Laser noise in cavity-optomechanical cooling and thermometry

We review and study the roles of quantum and classical fluctuations in recent cavity-optomechanical experiments which have now reached the quantum regime (mechanical phonon occupancy ?1) using resolved sideband laser cooling. In particular, both the laser noise heating of the mechanical resonator and the form of the optically transduced mechanical spectra, modified by quantum and classical laser noise squashing, are derived under various measurement conditions. Using this theory, we analyze recent ground-state laser cooling and motional sideband asymmetry experiments with nanoscale optomechanical crystal resonators.

[1]  T. Kippenberg,et al.  Electromechanically induced absorption in a circuit nano-electromechanical system , 2012, 1209.4470.

[2]  F. Khalili,et al.  Quantum back-action in measurements of zero-point mechanical oscillations , 2012, 1206.0793.

[3]  M. Gorodetsky,et al.  Phase noise measurement of external cavity diode lasers and implications for optomechanical sideband cooling of GHz mechanical modes , 2011, 1112.6277.

[4]  D. Bouwmeester,et al.  High finesse opto-mechanical cavity with a movable thirty-micron-size mirror. , 2006, Physical review letters.

[5]  M. Aspelmeyer,et al.  Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems , 2009, 0903.1637.

[6]  P. Hakonen,et al.  Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator , 2012, Nature.

[7]  H J Mamin,et al.  Feedback cooling of a cantilever's fundamental mode below 5 mK. , 2007, Physical review letters.

[8]  S. Girvin,et al.  Introduction to quantum noise, measurement, and amplification , 2008, 0810.4729.

[9]  C. Simon,et al.  Optomechanical entanglement in the presence of laser phase noise , 2011, 1106.0788.

[10]  Erik Lucero,et al.  Quantum ground state and single-phonon control of a mechanical resonator , 2010, Nature.

[11]  O. Arcizet,et al.  Optomechanical coupling in a two-dimensional photonic crystal defect cavity , 2010, CLEO: 2011 - Laser Science to Photonic Applications.

[12]  Oskar Painter,et al.  Optimized optomechanical crystal cavity with acoustic radiation shield , 2012, 1206.2099.

[13]  J. Teufel,et al.  Circuit cavity electromechanics in the strong-coupling regime , 2010, Nature.

[14]  S. Girvin,et al.  Single-photon optomechanics. , 2011, Physical review letters.

[15]  Oskar Painter,et al.  Proposal for an optomechanical traveling wave phonon–photon translator , 2010, 1009.3529.

[16]  Oskar Painter,et al.  Observation of quantum motion of a nanomechanical resonator. , 2012, Physical review letters.

[17]  T. Briant,et al.  Radiation-pressure cooling and optomechanical instability of a micromirror , 2006, Nature.

[18]  M. Aspelmeyer,et al.  Laser cooling of a nanomechanical oscillator into its quantum ground state , 2011, Nature.

[19]  P. M. Echternach,et al.  Nanomechanical measurements of a superconducting qubit , 2009, Nature.

[20]  Mika A. Sillanpää,et al.  Microwave amplification with nanomechanical resonators , 2011, Nature.

[21]  V. Aksyuk,et al.  Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator. , 2010, Nano letters.

[22]  C. Gardiner,et al.  Squeezing of intracavity and traveling-wave light fields produced in parametric amplification , 1984 .

[23]  T. Kippenberg,et al.  Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit , 2009 .

[24]  Hailin Wang,et al.  Resolved-sideband and cryogenic cooling of an optomechanical resonator , 2009 .

[25]  Reynaud,et al.  Quantum-noise reduction using a cavity with a movable mirror. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[26]  D. Stamper-Kurn,et al.  Optical detection of the quantization of collective atomic motion. , 2011, Physical review letters.

[27]  O. Arcizet,et al.  Resolved Sideband Cooling of a Micromechanical Oscillator , 2007, 0709.4036.

[28]  S. Deleglise,et al.  Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode , 2012, CLEO 2012.

[29]  Edith Innerhofer,et al.  An all-optical trap for a gram-scale mirror. , 2006, Physical review letters.

[30]  Qiang Lin,et al.  Supplementary Information for “ Electromagnetically Induced Transparency and Slow Light with Optomechanics ” , 2011 .

[31]  K. Vahala,et al.  A picogram- and nanometre-scale photonic-crystal optomechanical cavity , 2008, Nature.

[32]  Mohammad Hafezi,et al.  Slowing and stopping light using an optomechanical crystal array , 2010, 1006.3829.

[33]  S. Girvin,et al.  Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane , 2007, Nature.

[34]  Khaled Karrai,et al.  Cavity cooling of a microlever , 2004, Nature.

