We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.Comment: 4 pages, 3 figure
Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady states of the mechanical oscillator when multiphoton transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.
We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong laser drive is detuned by half the mechanical frequency, optomechanically induced transparency also occurs due to resonant two-photon processes. The cavity response to a second probe drive is in this case nonlinear in the probe power. These effects should be observable with optomechanical coupling strengths that have already been realized in experiments.
We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator's mean phonon numbern is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 ± 0.22 (corresponding to a mode temperature T = 28 ± 7 μK). We also infern from the calibrated area of each of the two sidebands, and from the oscillator's total damping. The values ofn inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator's temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator. Cavity optomechanical systems operating in the quantum regime are expected to play an important role in advancing the control of electromagnetic fields and mechanical oscillators, interfacing disparate quantum systems, detecting gravitational waves, constraining modifications to orthodox quantum mechanics, and testing hypotheses about quantum gravity [1][2][3][4][5][6][7][8][9][10][11]. The utility of optomechanical systems in these areas reflects their particular combination of long relaxation times, unitary coupling to electromagnetic fields in the microwave and near-infrared domains, and access to the quantum behavior of massive objects.Optomechanical experiments have been based primarily on systems in which the mechanical oscillator and the cavity field are prepared in Gaussian states, couple weakly to each other at the quantum level (i.e., the bare optomechanical coupling rate g 0 is much less than the oscillator frequency ω m and the cavity damping rate κ), and are probed via linear measurements of the fields leaving the cavity. (Some optomechanics experiments have demonstrated nonlinear measurements of the cavity fields [12,13], although without resolving non-Gaussian behavior.) Within this paradigm of Gaussian states, weak coupling, and linear measurements, quantum effects can manifest themselves as apparent fluctuations of quantities which, according to classical mechanics, could be noiseless [14]. Depending on the specific type of measurement, these quantum fluctuations may be ascribed to the cavity field, the mechanical oscillator, or both [15,16].One such experiment is a heterodyne measurement of the light leaving an optomechanical cavity that is driven on resonance by a single laser. Classically, the thermal motion of the mechanical oscillator inside the cavity adds modulation sidebands to the laser beam. In the spectrum of the heterodyne signal, the area of these sidebands will be equal, and will be proportional to the oscillator's temperature.In the quantum treatment described in Refs. [15,16] of the same measurement, the heterodyne spectrum arises from four distinct c...
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