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...

Cavity optomechanics offers powerful methods for controlling optical fields and mechanical motion. A number of proposals have predicted that this control can be extended considerably in devices where multiple cavity modes couple to each other via the motion of a single mechanical oscillator. Here we study the dynamic properties of such a multimode optomechanical device, in which the coupling between cavity modes results from mechanically induced avoided crossings in the cavity's spectrum. Near the avoided crossings we find that the optical spring shows distinct features that arise from the interaction between cavity modes. Precisely at an avoided crossing, we show that the particular form of the optical spring provides a classical analogue of a quantum non-demolition measurement of the intracavity photon number. The mechanical oscillator's Brownian motion, an important source of noise in these measurements, is minimized by operating the device at cryogenic temperature (500 mK).

We demonstrate a cryogenic optomechanical system comprising a flexible Si 3 N 4 membrane placed at the center of a free-space optical cavity in a 400 mK cryogenic environment. We observe a mechanical quality factor Q > 4 × 10 6 for the 261 kHz fundamental drum-head mode of the membrane, and a cavity resonance halfwidth of 60 kHz. The optomechanical system therefore operates in the resolved sideband limit. We monitor the membrane's thermal motion using a heterodyne optical circuit capable of simultaneously measuring both of the mechanical sidebands, and find that the observed optical spring and damping quantitatively agree with theory. The mechanical sidebands exhibit a Fano lineshape, and to explain this we develop a theory describing heterodyne measurements in the presence of correlated classical laser noise. Finally, we 4 These authors contributed equally to this work.

No abstract

No abstract