Rapid cooling of a strain-coupled oscillator by optical phaseshift measurement

Abstract

We consider an optical probe that interacts with an ensemble of rare earth ions doping a materialin the shape of a cantilever. By optical spectral hole burning, the inhomogeneously broadenedtransition in the ions is prepared to transmit the probe field within a narrow window, but bendingof the cantilever causes strain in the material which shifts the ion resonances. The motion of thecantilever may thus be registered by the phase shift of the probe. By continuously measuringthe optical field we induce a rapid reduction of the position and momentum uncertainty of thecantilever. Doing so, the probing extracts entropy and thus effectively cools the thermal state ofmotion towards a known, conditional oscillatory motion with strongly reduced thermal fluctuations.Moreover, as the optical probe provides a force on the resonator proportional to its intensity, it ispossible to exploit the phase shift measurements in order to create an active feedback loop, whicheliminates the thermal fluctuations of the resonator. We describe this system theoretically, andprovide numerical simulations which demonstrate the rapid reduction in resonator position andmomentum uncertainty, as well as the implementation of the active cooling protocol.

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• Inhomogeneous response of an ion ensemble from mechanical stress
• Single-shot non-Gaussian Measurements for Optical Phase Estimation
• Precision measurements of electric-field-induced frequency displacements of an ultranarrow optical transition in ions in a solid
• Anomalous sub-kelvin thermal frequency shifts of ultra narrow-linewidth solid state emitters
• Multi-mode Heterodyne Laser Interferometry Realized via Software Defined Radio
• First-order thermal insensitivity of the frequency of a narrow spectral hole in a crystal
• Microscale crystalline rare-earth doped resonators for strain-coupled optomechanics
• Thermal-noise Limits to the Frequency Stability of Burned Spectral Holes
• Position- and momentum-squeezed quantum states in micro-scale mechanical resonators
• From Heat Capacity to Coherence in Ultra-Narrow-Linewidth Solid-State Optical Emitters at Sub-Kelvin Temperatures