Laser theory for optomechanics: Limit cycles in the quantum regime

Physical Review X

Volumn 4, Issue 1, 2014, Pages

  Lörch, Niels ^a,b   Qian, Jiang ^c   Clerk, Aashish ^d   Marquardt, Florian ^e,f   Hammerer, Klemens ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^c UNIVERSITY OF MUNICH   (Germany)

^d MCGILL UNIVERSITY   (Canada)

^e UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^f MAX PLANCK INSTITUTE FOR THE SCIENCE OF LIGHT   (Germany)

Author keywords

Nanophysics; Quantum physics

Indexed keywords

MONTE CARLO METHODS; QUANTUM ELECTRONICS;

MASTER EQUATIONS; MECHANICAL RESONATORS; NANOPHYSICS; NUMERICAL SOLUTION; OPTO-MECHANICAL SYSTEMS; QUANTUM PHYSICS; STRONG-COUPLING REGIME; WIGNER FUNCTIONS;

LASER THEORY;

EID: 84900341620     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.011015     Document Type: Article

References (57)

1. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity Optomechanics, arXiv:1303.0733.
2. P. Meystre, A Short Walk through Quantum Optomechanics, Ann. Phys. (Berlin) 525, 215 (2013).
3. Y. Chen, Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics, J. Phys. B 46, 104001 (2013).
4. J. D. Teufel, T. Donner, D. Li, J.W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K.W. Lehnert, and R.W. Simmonds, Sideband Cooling of Micromechanical Motion to the Quantum Ground State, Nature (London) 475, 359 (2011).
5. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, Laser Cooling of a Nanomechanical Oscillator into Its Quantum Ground State, Nature (London) 478, 89 (2011).
6. D.W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, Non-classical Light Generated by Quantum-Noise-Driven Cavity Optomechanics, Nature (London) 488, 476 (2012).
7. A. H. Safavi-Naeini, S. Groeblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Squeezing of Light via Reflection from a Silicon Micromechanical Resonator, arXiv:1302.6179.
8. K.W. Murch, K. L. Moore, S. Gupta, and D. M. Stamper-Kurn, Observation of Quantum-Measurement Backaction with an Ultracold Atomic Gas, Nat. Phys. 4, 561 (2008).
9. T. P. Purdy, R.W. Peterson, and C. A. Regal, Observation of Radiation Pressure Shot Noise on a Macroscopic Object, Science 339, 801 (2013).
10. T. A. Palomaki, J.W. Harlow, J. D. Teufel, R.W. Simmonds, and K.W. Lehnert, Coherent State Transfer between Itinerant Microwave Fields and a Mechanical Oscillator, Nature (London) 495, 210 (2013).
11. T. A. Palomaki, J. D. Teufel, R.W. Simmonds, and K.W. Lehnert, Entangling Mechanical Motion with Microwave Fields, Science 342, 710 (2013).
12. S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, Quantum Entanglement and Teleportation in Pulsed Cavity Optomechanics, Phys. Rev. A 84, 052327 (2011).
13. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity, Phys. Rev. Lett. 95, 033901 (2005).
14. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Temporal Behavior of Radiation-Pressure-Induced Vibrations of an Optical Microcavity Phonon Mode, Phys. Rev. Lett. 94, 223902 (2005).
15. M. Ludwig, C. Neuenhahn, C. Metzger, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Self-Induced Oscillations in an Optomechanical System Driven by Bolometric Backaction, Phys. Rev. Lett. 101, 133903 (2008).
16. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E.M. Weig, J. P. Kotthaus, and T. J. Kippenberg, Near-Field Cavity Optomechanics with Nanomechanical Oscillators, Nat. Phys. 5, 909 (2009).
17. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, Phonon Laser Action in a Tunable Two-Level System, Phys. Rev. Lett. 104, 083901 (2010).
18. S. Zaitsev, A. K. Pandey, O. Shtempluck, and E. Buks, Forced and Self-Excited Oscillations of an Optomechanical Cavity, Phys. Rev. E 84, 046605 (2011).
19. F. Marquardt, J. G. E. Harris, and S. M. Girvin, Dynamical Multistability Induced by Radiation Pressure in High-Finesse Micromechanical Optical Cavities, Phys. Rev. Lett. 96, 103901 (2006).
20. S. Zaitsev, O. Gottlieb, and E. Buks, Nonlinear Dynamics of a Microelectromechanical Mirror in an Optical Resonance Cavity, Nonlinear Dynamics 69, 1589 (2012).
21. J. B. Khurgin, M.W. Pruessner, T. H. Stievater, and W. S. Rabinovich, Laser-Rate-Equation Description of Optomechanical Oscillators, Phys. Rev. Lett. 108, 223904 (2012).
22. J. B. Khurgin, M.W. Pruessner, T. H. Stievater, and W. S. Rabinovich, Optically Pumped Coherent Mechanical Oscillators: The Laser Rate Equation Theory and Experimental Verification, New J. Phys. 14, 105022 (2012).
