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arXiv:1005.4085 · Physical Review Letters

Tunable Cavity Optomechanics with Ultracold Atoms

Thomas Purdy, Daniel W. C. Brooks, Thierry Botter, Nathan Brahms, Zhaoyuan Ma, Dan Stamper-Kurn

Published Sep 22, 2010• 250 citations
arXivHTMLPDF

Abstract

We present an atom-chip-based realization of quantum cavity optomechanics with cold atoms localized within a Fabry-Perot cavity. Effective subwavelength 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 medium. We observe effects of such tuning on cavity optical nonlinearity and optomechanical frequency shifts, providing their first characterization in the quadratic-coupling regime.

DOI
10.1103/physrevlett.105.133602

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We present an atom-chip-based realization of quantum cavity optomechanics with cold atoms localized within a Fabry-Perot cavity. Effective subwavelength 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 medium. We observe effects of such tuning on cavity optical nonlinearity and optomechanical frequency shifts, providing their first characterization in the quadratic-coupling regime.
Ultracold fermionic atoms placed in a synthetic magnetic field arrange themselves in Landau levels. We theoretically study the optomechanical interaction between the light field and collective excitations of such fermionic atoms in synthetic magnetic field by placing them inside a Fabry-Perot cavity. We derive the effective Hamiltonian for particle hole excitations from a filled Landau level using a bosonization technique and obtain an expression for the cavity transmission spectrum. Using this we show that the cavity transmission spectrum demonstrates cold atom analog of Shubnikov‐de Haas oscillation in electronic condensed matter systems. We discuss the experimental consequences for this oscillation for such a system and the related optical bistability. By allowing an ultracold atomic ensemble to interact with a selected mode of a high-finesse cavity it is possible to probe the quantum many-body state of such an ultracold atomic system. The resulting cavity optomechanics or cavity quantum electrodynamics with ultracold atoms has recently witnessed a significant development [1]. The experimental successes include the coupling of collective density excitation of an ultracold bosonic condensate with a single-cavity mode and observation of the coupled dynamics through cavity transmission [2], a strongly coupled cavity mode with a highly localized ultracold atomic condensate trapped inside a single antinode of a cavity field [3], demonstration of strong ultracold atomcavity-coupling-induced optical nonlinearity even at low photon density [4], and selected atom-photon coupling of a single atomic ensemble in a multiensemble system [5 ]t o name a few. In another development, there has been significant experimental and theoretical progress in studying the effect of optically induced artificial or synthetic gauge field [6] on such neutral atoms, making it a playground for quantum simulation of phenomena that occur when an electronic condensed matter system is placed in a real magnetic field. The experimental achievements in this direction include the observation of vortices, Abrikosov vortex lattice in trapped ultracold atomic superfluid initially by achieving the synthetic magnetic field through the rotation of the trap [7], and later by Raman laser induced spatially varying coupling of the hyperfine states of such ultracold atoms [8]. A more recent development in this direction includes the creation of optical flux lattices [9], realization of spin-orbit coupling for such neutral ultracold bosonic [10] and fermionic atoms [11] with the possibility of creating ultracold atomic analogs of topological condensed matter phases [12]. This Letter aims to combine these two developments by considering a system of such ultracold atoms trapped inside a high-finesse Fabry-Perot cavity interacting with
A common goal of recent research is the elucidation and control over quantum mechanical behavior in ever-larger physical systems. In this thesis I present an alternative target for investigating the quantum motion of macroscopic bodies: the collective motion of an ultracold atomic gas trapped within a high-finesse Fabry-Perot optical cavity in the single-atom strong-coupling regime of cavity quantum electrodynamics (CQED). When ultracold atoms are trapped in the Lamb-Dicke regime, the cavity-mode structure selects a single collective degree of freedom that is at once actuated by the optical forces from cavity probe light and measured by the cavity’s optical properties. Dispersive optical bistability arising from collective motion of the atomic medium was observed. Measurement of the collective motion was subject to quantum measurement backaction by the quantum force fluctuations of the cavity optical field. The strength and spectrum of these backaction force fluctuations was measured by quantifying the cavity-light-induced heating rate of the intracavity atomic ensemble, finding quantitative agreement with the expected heating rate from quantum optical fluctuations. Dynamical phenomena in the optomechanical system were explored experimentally and theoretically. Quantum limited measurements are discussed and were
Cavity optomechanics represents a frontier research direction in quantum science and technology, centered on the control and exploration of interactions between electromagnetic fields and mechanical motion. Rooted in quantum mechanics, this field realizes efficient coupling and precise manipulation of optical fields and mechanical vibrations through the structural design and precise regulation of optical microcavities and mechanical oscillators, thereby revealing and harnessing novel quantum phenomena. In recent years, cavity optomechanics has evolved into an interdisciplinary frontier integrating quantum optics, condensed matter physics, and quantum precision measurement, exhibiting profound application in both fundamental physics research and quantum information science. With advancements in technologies such as nanomanufacturing and laser cooling, optomechanical interactions have been successfully demonstrated in various experimental systems. Among these platforms, cavity cold-atom systems stand out as one of the ideal platforms for implementing quantum optomechanics. Featuring exceptional environmental isolation, long quantum coherence times, and strong light-matter interaction, these systems provide a crucial testbed for exploring strong and even ultrastrong optomechanical coupling effects as well as rich nonlinear quantum phenomena. This paper reviews the recent progress in optomechanical control and manipulation based on cavity cold-atom systems. We first outline the fundamental principles of standard cavity optomechanical systems. Then, we describe the experimental realization of linear and nonlinear optomechanical couplings in cold-atom systems. After that, we focus on the representative applications of this platform in high-precision quantum sensing, quantum memory, and the preparation of macroscopic nonclassical states. Finally, we give an outlook and challenges in this field.
We give a brief overview of the basic aspects of the optomechanical interaction between a light field and a mechanical mode of ultracold bosonic and fermionic atomic gases inside a Fabry–Pérot cavity, showing that these systems provide a ‘bottom up’ approach to cavity optomechanics. In contrast to the case of a Bose condensate, where the effective ‘moving mirror’ is a side mode whose occupation results simply from photon recoil, for fermionic atoms this ‘mirror’ is a collective density oscillation associated with particle–hole excitations. We also discuss the experimental consequences of the optomechanical coupling in optical bistability.
In many experiments isolated atoms and ions have been inserted into high-finesse optical resonators for the study of fundamental quantum optics and quantum information. Here, we introduce another application of such a system, as the realization of cavity optomechanics where the collective motion of an atomic ensemble serves the role of a moveable optical element in an optical resonator. Compared with other optomechanical systems, such as those incorporating nanofabricated cantilevers or the large cavity mirrors of gravitational observatories, our cold-atom realization offers direct access to the quantum regime. We describe experimental investigations of optomechanical effects, such as the bistability of collective atomic motion and the first quantification of measurement backaction for a macroscopic object, and discuss future directions for this nascent field.