Nonlinear atom-field dynamics in high-Q cavities: from a BEC to a thermal gas |
Optics Express, Vol. 19, Issue 12, pp. 11242-11255 (2011)
http://dx.doi.org/10.1364/OE.19.011242
Acrobat PDF (1583 KB)
Abstract
A cold gas of polarizable particles moving in the optical potential of a standing wave high finesse optical resonator acts as a dynamic refractive index. For a sufficiently strong cavity pump the optical forces generated by the intra cavity field perturb the particles phase space distribution, which shifts the optical resonance frequency and induces a nonlinear optical response. By help of the corresponding Vlasov equation we predict that beyond the known phenomenon of optical bi-stability one finds regions in parameter space, where no stable stationary solution exists. The atom field dynamics then exhibits oscillatory solutions converging to stable limit cycles of the system. The linearized analytical predictions agree well with corresponding numerical solutions of the full time dependent equations and first experimental observation in both cases.
© 2011 OSA
1. Introduction
1. D. Kruse, M. Ruder, J. Benhelm, C. von Cube, C. Zimmermann, P. W. Courteille, T. Elsässer, B. Nagorny, and A. Hemmerich, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 67, 051802 (2003). [CrossRef]
2. M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008). [CrossRef]
3. P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003). [CrossRef]
5. P. Domokos, P. Horak, and H. Ritsch, “Semiclassical theory of cavity-assisted atom cooling,” J. Phys. B 34, 187–198 (2001). [CrossRef]
6. J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped bose-einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009). [CrossRef]
7. S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009). [CrossRef]
8. T. Grießer, H. Ritsch, M. Hemmerling, and G. Robb, “A Vlasov approach to bunching and selfordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010). [CrossRef]
9. J. Javaloyes, M. Perrin, G. L. Lippi, and A. Politi, “Self-generated cooperative light emission induced by atomic recoil,” Phys. Rev. A 70, 023405 (2004). [CrossRef]
10. R. Bach, K. Burnett, M. d’Arcy, and S. Gardiner, “Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: application to the classical-like dynamics of quantum accelerator modes,” Phys. Rev. A 71, 33417 (2005). [CrossRef]
11. S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99, 213601 (2007). [CrossRef]
12. A. Vukics, W. Niedenzu, and H. Ritsch, “Cavity nonlinear optics with few photons and ultracold quantum particles,” Phys. Rev. A 79, 013828 (2009). [CrossRef]
13. F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008). [CrossRef] [PubMed]
14. D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009). [CrossRef]
3. Steady states
4. Stability analysis
4.1. Small Perturbation Analysis
4.2. Limit of zero temperature-BEC
16. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007). [CrossRef] [PubMed]
4.3. Thermal gas - classical limit
8. T. Grießer, H. Ritsch, M. Hemmerling, and G. Robb, “A Vlasov approach to bunching and selfordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010). [CrossRef]
4.4. Graphical solution of the stability problem
5. Long-time behavior
5.1. Classification
5.2. Limit cycles frequencies close to threshold
6. Conclusions and outlook
13. F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008). [CrossRef] [PubMed]
18. T. Valenzuela, M. Cristiani, H. Gothe, and J. Eschner, “Cold Ytterbium atoms in high-finesse optical cavities: cavity cooling and collective interactions,” in “Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe-EQEC 2009. European Conference on,” (IEEE, 2009), p. 1. [CrossRef]
7. S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009). [CrossRef]
7. Appendix: quantum and classical mean field limit
8. T. Grießer, H. Ritsch, M. Hemmerling, and G. Robb, “A Vlasov approach to bunching and selfordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010). [CrossRef]
Acknowledgments
References and links
1. | D. Kruse, M. Ruder, J. Benhelm, C. von Cube, C. Zimmermann, P. W. Courteille, T. Elsässer, B. Nagorny, and A. Hemmerich, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 67, 051802 (2003). [CrossRef] |
2. | M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008). [CrossRef] |
3. | P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003). [CrossRef] |
4. | P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997). [CrossRef] |
5. | P. Domokos, P. Horak, and H. Ritsch, “Semiclassical theory of cavity-assisted atom cooling,” J. Phys. B 34, 187–198 (2001). [CrossRef] |
6. | J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped bose-einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009). [CrossRef] |
7. | S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009). [CrossRef] |
8. | T. Grießer, H. Ritsch, M. Hemmerling, and G. Robb, “A Vlasov approach to bunching and selfordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010). [CrossRef] |
