Multi-phonon relaxation and generation of quantum states in a nonlinear mechanical oscillator

New Journal of Physics

Volumn 15, Issue , 2013, Pages

  Voje, A ^a   Croy, A ^a   Isacsson, A ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ANHARMONIC OSCILLATORS; DISSIPATIVE QUANTUM DYNAMICS; MACROSCOPIC SUPERPOSITION STATE; MECHANICAL OSCILLATORS; NANOMECHANICAL SYSTEMS; QUANTUM OSCILLATORS; THERMAL EXCITATION; ZERO TEMPERATURES;

MECHANICAL ENGINEERING; OSCILLATORS (MECHANICAL); OSCILLISTORS; PHONONS; RELAXATION OSCILLATORS;

QUANTUM THEORY;

EID: 84879028923     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/15/5/053041     Document Type: Article

References (40)

1. Poot M and van der Zant H S J 2012 Mechanical systems in the quantum regime Phys. Rep. 511 273-335
2. O'Connell A D et al 2010 Quantum ground state and single-phonon control of a mechanical resonator Nature 464 697-703
3. Teufel J D, Donner T, Li D, Harlow J W, Allman M S, Cicak K, Sirois A J, Whittaker J D, Lehnert K W and Simmonds R W 2011 Sideband cooling of micromechanical motion to the quantum ground state Nature 475 359-63
4. Chan J, Alegre T P M, Safavi-Naeini A H, Hill J T, Krause A, Gröblacher S, Aspelmeyer M and Painter O 2011 Laser cooling of a nanomechanical oscillator into its quantum ground state Nature 478 89-92
5. Voje A, Kinaret J M and Isacsson A 2012 Generating macroscopic superposition states in nanomechanical graphene resonators Phys. Rev. B 85 205415
6. Rips S, Kiffner M, Wilson-Rae I and Hartmann M J 2012 Steady-state negative Wigner functions of nonlinear nanomechanical oscillators New J. Phys. 14 023042
7. Atalaya J, Isacsson A and Kinaret J M 2008 Continuum elastic modeling of graphene resonators Nano Lett. 8 4196-200
8. Zwanzig R 1973 Nonlinear generalized Langevin equations J. Stat. Phys. 9 215-20
9. Lindenberg K and Seshadri V 1981 Dissipative contributions of internal multiplicative noise: I. Mechanical oscillator Physica A 109 483-99
10. Dykman M and Krivoglaz M 1984 Theory of nonlinear oscillator interacting with a medium Sov. Sci. Rev. A 5 265-441
11. Zaitsev S, Shtempluck O, Buks E and Gottlieb O 2012 Nonlinear damping in a micromechanical oscillator Nonlinear Dyn. 67 859-83
12. Eichler A, Moser J, Chaste J, Zdrojek M, Wilson-Rae I and Bachtold A 2011 Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene Nature Nanotechnol. 6 339-42
13. Croy A, Midtvedt D, Isacsson A and Kinaret J M 2012 Nonlinear damping in graphene resonators Phys. Rev. B 86 235435
14. Simaan H D and Loudon R 1978 Off-diagonal density matrix for single-beam two-photon absorbed light J. Phys. A: Math. Gen. 11 435
15. Gilles L and Knight P L 1993 Two-photon absorption and nonclassical states of light Phys. Rev. A 48 1582-93
16. Gilles L, Garraway B M and Knight P L 1994 Generation of nonclassical light by dissipative two-photon processes Phys. Rev. A 49 2785-99
17. Loudon R 1984 Squeezing in resonance fluorescence Opt. Commun. 49 24-8 (Pubitemid 14553757)
18. Everitt M J, Spiller T P, Milburn G J, Wilson R D and Zagoskin A M 2012 Cool for cats arXiv:1212.4795
19. Shen Y R 1967 Quantum statistics of nonlinear optics Phys. Rev. 155 921-31
20. Nunnenkamp A, Børkje K, Harris J G E and Girvin S M 2010 Cooling and squeezing via quadratic optomechanical coupling Phys. Rev. A 82 021806
21. Wangsness R K and Bloch F 1953 The dynamical theory of nuclear induction Phys. Rev. 89 728-39
22. Bloch F 1957 Generalized theory of relaxation Phys. Rev. 105 1206-22
23. Redfield A G 1965 The theory of relaxation processes Adv. Magn. Reson. 1 1
24. Glauber R J 1963 Coherent and incoherent states of the radiation field Phys. Rev. 131 2766-88
25. Yurke B and Stoler D 1986 Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion Phys. Rev. Lett. 57 13-6
26. Breuer H P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
27. Dykman M 2012 private communication
28. Gardiner C W and Zoller P 2004 Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Berlin: Springer)
29. Milburn G J and Holmes C A 1986 Dissipative quantum and classical Liouville mechanics of the anharmonic oscillator Phys. Rev. Lett. 56 2237-40
30. Phoenix S J D 1990 Wave-packet evolution in the damped oscillator Phys. Rev. A 41 5132-8
31. Moya-Cessa H 2006 Decoherence in atom-field interactions: a treatment using superoperator techniques Phys. Rep. 432 1-41 (Pubitemid 44313499)
32. Walls D F and Drummond P D 1980 Quantum theory of optical bistability: I. Nonlinear polarisability model J. Phys. A: Math. Gen. 13 725-41
33. Landauer R 1962 Fluctuations in bistable tunnel diode circuits J. Appl. Phys. 33 2209-16
34. Haken H 1974 Exact stationary solution of the master equation for systems far from thermal equilibrium in detailed balance Phys. Lett. A 46 443-4
35. Haag G and Hänggi P 1979 Exact solutions of discrete master equations in terms of continued fractions Z. Phys. B 34 411-7
36. Dodonov V V and Mizrahi S S 1997 Exact stationary photon distributions due to competition between one- and two-photon absorption and emission J. Phys. A: Math. Gen. 30 5657 (Pubitemid 127112256)
37. Weisstein E W 2003 CRC Concise Encyclopedia of Mathematics (London: Chapman and Hall)
38. Schleich W P 2001 Quantum Optics in Phase Space (Berlin: Wiley-VCH)
39. Lifshitz R and Cross M C 2008 Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators (New York: Wiley-VCH) chapter 1
40. Abramowitz M and Stegun I A 1965 Handbook of Mathematical Functions (New York: Dover)