Converting low-frequency electrical signals into much higher frequency optical signals has enabled modern communications networks to leverage both the strengths of microfabricated electrical circuits and optical fiber transmission, allowing information networks to grow in size and complexity. A microwave-to-optical converter in a quantum information network could provide similar gains by linking quantum processors via low-loss optical fibers and enabling a large-scale quantum network. However, no current technology can convert low-frequency microwave signals into high-frequency optical signals while preserving their fragile quantum state. For this demanding application, a converter must provide a near-unitary transformation between different frequencies; that is, the ideal transformation is reversible, coherent, and lossless. Here we demonstrate a converter that reversibly, coherently, and efficiently links the microwave and optical portions of the electromagnetic spectrum. We use our converter to transfer classical signals between microwave and optical light with conversion efficiencies of ∼10%, and achieve performance sufficient to transfer quantum states if the device were further precooled from its current 4 kelvin operating temperature to below 40 millikelvin. The converter uses a mechanically compliant membrane to interface optical light with superconducting microwave circuitry, and this unique combination of technologies may provide a way to link distant nodes of a quantum information network. IntroductionModern communication networks manipulate information at several gigahertz with microprocessors and distribute information at hundreds of terahertz via optical fibers. A similar frequency dichotomy is developing in quantum information processing. Superconducting qubits operating at several gigahertz have recently emerged as promising high-fidelity and intrinsically scalable quantum processors [1][2][3]. Conversely, optical frequencies provide access to low-loss transmission [4] and long-lived quantum-compatible storage [5,6]. Converting information between gigahertz-frequency "microwave light" that can be deftly manipulated and terahertzfrequency "optical light" that can be efficiently distributed will enable small-scale quantum systems [7][8][9] to be combined into larger, fully-functional quantum networks [10,11]. But no current technology can transform information between these vastly different frequencies while preserving the fragile quantum state of the information. For this demanding application, a frequency converter must provide a near-unitary transformation between microwave light and optical light; that is, the ideal transformation is reversible, coherent, and lossless.Certain nonlinear materials provide a link between microwave and optical light, and these are commonly used in electro-optic modulators (EOMs) for just this purpose. While EOMs might be capable of reversible frequency conversion [12,13], such conversion has not yet been demonstrated, and even optimized EOMs [14,15] have predicted ...

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of 1.7 +/- 0.2 dB below the shot noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.Comment: 12 pages, 8 figure

The quantum mechanics of position measurement of a macroscopic object is typically inaccessible because of strong coupling to the environment and classical noise. In this work, we monitor a mechanical resonator subject to an increasingly strong continuous position measurement and observe a quantum mechanical back-action force that rises in accordance with the Heisenberg uncertainty limit. For our optically based position measurements, the back-action takes the form of a fluctuating radiation pressure from the Poisson-distributed photons in the coherent measurement field, termed radiation pressure shot noise. We demonstrate a back-action force that is comparable in magnitude to the thermal forces in our system. Additionally, we observe a temporal correlation between fluctuations in the radiation force and in the position of the resonator.

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 have produced Bose-Einstein condensates in a ring-shaped magnetic waveguide. The fewmillimeter diameter non-zero bias ring is formed from a time-averaged quadrupole ring. Condensates which propagate around the ring make several revolutions within the time it takes for them to expand to fill the ring. The ring shape is ideally suited for studies of vorticity in a multiply-connected geometry and is promising as a rotation sensor. Scalar superfluids are characterized by a complex order parameter Ψ(r) which is uniquely defined throughout the fluid. This implies the irrotational motion of the fluid in the space where Ψ(r) = 0, leading to the Meissner effect in charged superfluids and to the Hess-Fairbank effect in neutral ones. Given this constraint, rotational motion of superfluids (or magnetic flux density in type-II superconductors) is accommodated by lines of quantized vorticity which disrupt the simple connectivity of the fluid. Multiple connectivity can also be imposed by the proper design of containers for the fluids. Such geometries are enlisted to translate phase variations of Ψ(r) into sensors of external fields. For example, a SQUID magnetometer makes use of a superconducting ring interrupted by Josephson junctions to allow continuous sensitivity to magnetic fields. A similar geometry was used in a superfluid 3 He gyroscope [1].Dilute gas superfluids enable novel forms of matterwave interferometry. Precise sensors of rotation, acceleration, and other sources of quantal phases [2, 3] using trapped or guided atoms have been envisioned. In particular, the sensitivity of atom-interferometric gyroscopes is proportional to the area enclosed by the closed loop around which atoms are guided [4]. Such considerations motivate the development of closed-loop atom waveguides which enclose a sizeable area.A number of multiply-connected trapping geometries for cold atoms have been discussed. Optical traps using high-order Gauss-Laguerre beams were proposed [5,6], and hollow light beams were used to trap non-degenerate atoms in an array of small-radius rings [7]. Large-scale magnetic "storage rings" were developed for cold neutrons [8] and discussed for atomic hydrogen [9]. More recently, closed-loop magnetic waveguides were demonstrated for laser cooled atoms [10,11]. Unfortunately, these guides are characterized by large variations in the potential energy along the waveguide and by high transmission losses at points where the magnetic field vanishes.In this Letter, we report the creation of a smooth, stable circular waveguide for ultracold atoms. A simple arrangement of coaxial electromagnetic coils was used to produce a static ring-shaped magnetic trap, which we call the quadrupole ring (Qring), in which strong transverse confinement is provided by a two-dimensional quadrupole field. Atoms trapped in the Qring experience large Majorana losses, but we can eliminate such losses with a timeorbiting ring trap (TORT) [12]. In this manner, stable circular waveguides with diameters ranging from 1.2 to 3 mm were produced. F...

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 study the mechanical quality factors of bilayer aluminum-silicon-nitride membranes. By coating ultrahigh-Q Si(3)N(4) membranes with a more lossy metal, we can precisely measure the effect of material loss on Q's of tensioned resonator modes over a large range of frequencies. We develop a theoretical model that interprets our results and predicts the damping can be reduced significantly by patterning the metal film. Using such patterning, we fabricate Al-Si(3)N(4) membranes with ultrahigh Q at room temperature. Our work elucidates the role of material loss in the Q of membrane resonators and informs the design of hybrid mechanical oscillators for optical-electrical-mechanical quantum interfaces.

The radiation pressure of light can act to damp and cool the vibrational motion of a mechanical resonator. In understanding the quantum limits of this cooling, one must consider the effect of shot noise fluctuations on the final thermal occupation. In optomechanical sideband cooling in a cavity, the finite Stokes Raman scattering defined by the cavity linewidth combined with shot noise fluctuations dictates a quantum backaction limit, analogous to the Doppler limit of atomic laser cooling. In our work we sideband cool to the quantum backaction limit by using a micromechanical membrane precooled in a dilution refrigerator. Monitoring the optical sidebands allows us to directly observe the mechanical object come to thermal equilibrium with the optical bath.