Standard Quantum Limit for Probing Mechanical Energy Quantization

Abstract

We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a strong-coupling regime -- the decay rate of external degrees of freedom is smaller than the parametric coupling rate. In the case for cavity-assisted optomechanical systems, e.g. the one proposed by Thompson et al., zero-point motion of the mechanical oscillator needs to be comparable to linear dynamical range of the optical system which is characterized by the optical wavelength divided by the cavity finesse.

4 pages, 2 figures. Accepted by Phys. Rev. Lett

References in corpus (27)

• Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
• Optomechanical entanglement between a movable mirror and a cavity field
• Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
• Theory of ground state cooling of a mechanical oscillator using dynamical back-action
• Radiation-pressure cooling and optomechanical instability of a micro-mirror
• Self-cooling of a micro-mirror by radiation pressure
• Resolving photon number states in a superconducting circuit
• Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
• Cooling of a micro-mechanical oscillator using radiation pressure induced dynamical back-action
• Cooling a nanomechanical resonator with quantum back-action
• Cooling of a mirror by radiation pressure
• Dispersive optomechanics: a membrane inside a cavity
• Feedback cooling of a cantilever's fundamental mode below 5 mK
• An all-optical trap for a gram-scale mirror
• Optomechanical Cooling of a Macroscopic Oscillator by Homodyne Feedback
• Steady state entanglement in the mechanical vibrations of two dielectric membranes
• Quantum Noise Interference and Back-action Cooling in Cavity Nanomechanics
• Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK
• Optomechanical trapping and cooling of partially transparent mirrors
• Trapping and Cooling a mirror to its quantum mechanical ground state
• Scheme for teleportation of quantum states onto a mechanical resonator
• Using a qubit to measure photon number statistics of a driven, thermal oscillator
• Entanglement of macroscopic test masses and the Standard Quantum Limit in laser interferometry
• A Quantum Non-demolition measurement of Fock states of mesoscopic mechanical oscillators
• Continous Measurement of the Energy Eigenstates of a Nanomechanical Resonator without a Non-Demolition Probe
• Measurement of energy eigenstates by a slow detector
• Quantum limits and symphotonic states in free-mass gravitational-wave antennae

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