23. M. Ludwig, B. Kubala, and F. Marquardt, The Optomechanical Instability in the Quantum Regime, New J. Phys. 10, 095013 (2008).
24. K. J. Vahala, Back-action Limit of Linewidth in an Optomechanical Oscillator, Phys. Rev. A 78, 023832 (2008).
25. D. A. Rodrigues and A. D. Armour, Amplitude Noise Suppression in Cavity-Driven Oscillations of a Mechanical Resonator, Phys. Rev. Lett. 104, 053601 (2010).
26. A. D. Armour and D. A. Rodrigues, Quantum Dynamics of a Mechanical Resonator Driven by a Cavity, C.R. Phys. 13, 440 (2012).
27. J. Qian, A. A. Clerk, K. Hammerer, and F. Marquardt, Quantum Signatures of the Optomechanical Instability, Phys. Rev. Lett. 109, 253601 (2012).
28. P. D. Nation, Nonclassical Mechanical States in an Optomechanical Micromaser Analogue, Phys. Rev. A 88, 053828 (2013).
29. M. Dykman and M. Krivoglatz, Spectral Distribution of Nonlinear Oscillators with Nonlinear Friction Due to a Medium, Phys. Status Solidi B 68, 111 (1975).
30. M. Lax, Classical Noise. V. Noise in Self-Sustained Oscillators, Phys. Rev. 160, 290 (1967).
31. F. Haake and M. Lewenstein, Adiabatic Expansion for the Single-Mode Laser, Phys. Rev. A 27, 1013 (1983).
32. C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics, Springer Series in Synergetics (Springer, New York, 2004).
33. J. B. Khurgin, Phonon Lasers Gain a Sound Foundation, Physics 3, 16 (2010).
34. P. Rabl, Photon Blockade Effect in Optomechanical Systems, Phys. Rev. Lett. 107, 063601 (2011).
35. A. Nunnenkamp, K. Børkje, and S.M. Girvin, Single-Photon Optomechanics, Phys. Rev. Lett. 107, 063602 (2011).
36. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction, Phys. Rev. Lett. 99, 093901 (2007).
37. F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion, Phys. Rev. Lett. 99, 093902 (2007).
38. m for an oscillator of mass m.
39. G. D. Mahan, Many-Particle Physics, Physics of Solids and Liquids (Springer, New York, 2000).
40. P. D. Drummond and D. F. Walls, Quantum Theory of Optical Bistability. I. Nonlinear Polarisability Model, J. Phys. A 13, 725 (1980).
41. A. Mari and J. Eisert, Gently Modulating Optomechanical Systems, Phys. Rev. Lett. 103, 213603 (2009).
42. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Ground-State Cooling of a Micromechanical Oscillator: Comparing Cold Damping and Cavity-Assisted Cooling Schemes, Phys. Rev. A 77, 033804 (2008).
43. R. Ghobadi, A. R. Bahrampour, and C. Simon, Quantum Optomechanics in the Bistable Regime, Phys. Rev. A 84, 033846 (2011).
44. S. Aldana, C. Bruder, and A. Nunnenkamp, On the Equivalence between an Optomechanical System and a Kerr Medium, Phys. Rev. A 88, 043826 (2013).
45. G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, Collective Dynamics in Optomechanical Arrays, Phys. Rev. Lett. 107, 043603 (2011).
46. Y. M. Golubev and I. V. Sokolov, Photon Antibunching in a Coherent Light Source and Suppression of the Photorecording Noise, J. Exp. Theor. Phys. 60, 234 (1984).
47. Y. M. Golubev, Excitation of the Active Medium of a Micromaser by Light from a Sub-Poissonian Optical Laser, J. Exp. Theor. Phys. 80, 212 (1995).
48. J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H. J. Kimble, Experimental Realization of a One-Atom Laser in the Regime of Strong Coupling, Nature (London) 425, 268 (2003).
49. S. Y. Kilin and A. B. Mikhalychev, Single-Atom Laser Generates Nonlinear Coherent States, Phys. Rev. A 85, 063817 (2012).
50. J. Dalibard, Y. Castin, and K. Mølmer, Wave-Function Approach to Dissipative Processes in Quantum Optics, Phys. Rev. Lett. 68, 580 (1992).
51. R. Dum, P. Zoller, and H. Ritsch, Monte Carlo Simulation of the Atomic Master Equation for Spontaneous Emission, Phys. Rev. A 45, 4879 (1992).
52. K. Mølmer, Y. Castin, and J. Dalibard, Monte Carlo Wave-Function Method in Quantum Optics, J. Opt. Soc. Am. B 10, 524 (1993).
53. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An Open-Source Python Framework for the Dynamics of Open Quantum Systems, Comput. Phys. Commun. 183, 1760 (2012).
54. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python Framework for the Dynamics of Open Systems, Comput. Phys. Commun. 184, 1234 (2013).
55. T. E. Oliphant, Python for Scientific Computing, Comput. Sci. Eng. 9, 10 (2007).
56. S. M. Barnett and P. L. Knight, Dissipation in a Fundamental Model of Quantum Optical Resonance, Phys. Rev. A 33, 2444 (1986).
57. J. I. Cirac, Interaction of a Two-Level Atom with a Cavity Mode in the Bad-Cavity Limit, Phys. Rev. A 46, 4354 (1992).