Optomechanical systems, in which light drives and is affected by the motion of a massive object, will comprise a new framework for nonlinear quantum optics, with applications ranging from the storage and transduction of quantum information to enhanced detection sensitivity in gravitational wave detectors. However, quantum optical effects in optomechanical systems have remained obscure, because their detection requires the object’s motion to be dominated by vacuum fluctuations in the optical radiation pressure; so far, direct observations have been stymied by technical and thermal noise. Here we report an implementation of cavity optomechanics using ultracold atoms in which the collective atomic motion is dominantly driven by quantum fluctuations in radiation pressure. The back-action of this motion onto the cavity light field produces ponderomotive squeezing. We detect this quantum phenomenon by measuring sub-shot-noise optical squeezing. Furthermore, the system acts as a low-power, high-gain, nonlinear parametric amplifier for optical fluctuations, demonstrating a gain of 20 dB with a pump corresponding to an average of only seven intracavity photons. These findings may pave the way for low-power quantum optical devices, surpassing quantum limits on position and force sensing, and the control and measurement of motion in quantum gases.

We present an atom-chip-based realization of quantum cavity optomechanics with cold atoms localized within a Fabry-Perot cavity. Effective sub-wavelength positioning of the atomic ensemble allows for tuning the linear and quadratic optomechanical coupling parameters, varying the sensitivity to the displacement and strain of a compressible gaseous cantilever. We observe effects of such tuning on cavity optical nonlinearity and optomechanical frequency shifts, providing their first characterization in the quadratic-coupling regime.Experimental realizations of cavity optomechanics, wherein the motion of a mechanically compliant cantilever is measured by its interaction with an electromagnetic resonator, serve as paradigms for understanding open quantum systems and the limits of quantum measurement [1]. In most realizations, cavity optomechanical phenomena, such as optical cooling [2][3][4][5] and confinement [6,7] of the cantilever or optical nonlinearity [8,9] and squeezing [10,11], arise from the dominant linear coupling between cavity photons and the cantilever position. Recent experiments on thin SiN membranes positioned within a Fabry-Perot cavity [12,13] have highlighted the new capabilities afforded by quadratic optomechanical coupling, such as measurement of the cantilever energy and of phonon shot noise [14].Here, we demonstrate a tunable cavity optomechanical system constructed by integrating a microfabricated atom chip with a Fabry-Perot optical resonator. We tune the optomechanical sensitivity to the displacement and the strain of an atomic ensemble, arising from linear and quadratic optomechanical coupling, respectively, by positioning cold atoms with nm-scale precision within the resonator mode. The ensemble thereby serves as the quantum analogue of the SiN membranes used in recent experiments [12,13]. We study effects of tunable coupling on optomechanical bistability and the optomechanical frequency shift, providing the first characterization of optomechanical effects in the quadratic-coupling regime. The agreement between our measurements and theory establishes the equivalence of cavity optomechanical systems using either solid-or gas-phase cantilevers.We begin by adapting recent theoretical descriptions of cavity optomechanics using cold atoms [15] to highlight the new capabilities presented in this work. Consider the motion of N identical atoms along the axis (ẑ) of a FabryPerot optical resonator and confined within a harmonic potential with mechanical frequency ω z and centered at position z 0 . The interaction of atom i at z i = z 0 + δz i with the cavity field is characterized by the angular frequency g(z i ) = g 0 sin(φ 0 + k p δz i ), where φ 0 = k p z 0 , k p is the resonant cavity wavevector and g 0 is determined by the cavity mode volume, the optical frequency, and atomic dipole matrix elements. Assuming the detuning ∆ ca = ω c − ω a between the cavity (ω c ) and the atomicelectronic (ω a ) resonance frequencies is large, we retain the dispersive atoms-cavity interaction, and expand to sec...

We demonstrate and characterize a high-flux beam source for cold, slow atoms or molecules. The desired species is vaporized using laser ablation, then cooled by thermalization in a cryogenic cell of buffer gas. The beam is formed by particles exiting a hole in the buffer gas cell. We characterize the properties of the beam (flux, forward velocity, temperature) for both an atom (Na) and a molecule (PbO) under varying buffer gas density, and discuss conditions for optimizing these beam parameters. Our source compares favorably to existing techniques of beam formation, for a variety of applications.

We directly measure the quantized collective motion of a gas of thousands of ultracold atoms, coupled to light in a high-finesse optical cavity. We detect strong asymmetries, as high as 3:1, in the intensity of light scattered into low- and high-energy motional sidebands. Owing to high cavity-atom cooperativity, the optical output of the cavity contains a spectroscopic record of the energy exchanged between light and motion, directly quantifying the heat deposited by a quantum position measurement's backaction. Such backaction selectively causes the phonon occupation of the observed collective modes to increase with the measurement rate. These results, in addition to providing a method for calibrating the motion of low-occupation mechanical systems, offer new possibilities for investigating collective modes of degenerate gases and for diagnosing optomechanical measurement backaction.

The Heisenberg uncertainty principle sets a lower bound on the noise in a force measurement based on continuously detecting a mechanical oscillator's position. This bound, the standard quantum limit, can be reached when the oscillator subjected to the force is unperturbed by its environment and when measurement imprecision from photon shot noise is balanced against disturbance from measurement back-action. We applied an external force to the center-of-mass motion of an ultracold atom cloud in a high-finesse optical cavity and measured the resulting motion optically. When the driving force is resonant with the cloud's oscillation frequency, we achieve a sensitivity that is a factor of 4 above the standard quantum limit and consistent with theoretical predictions given the atoms' residual thermal disturbance and the photodetection quantum efficiency.