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An Introduction to Cavity Optomechanics

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An Introduction to Cavity Optomechanics An introduction to cavity optomechanics Andreas Nunnenkamp University of Basel 1. What? Why? How? 2. Sideband cooling 3. Strong-coupling regime 4. Dissipative coupling Introduction Mechanical effects of light Dipole or gradient force Scattering force • ac-Stark shift • radiation pressure • optical lattices • laser cooling Loudon, The Quantum Theory of Light (OSP) Foot, Atomic Physics (OUP) Radiation-pressure force 2E k ∆p =2k = c k ∆p∆N 2Pin − F = = ∆t c Loudon, The Quantum Theory of Light (OSP) Foot, Atomic Physics (OUP) Cavity optomechanics radiation pressure force mechanical cavity drive cavity mode oscillator Marquardt & Girvin, Physics 2, 40 (2009) Kippenberg & Vahala, Science 321, 1172 (2008) REVIEW sitivity by increasing optical power in interfer- scopic and which is harmonically suspended. This Many more structures exist that should ometers. On the other hand, a red-detuned pump end mirror has been realized in multiple ways, also realize an optomechanical interaction in wave can create a radiation component of mechan- such as from an etched, high-reflectivity mirror an efficient manner. In particular, nanopho- ical damping that leads to cooling of the mechan- substrate (14, 15), a miniaturized and harmonical- tonic devices such as photonic crystal mem- ical mode; i.e., a reduction of the mechanical ly suspended gram-scale mirror (28), or an atomic brane cavities or silicon ring resonators might mode’sBrownianmotion(9, 26). force cantilever on which a high-reflectivity and be ideal candidates owing to their small mode One description of this process is given in micron-sized mirror coating has been transferred volume, high-Finesse, and finite rigidity. Owing Fig. 2B, wherein a feedback loop that is inherent (29). A natural optomechanical coupling can occur to their small length scale, these devices ex- to the cavity optomechanical system is described. in optical microcavities, such as microtoroidal hibit fundamental flexural frequencies well The elements of this loop include the mechanical cavities (13)ormicrospheres,whichcontainco- into the gigahertz regime, but their mechanical and optical oscillators coupled through two dis- existingExperiments high-Q,opticalwhisperinggallerymodes, & qualityMotivation factors have so far not been studied, tinct paths. Along the upper path, a force acting and radio-frequency mechanical modes. This cou- nor has optomechanical coupling been ob- on the mechanical oscillator (for instance, the pling can also be optimized for high optical and served. As described in the next section, such thermal Langevin force or a signal force) causes a mechanical Q (30). In the case of hybrid systems, high frequencies are interesting in the context mechanical displacement, which (for a detuned of regenerative oscillation and ground laser) changes the cavity field due to the opto- state cooling. mechanical coupling (the interferometric mea- kg Hz 1. Mechanical sensing 2. Quantum network Gravity wave Cooling and Amplification Using surement process). However, the amplitude detectors fluctuations, which contain information on the (LIGO, Virgo, GEO,..) Dynamical Back-Action mirror position, are also coupled back to the The cooling of atoms or ions using radi- mechanical oscillator via radiation pressure Harmonically ation pressure has received substantial (lower path), resulting in a back-action. A blue- suspended attention and has been a successful tool detuned pump wave sets up positive feedback gram-scale mirrors in atomic and molecular physics. Dy- (the instability), whereas red detuning introduces namical back-action allows laser cooling negative feedback. Resonant optical probing of mechanical oscillators in a similar man- (where the excitation frequency equals the cavity Mirror coated ner. The resemblance between atomic on April 22, 2011 AFM-cantilevers Mechanical frequency resonance frequency, w = w0) interrupts the laser cooling and the cooling of a mechan- feedback loop because changes in position only icalRugar oscillator et al. coupled, Nature to 430 an optical, 329 (or(2004) Rabl et al., Nature Physics 6, 602 (2010) change the phase, not the amplitude, of the field. electronic) resonator is a rigorous one Micromirrors As described below, this feedback circuit also Mass (34). In both cases, the motion (of the clarifies the relation between “feedback cooling” ion, atom, or mirror) induces a change in and cooling by dynamic back-action. the resonance frequency, thereby cou- pling the motion to the optical3. (or cavity)Quantum-classical transition SiN membranes Experimental Systems 3 resonance (Fig. 2C). Indeed, early work Systems that exhibit radiation-pressure dynamic