Florian Marquardt

Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane.

Macroscopic mechanical objects and electromagnetic degrees of freedom can couple to each other through radiation pressure. Optomechanical systems in which this coupling is sufficiently strong are predicted to show quantum effects and are a topic of considerable interest. Devices in this regime would offer new types of control over the quantum state of both light and matter, and would provide a new arena in which to explore the boundary between quantum and classical physics. Experiments so far have achieved sufficient optomechanical coupling to laser-cool mechanical devices, but have not yet reached the quantum regime. The outstanding technical challenge in this field is integrating sensitive micromechanical elements (which must be small, light and flexible) into high-finesse cavities (which are typically rigid and massive) without compromising the mechanical or optical properties of either. A second, and more fundamental, challenge is to read out the mechanical element’s energy eigenstate. Displacement measurements (no matter how sensitive) cannot determine an oscillator’s energy eigenstate, and measurements coupling to quantities other than displacement have been difficult to realize in practice. Here we present an optomechanical system that has the potential to resolve both of these challenges. We demonstrate a cavity which is detuned by the motion of a 50-nm-thick dielectric membrane placed between two macroscopic, rigid, high-finesse mirrors. This approach segregates optical and mechanical functionality to physically distinct structures and avoids compromising either. It also allows for direct measurement of the square of the membrane’s displacement, and thus in principle the membrane’s energy eigenstate. We estimate that it should be practical to use this scheme to observe quantum jumps of a mechanical system, an important goal in the field of quantum measurement.

Quantum theory of cavity-assisted sideband cooling of mechanical motion.

We present a quantum-mechanical theory of the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the optomechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good-cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.

Introduction to Quantum Noise, Measurement and Amplication

The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical--quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.

Dynamical Multistability Induced by Radiation Pressure in High-Finesse Micromechanical Optical Cavities

We analyze the nonlinear dynamics of a high-finesse optical cavity in which one mirror is mounted on a flexible mechanical element. We find that this system is governed by an array of dynamical attractors, which arise from phase locking between the mechanical oscillations of the mirror and the ringing of the light intensity in the cavity. We develop an analytical theory to map out the diagram of attractors in parameter space, derive the slow amplitude dynamics of the system, including thermal fluctuations, and suggest a scheme for exploiting the dynamical multistability in the measurement of small displacements.

Observation of spontaneous Brillouin cooling

A novel mechanism for cooling tiny mechanical resonators is now demonstrated. Inelastic scattering of light from phonons in an electrostrictive material attenuates the Brownian motion of the mechanical mode.

Back-action evasion and squeezing of a mechanical resonator using a cavity detector

We study the quantum measurement of a cantilever using a parametrically coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al (Braginsky V, Vorontsov Y I and Thorne K P 1980 Science 209 547), allows a back-action free measurement of one quadrature of the cantilevers motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also study the conditional dynamics of the measurement, and discuss how such a scheme (when coupled with feedback) can be used to generate and detect squeezed states of the oscillator. Our results are relevant to experiments in optomechanics, and to experiments in quantum electromechanics employing stripline resonators coupled to mechanical resonators.

Quantum squeezing of motion in a mechanical resonator

Manipulation of a quantum squeeze The uncertainty principle of quantum mechanics dictates that even when a system is cooled to its ground state, there are still fluctuations. This zero-point motion is unavoidable but can be manipulated. Wollman et al. demonstrate such manipulation with the motion of a micrometer-sized mechanical system. By driving up the fluctuations in one of the variables of the system, they are able to squeeze the other related variable below the expected zero-point limit. Quantum squeezing will be important for realizing ultrasensitive sensors and detectors. Science, this issue p. 952 The fluctuating motion of a mechanical system can be squeezed below the zero-point limit. According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.

Strong Coupling of a Mechanical Oscillator and a Single Atom

We propose and analyze a setup to achieve strong coupling between a single trapped atom and a mechanical oscillator. The interaction between the motion of the atom and the mechanical oscillator is mediated by a quantized light field in a laser driven high-finesse cavity. In particular, we show that high fidelity transfer of quantum states between the atom and the mechanical oscillator is in reach for existing or near future experimental parameters. Our setup provides the basic toolbox from atomic physics for coherent manipulation, preparation, and measurement of micromechanical and nanomechanical oscillators.

Collective dynamics in optomechanical arrays

Summary form only given. The field of optomechanics [1] seeks to explore the interaction between light and mechanical motion. Optomechanical system are typically composed of a single mechanical and a single optical mode interacting via radiation pressure: Ĥint = -ħg0 â†â(b + b†), where â/b are the photon/phonon operators. In this talk, we will introduce arrays of optomechanical cells, and discuss our first theoretical results on the nonlinear dynamics of such a setup [2,3].First we have studied the classical nonlinear dynamics of optomechanical arrays. For blue-detuned laser drive, a Hopf bifurcation towards self-sustained mechanical oscillations takes place. For static disorder of the frequencies in the array, we have shown that there can be a transition towards phase-locking. The slow dynamics of the mechanical oscillation phase field is described by a specific modification of the Kuramoto equation known in synchronization physics: in the simplest case δ φ = -δΩ - Ksin(2δφ), for the phase difference δφ between two cells with frequency difference δΩ, corresponding to a particle sliding down in a tilted washboard potential.In a second step, we have turned towards the quantum dynamics of arrays without static disorder [3]. There, the effects of the fundamental quantum noise can lead to phase diffusion. Upon increasing the coupling between cells, we observe a transition between incoherent mechanical oscillations and a collective phase-coherent mechanical state. To study the driven-dissipative dynamics, we employ a mean-field approach based on the Lindblad master equation, as well as semiclassical Langevin equations. We will also discuss the prospects of observing this non-equilibrium dynamics in an experimental implementation based on currently available setups. Very promising candidates in this regard are optomechanical crystal setups, where defects in photonic crystal structures are used to generate co-localized optical and mechanical modes in a two-dimensional geometry [4].

Self-Induced Oscillations in an Optomechanical System Driven by Bolometric Backaction

We have explored the nonlinear dynamics of an optomechanical system consisting of an illuminated Fabry-Perot cavity, one of whose end mirrors is attached to a vibrating cantilever. The backaction induced by the bolometric light force produces negative damping such that the system enters a regime of nonlinear oscillations. We study the ensuing attractor diagram describing the nonlinear dynamics. A theory is presented that yields quantitative agreement with experimental results. This includes the observation of a regime where two mechanical modes of the cantilever are excited simultaneously.