Direct measurement of optical-trap-induced decoherence

Abstract

Thermal decoherence is a major obstacle to the realization of quantum coherence for massive mechanical oscillators. Although optical trapping has been used to reduce the thermal decoherence rate for such oscillators, it also increases the rate by subjecting the oscillator to stochastic forces resulting from the frequency fluctuations of the optical field, thereby setting a fundamental limit on the reduction. This is analogous to the noise penalty in an active feedback system. Here, we directly measure the rethermalizaton process for an initially cooled and optically trapped suspended mirror, and identify the current limiting decoherence rate as due to the optical trap. Our experimental study of the trap-induced decoherence rate will enable future advances in the probing of fundamental quantum mechanics in the bad cavity regime, such as testing of deformed commutators. Introduction.-Various types of optical potentials have been used to change the dynamics of mechanical systems, including atoms, thin membranes and suspended mirrors in order to, e.g. observe signatures of shot-noise radiation-pressure fluctuations [1], enhance the quality factor of the system [2], and improve the sensitivity of gravitational-wave detectors [3][4][5][6]. Since an optical potential works as an ideal spring for the trapped mode in terms of energy dissipation, it can reduce the number of quanta in the mode (the so-called "optical dilution" effect) so that even a low-frequency massive oscillator will exhibit quantum behavior [7]. Progress towards this quantum regime is underway [2,[8][9][10] in the field of cavity optomechanics [11] particularly in the bad cavity regime, where the optical linewidth is broader than that of the mechanical resonance. Although the bad cavity condition is often not promising in terms of coherence because of the slow mechanical oscillation, it enables us to detect gravitational-waves [12], and potentially to probe deformed commutators [13,14], generate entangled states [15][16][17], and test wavefunction collapse models [18][19][20][21][22].

Demonstration of Displacement Sensing of a mg-Scale Pendulum for mm- and mg-Scale Gravity Measurements

“…A few experiments involving displacement sensing of a mg-scale oscillator have been carried out so far in the field of the gravitational-wave detectors [24][25][26]. However, to the best of our knowledge, no experiment exists which has sufficient sensitivity to resolve the effect of gravity of the mg-and mm-scale.…”

“…( 1) for an integration time of one second. Our displacement sensor is an optical ring cavity with a movable planar end mirror, which was initially constructed for the purpose of realizing active feedback cooling of a movable mirror [26], based on the technology of gravitational-wave detectors [24]. All of the applications for active feedback cooling, measuring gravity, and measuring gravitational-waves rely on sensitive displacement measurements, and hence our approach is a top-down approach for both gravity measurements and quantum experiments.…”

“…Based on the analysis of transfer functions of the optomechanical system as in Ref. [26], we obtained a voltage-to-displacement conversion factor of 2 × 10 −10 m/V, allowing us to analyze the displacement of the movable mirror by monitoring the intensity of the cavity output. In addition, we apply active feedback cooling to the system in order to prevent instability due to the negative value of the optically trapped COM's dissipation rate.…”

Conditional mechanical squeezing of a macroscopic pendulum near quantum regimes

“…1 (a). Laser light enters the cavity and receives an intensity shift proportional to the mechanical position, which is read out via direct photo detection and fed back to the pendulum for cooling [40]. We analyze the following linearized Hamiltonian in a rotating frame at the laser frequency ω…”

“…Main data in the time domain.-The main data was measured with an incident laser power of 30 mW and it is calibrated to displacement (the calibration factor is −2.3(4) × 10 −10 m/V) based on a transfer function analysis [36,40,44]. The cavity length was detuned from resonance such that the pendulum's resonance (ω m /2π) increases to 280 (7) Hz, leading to a mean value of the detuning of roughly 0.03 × κ or 1.2 × κ, because of the nonlinearity in Eq.…”