9. | J. Javaloyes, M. Perrin, G. L. Lippi, and A. Politi, “Self-generated cooperative light emission induced by atomic recoil,” Phys. Rev. A 70, 023405 (2004). [CrossRef] |
10. | R. Bach, K. Burnett, M. d’Arcy, and S. Gardiner, “Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: application to the classical-like dynamics of quantum accelerator modes,” Phys. Rev. A 71, 33417 (2005). [CrossRef] |
11. | S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99, 213601 (2007). [CrossRef] |
12. | A. Vukics, W. Niedenzu, and H. Ritsch, “Cavity nonlinear optics with few photons and ultracold quantum particles,” Phys. Rev. A 79, 013828 (2009). [CrossRef] |
13. | F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008). [CrossRef] [PubMed] |
14. | D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009). [CrossRef] |
15. | D. C. Montgomery, Theory of the unmagnetized plasma (Gordon & Breach, 1971). |
16. | F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007). [CrossRef] [PubMed] |
17. | M. Cristiani and J. Eschner (personal communication, 2011). |
18. | T. Valenzuela, M. Cristiani, H. Gothe, and J. Eschner, “Cold Ytterbium atoms in high-finesse optical cavities: cavity cooling and collective interactions,” in “Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe-EQEC 2009. European Conference on,” (IEEE, 2009), p. 1. [CrossRef] |
OCIS Codes
(190.1450) Nonlinear optics : Bistability
(270.3100) Quantum optics : Instabilities and chaos
ToC Category:
Quantum Optics
History
Original Manuscript: January 19, 2011
Revised Manuscript: March 14, 2011
Manuscript Accepted: March 14, 2011
Published: May 25, 2011
Citation
Tobias Grießer and Helmut Ritsch, "Nonlinear atom-field dynamics in high-Q cavities: from a BEC to a thermal gas," Opt. Express 19, 11242-11255 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11242
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References
- D. Kruse, M. Ruder, J. Benhelm, C. von Cube, C. Zimmermann, P. W. Courteille, T. Elsässer, B. Nagorny, and A. Hemmerich, “Cold atoms in a high-Q ring cavity,” Phys. Rev. A 67, 051802 (2003). [CrossRef]
- M. Khudaverdyan, W. Alt, I. Dotsenko, T. Kampschulte, K. Lenhard, A. Rauschenbeutel, S. Reick, K. Schörner, A. Widera, and D. Meschede, “Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator,” New J. Phys. 10, 073023 (2008). [CrossRef]
- P. Domokos and H. Ritsch, “Mechanical effects of light in optical resonators,” J. Opt. Soc. Am. B 20, 1098–1130 (2003). [CrossRef]
- P. Horak, G. Hechenblaikner, K. M. Gheri, H. Stecher, and H. Ritsch, “Cavity-induced atom cooling in the strong coupling regime,” Phys. Rev. Lett. 79, 4974–4977 (1997). [CrossRef]
- P. Domokos, P. Horak, and H. Ritsch, “Semiclassical theory of cavity-assisted atom cooling,” J. Phys. B 34, 187–198 (2001). [CrossRef]
- J. M. Zhang, F. C. Cui, D. L. Zhou, and W. M. Liu, “Nonlinear dynamics of a cigar-shaped bose-einstein condensate in an optical cavity,” Phys. Rev. A 79, 033401 (2009). [CrossRef]
- S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, and T. Esslinger, “Dynamical coupling between a Bose–Einstein condensate and a cavity optical lattice,” Appl. Phys. B 95, 213–218 (2009). [CrossRef]
- T. Grießer, H. Ritsch, M. Hemmerling, and G. Robb, “A Vlasov approach to bunching and selfordering of particles in optical resonators,” Eur. Phys. J. D 58, 349–368 (2010). [CrossRef]
- J. Javaloyes, M. Perrin, G. L. Lippi, and A. Politi, “Self-generated cooperative light emission induced by atomic recoil,” Phys. Rev. A 70, 023405 (2004). [CrossRef]
- R. Bach, K. Burnett, M. d’Arcy, and S. Gardiner, “Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: application to the classical-like dynamics of quantum accelerator modes,” Phys. Rev. A 71, 33417 (2005). [CrossRef]
- S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, “Cavity nonlinear optics at low photon numbers from collective atomic motion,” Phys. Rev. Lett. 99, 213601 (2007). [CrossRef]
- A. Vukics, W. Niedenzu, and H. Ritsch, “Cavity nonlinear optics with few photons and ultracold quantum particles,” Phys. Rev. A 79, 013828 (2009). [CrossRef]
- F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose–Einstein condensate,” Science 322, 235–238 (2008). [CrossRef] [PubMed]
- D. Nagy, P. Domokos, A. Vukics, and H. Ritsch, “Nonlinear quantum dynamics of two BEC modes dispersively coupled by an optical cavity,” Eur. Phys. J. D 55, 659–668 (2009). [CrossRef]
- D. C. Montgomery, Theory of the unmagnetized plasma (Gordon & Breach, 1971).
- F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose–Einstein condensate,” Nature 450, 268–271 (2007). [CrossRef] [PubMed]
- M. Cristiani and J. Eschner (personal communication, 2011).
- T. Valenzuela, M. Cristiani, H. Gothe, and J. Eschner, “Cold Ytterbium atoms in high-finesse optical cavities: cavity cooling and collective interactions,” in “Lasers and Electro-Optics 2009 and the European Quantum Electronics Conference. CLEO Europe-EQEC 2009. European Conference on ,” (IEEE, 2009), p. 1. [CrossRef]
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