dicke model,” Proc. Natl. Acad. Sci. USA 112, 3290–3295 (2015).
[Crossref]

Science (1)

H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in context,” Science 298, 1372–1377 (2002).
[Crossref]

Other (2)

J. Gelhausen, M. Buchhold, and P. Strack, “Many-body quantum optics with decaying atomic spin states:(γ, κ) Dicke model,” arXiv:1605.07637 (2016).

S. J. Masson, M. D. Barrett, and A. S. Parkins are preparing a manuscript to be called “Quantum spin-nematic squeezing via cavity-mediated spin-mixing dynamics in a spinor gas.”

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1.
Fig. 1.

(a) Experimental setup. Atoms in a high finesse cavity are driven from the side by two linearly polarized lasers with the electric fields along the axis of the cavity. A magnetic field of 0.225  mT is orthogonal to the cavity axis. (b) Spin-1 Dicke model scheme: each laser field provides a cavity-assisted Raman coupling between m states that can be described by the spin-1 ladder operators S±, as discussed in Section B.

Fig. 2.
Fig. 2.

(a) Experimental (b) and theoretical phase transition diagrams for the spin-1 Dicke system. The vertical axis of (a) and (b) represents the ratio of the coupling strengths (λ+/λ), and the horizontal axis represents the higher value of the coupling strength max{λ+,λ}. Red and yellow regions represent the normal and oscillatory superradiant states, respectively. White and gray regions represent trivial states in which all atoms are in |+1 or |1. Designation of states for the experimental results in (a) are based on the cavity output and its Fourier transform, as discussed in the text, and individual measurements are indicated by dots of the appropriate color. Theoretical results are based on the steady state of the system after a long integration time. In (c) and (d), representative cavity outputs (I)–(IV) are given for the corresponding locations indicated in (a) and (b). Note that the experimental outputs in (c) include the 200 μs time over which the power is ramped to its final value.

Equations (17)

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

H^=ωa^a^+ω0J^z+gc(a^J^++a^J^)+gp(a^J^+a^J^+),
ρ˙=i[H,ρ]+κ(2aρaaaρρaa),
H=ωaa+ω0Jz+λ2N(aJ++aJ)+λ+2N(aJ+aJ+).
J±=j=1NS±,j=j=1N2(|±1j0j|+|0j1j|),
Jz=j=1NSz,j=j=1N(|1j1j||1j1j|),
ω=(ωcω++ω2+ωd),
ω0=(ωz+ω+ω2),
λ±=2NgΩ±24Δ,
ωd=23Ng2Δ
Ω±=E±P3/22,3,3|r·σ^+|2S1/2,2,2.
δ±=ω±±ωz(ωc+ωd)=(ω±ω0).
γs=γa3Ω±2Δ2=96λ±2NCκ,
α˙=καiωαiλβiλ+β*,
β˙=iω0β+2iλαw+2iλ+α*w,
w˙=iλ(α*βαβ*)+iλ+(αβα*β*),
α=a2N,β=J2N,w=Jz2N.
(a+a)Jz(a+a)Jz,(a+a)J±(a+a)J±.

Metrics