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Physica Scripta

Optomechanics of ultracold atomic gases

Rina Kanamoto, Pierre Meystre

Published Aug 18, 2010• 35 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/82/03/038111

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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.
We explore theoretically the optomechanical interaction between a light field and a mechanical mode of ultracold fermionic atoms inside a Fabry-Pérot cavity. The low-lying phonon mode of the fermionic ensemble is a collective density oscillation associated with particle-hole excitations, and is mathematically analogous to the momentum side-mode excitations of a bosonic condensate. The mechanical motion of the fermionic particle-hole system behaves hence as a "moving mirror." We derive an effective system Hamiltonian that has the form of generic optomechanical systems. We also discuss the experimental consequences the optomechanical coupling in optical bistability and in the noise spectrum of the system.
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.
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
This dissertation contains a study of ultracold atoms in optical cavities. We particularly focus on two aspects of the coupled atom-cavity systems. In the first aspect, we implement the quantum nature of the light field to probe the quantum state of the atoms. This is interesting due to the nondestructive nature of the characterization of many-body atomic states. In the second aspect we study the cavity optomechanics that investigates the coupling of mechanical and optical degrees of freedom via radiation pressure. The optomechanical cavity provides an interesting nonlinear system to study the coupling between atoms and the intracavity field.In the context of cavity quantum electrodynamics we study the reflection of two counter-propagating modes of the light field in a high-Q ring cavity by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. By using the Monte Carlo wave-function method to account for the cavity damping we also determine the two-time correlation function and the time-dependent physical spectrum of theretroreflected field. We find that the light field and the atoms become entangled if the latter are in a superfluid state. We also analyze quantitatively the entanglement between the atoms and the light.In cavity optomechanics the mechanical effect can either comes from a vibrating macroscopic oscillator or a collective density excitation of a Bose-Einstein condensate. First we use a Fabry-Perot-type cavity to study the opto-mechanically-induced bistable quantum phase transitions between superfluid and a Mott insulator states of an ultracold bosonic gases trapped inside the cavity. Secondly, we study the symmetricand antisymmetric collective density side modes of the BEC which results from the optomechanical effects of the light fields in a ring cavity.
We briefly review some of our recent and ongoing work on nanoscale optomechanics, an emerging area at the confluence of atomic, condensed matter and gravitational wave physics. A central tenet of optomechanics is the laser cooling of a moving mirror, typically an end mirror of a Fabry-Perot resonator, to a point near its quantum-mechanical ground state of vibration. Following a general introduction we discuss how the motion of such a macroscopic quantum oscillator can be squeezed, and then show how the placement of a ferroelectric tip on the oscillator allows the coherent manipulation and control of the center-of-mass motion of ultracold polar molecules.
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