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Register a new userStochastic Langevin propagation for classical and quantum optomechanics
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Interesting experimental signatures of quantum cavity optomechanics arise because the quantum back-action induces correlations between incident quantum shot noise and the cavity field. While the quantum linear theory of optomechanics (QLT) has provided vital understanding across many experimental platforms, in certain new set-ups it may be insufficient: analysis in the time domain may be needed, but QLT obtains only spectra in frequency space; and nonlinear behavior may be present. Direct solution of the stochastic equations of motion in time is an alternative, but unfortunately standard methods do not preserve the important optomechanical correlations. We introduce two-timescale stochastic Langevin (T2SL) propagation as an efficient and straightforward method to obtain time traces with the correct correlations. We show that T2SL, in contrast to standard stochastic simulations, can efficiently simulate correlation phenomena such as ponderomotive squeezing and reproduces accurately cavity sideband structures on the scale of the applied quantum noise and even complicated features entirely submerged below the quantum shot noise imprecision floor. We investigate nonlinear regimes and find where comparison is possible, that the method agrees with analytical results obtained with master equations at low temperatures and in perturbative regimes.
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Studying mechanical resonators via radiation pressure offers a rich avenue for the exploration of quantum mechanical behavior in a macroscopic regime. However, quantum state preparation and especially quantum state reconstruction of mechanical oscillators remains a significant challenge. Here we propose a scheme to realize quantum state tomography, squeezing and state purification of a mechanical resonator using short optical pulses. The scheme presented allows observation of mechanical quantum features despite preparation from a thermal state and is shown to be experimentally feasible using optical microcavities. Our framework thus provides a promising means to explore the quantum nature of massive mechanical oscillators and can be applied to other systems such as trapped ions.
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