has exploited this coupling to sense the back-action must address a range of design con- atomic trajectories of single atoms in www.sciencemag.org siderations, including physical size as well as Fabry-Perot cavities (35, 36)and,more dissipation. DynamicRealization back-action of an optomechanical relies on opti- interface between ultracold atoms and a membraneOptical microcavities recently, in the context of collective atomic 1, 2, 1, 2, 3, 1, 2, 3 Stephan Camerer, ∗ Maria Korppi, ∗ Andreas J¨ockel, 1, 2 1, 2 1, 2, 3, cal retardation; i.e., is most prominentDavid Hunger, for photonTheodor W. H¨ansch, and Philipp Treutlein † motion (37, 38). This coupling is not only 1Fakult¨at f¨ur Physik, Ludwig-Maximilians-Universit¨at, Schellingstraße 4, 80799 M¨unchen, Germany lifetimes comparable to or2Max-Planck-Institut exceeding f¨ur the Quantenoptik, me- Hans-Kopfermann-Str. 1, 85748 Garching, Germany restricted to atoms or cavities but also has 3Departement Physik, Universit¨at Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland chanical oscillation period. Very low optical dis-(Dated: July 20, 2011) CPW-resonators MHz been predicted for a variety of other We have realized a hybrid optomechanical system bypg coupling ultracold atoms to a micromechan- coupled to nano- sipation also means that photonsical membrane. The are atoms recycled are trapped in an optical lattice, which is formed by retro-reflection of a systems. For example, the cooling of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechan- resonators ical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the many times, thereby enhancingeffect of the the membrane weak vibrations photon onto the atoms as well as the backaction of the atomic motion mechanical oscillator can be achieved Downloaded from onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation Penrose & Bouwmeester et al., PRL 91,130401 (2003) pressure on the mirror. Onrate the of the membrane. other Our hand, observations the agree quantitatively with a simple model. using coupling to a quantum dot (39), a mechanical dissipation rate governs the rate of trapped ion (40), a Cooper pair box (41), Laser light can excert a force on material objects Fig. 3. Experimental cavity optomechanical systems. heating of the mechanicalthrough radiation mirror pressure and mode through the by optical the dipole an LC circuit (5, 32), or a microwave strip- force [1]. In the very active field of optomechanics [2], (Top to Bottom) Gravitational waveultracold detectors atoms in [photo environment, limitingsuch the light forces effectiveness are exploited for cooling of opto- and control line cavity (33). Although the feedback of the vibrations of mechanical oscillators, with possi- credit LIGO Laboratory], harmonicallyoptical suspended resonators gram- Marquardt & Girvin, Physics 2, 40 (2009) mechanical cooling.ble It applications also sets in precision the forcerequired sensing and am- studies of loop of Fig. 2B explains how damping quantum physics at macroscopic scales. This has many scale mirrors (28), coated atomic force microscopy canti- similarities with the field of ultracold atoms [3], where plification level necessary to induce regenerative FIG. 1: Optomechanical coupling of atoms and membrane. and instability can be introduced intoKippenberg the & Vahala, Science 321, 1172 (2008) radiation pressure forces are routinely used for laser cool- leversAlaserbeamofpower (29), coatedP is partially micromirrors reflected at a SiN mem- (14, 15), SiN3 membranes ing [1] and optical dipole forces are used for trapping and brane of reflectivity r and forms a 1D optical lattice for an ul- oscillations. Thesequantum considerations manipulation of atomic illustrate motion, most the notably dispersivelytracold atomic ensemble. coupled Motion of the membrane to an displaces optical cavity (31), optical cavity optomechanical system, the ori- in optical lattices [4, 5]. the lattice and thus couples to atomic motion. Conversely, importance of high opticalIn a number Finesse of recent theoretical and mechan- papers it has been microcavitiesatomic motion is imprinted ( as13 a power, 16 modulation), and∆P onto superconducting microwave gins of cooling and mechanical amplifi- proposed that light forces could also be used to couple the laser, thus modulating the radiation pressure force on the ical Q in system design.the motion of atoms in a trap to the vibrations of a single membrane. t is the transmittivity of the optics between atoms cation are better understood with the use resonatorsand membrane. Arrows coupled illustrate the todirection a of nanomechanical forces and beam (33). The mode of a mechanical oscillator [6–16]. In the resulting displacements at a specific point in time. In the main text, all It is only in thehybrid
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