[35]  D. Meschede Optics, light and lasers , 2004 .

[36]  S. Gigan,et al.  Self-cooling of a micromirror by radiation pressure , 2006, Nature.

[37]  A. Clerk,et al.  Back-action evasion and squeezing of a mechanical resonator using a cavity detector , 2008, 0802.1842.

[38]  Max Ludwig,et al.  The optomechanical instability in the quantum regime , 2008, 0803.3714.

[39]  G. S. Agarwal,et al.  Electromagnetically induced transparency in mechanical effects of light , 2009, 0911.4157.

[40]  A. Lemaître,et al.  High frequency GaAs nano-optomechanical disk resonator. , 2010, Physical review letters.

[41]  D. Hunger,et al.  Realization of an optomechanical interface between ultracold atoms and a membrane. , 2011, Physical Review Letters.

[42]  P. Meystre,et al.  Laser phase noise effects on the dynamics of optomechanical resonators , 2010, 1011.0455.

[43]  Michael R. Vanner,et al.  Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity , 2009, 0901.1801.

[44]  Collett,et al.  Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation. , 1985, Physical review. A, General physics.

[45]  S. Girvin,et al.  Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities. , 2005, Physical review letters.

[46]  R. Griffiths,et al.  Quantum Measurements , 2021, Introduction to Quantum Mechanics.

[47]  J. B. Hertzberg,et al.  Preparation and detection of a mechanical resonator near the ground state of motion , 2009, Nature.

[48]  L. Diósi Laser linewidth hazard in optomechanical cooling , 2008, 0803.3760.

[49]  Carlton M. Caves,et al.  Quantum-Mechanical Radiation-Pressure Fluctuations in an Interferometer , 1980 .

[50]  K. Vahala,et al.  Optomechanical crystals , 2009, Nature.

[51]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[52]  S. Deléglise,et al.  Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode , 2011, Nature.

[53]  Phillips,et al.  Observation of quantized motion of Rb atoms in an optical field. , 1992, Physical review letters.

[54]  Wineland,et al.  Laser cooling to the zero-point energy of motion. , 1989, Physical review letters.

[55]  Oskar Painter,et al.  Coherent optical wavelength conversion via cavity optomechanics , 2012, Nature Communications.

[56]  J. Teufel,et al.  Measuring nanomechanical motion with a microwave cavity interferometer , 2008, 0801.1827.

[57]  Florian Marquardt,et al.  Quantum theory of cavity-assisted sideband cooling of mechanical motion. , 2007, Physical review letters.

[58]  A. B. Manukin,et al.  Measurement of Weak Forces in Physics Experiments , 1977 .

[59]  V. Sandberg,et al.  ON THE MEASUREMENT OF A WEAK CLASSICAL FORCE COUPLED TO A QUANTUM MECHANICAL OSCILLATOR. I. ISSUES OF PRINCIPLE , 1980 .

[60]  Mika A. Sillanpää,et al.  Microwave amplification with nanomechanical resonators , 2013, ISSCC.

[61]  T J Kippenberg,et al.  Theory of ground state cooling of a mechanical oscillator using dynamical backaction. , 2007, Physical review letters.

[62]  King,et al.  Resolved-sideband Raman cooling of a bound atom to the 3D zero-point energy. , 1995, Physical review letters.

[63]  T. Baehr‐Jones,et al.  Harnessing optical forces in integrated photonic circuits , 2008, Nature.

[64]  S. Deleglise,et al.  Optomechanically Induced Transparency , 2011 .

[65]  K. Vahala,et al.  Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction , 2006, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[66]  S. Girvin,et al.  Observability of radiation-pressure shot noise in optomechanical systems , 2010, 1004.3587.

[67]  D. Stamper-Kurn,et al.  Linear Amplifier Model for Optomechanical Systems , 2011, 1107.4813.

[68]  P. Rabl,et al.  Photon blockade effect in optomechanical systems. , 2011, Physical review letters.

[69]  J. Teufel,et al.  Sideband cooling of micromechanical motion to the quantum ground state , 2011, Nature.

[70]  S. Girvin,et al.  Cryogenic optomechanics with a Si3N4 membrane and classical laser noise , 2012, 1209.2730.

[71]  O Painter,et al.  An optical fiber-taper probe for wafer-scale microphotonic device characterization. , 2007, Optics express.

[72]  J. Teufel,et al.  Sideband cooling of micromechanical motion to the quantum ground state , 2011, Nature.

[73]  T. J. Kippenberg,et al.  Cavity-assisted backaction cooling of mechanical resonators , 2008, 0805.1431.

[74]  D. Vitali,et al.  Effect of phase noise on the generation of stationary entanglement in cavity optomechanics , 2011, 1106.0029.