We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Einstein's theory of special relativity and the principle of causality imply that the speed of any moving object cannot exceed that of light in a vacuum (c) Nevertheless, there exist various proposals for observing faster-than-c propagation of light pulses, using anomalous dispersion near an absorption line, nonlinear and linear gain lines, or tunnelling barriers However, in all previous experimental demonstrations, the light pulses experienced either very large absorption or severe reshaping, resulting in controversies over the interpretation Here we use gain-assisted linear anomalous dispersion to demonstrate superluminal light propagation in atomic caesium gas The group velocity of a laser pulse in this region exceeds c and can even become negative, while the shape of the pulse is preserved We measure a group-velocity index of n(g) = -310(+/- 5); in practice, this means that a light pulse propagating through the atomic vapour cell appears at the exit side so much earlier than if it had propagated the same distance in a vacuum that the peak of the pulse appears to leave the cell before entering it The observed superluminal light pulse propagation is not at odds with causality, being a direct consequence of classical interference between its different frequency components in an anomalous dispersion region

Gain-assisted superluminal light propagation

Controlling the interaction between localized optical and mechanical excitations has recently become possible following advances in micro- and nanofabrication techniques. So far, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. Conversely, the optical response of these systems is also modified in the presence of mechanical interactions, leading to effects such as electromagnetically induced transparency (EIT) and parametric normal-mode splitting. In atomic systems, studies of slow and stopped light (applicable to modern optical networks and future quantum networks) have thrust EIT to the forefront of experimental study during the past two decades. Here we demonstrate EIT and tunable optical delays in a nanoscale optomechanical crystal, using the optomechanical nonlinearity to control the velocity of light by way of engineered photon-phonon interactions. Our device is fabricated by simply etching holes into a thin film of silicon. At low temperature (8.7 kelvin), we report an optically tunable delay of 50 nanoseconds with near-unity optical transparency, and superluminal light with a 1.4 microsecond signal advance. These results, while indicating significant progress towards an integrated quantum optomechanical memory, are also relevant to classical signal processing applications. Measurements at room temperature in the analogous regime of electromagnetically induced absorption show the utility of these chip-scale optomechanical systems for optical buffering, amplification, and filtering of microwave-over-optical signals.

/pdf/electromagnetically-induced-transparency-and-slow-light-with-1ue1i7b56y.pdf

Electromagnetically induced transparency and slow light with optomechanics

The linear Doppler shift is widely used to infer the velocity of approaching objects, but this shift does not detect rotation. By analyzing the orbital angular momentum of the light scattered from a spinning object, we observed a frequency shift proportional to product of the rotation frequency of the object and the orbital angular momentum of the light. This rotational frequency shift was still present when the angular momentum vector was parallel to the observation direction. The multiplicative enhancement of the frequency shift may have applications for the remote detection of rotating bodies in both terrestrial and astronomical settings.

https://science.sciencemag.org/content/sci/341/6145/537.full.pdf

Detection of a Spinning Object Using Light’s Orbital Angular Momentum

The semiclassical (SC) initial value representation (IVR) provides a potentially practical way for adding quantum mechanical effects to classical molecular dynamics (MD) simulations of the dynamics of complex molecular systems (i.e., those with many degrees of freedom). It does this by replacing the nonlinear boundary value problem of semiclassical theory by an average over the initial conditions of classical trajectories. This paper reviews the background and rebirth of interest in such approaches and surveys a variety of their recent applications. Special focus is on the ability to treat the dynamics of complex systems, and in this regard, the forward−backward (FB) version of the approach is especially promising. Several examples of the FB-IVR applied to model problems of many degrees of freedom show it to be capable of describing quantum effects quite well and also how these effects are quenched when some of the degrees of freedom are averaged over (“decoherence”).

The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations

Positive and negative subnatural-width resonances (SNWR) were observed in the absorption and fluorescence of rubidium vapor under excitation by two copropagating optical waves with variable frequency offset. The two optical fields resonantly couple Zeeman sublevels, belonging to the same ground-state hyperfine level (GSHL), to an intermediate excited state. The SNWR present opposite signs depending on which GSHL participates in the interaction with the two optical waves. For both Rb isotopes an increase in the transparency with reduced fluorescence occurs for the lower GSHL while the absorption and fluorescence are increased for the upper GSHL. The influence of external magnetic field, polarization, and intensity of applied optical fields on the SNWR is examined. The narrowest observed resonance has a width of 10 kHz (full width at half maximum). The origin of the SNWR is discussed in terms of coherent processes involving ground-state Zeeman sublevels.

https://researchbank.swinburne.edu.au/file/7019f7f1-d5f5-432f-90b5-3240d42e181f/1/PDF (Published version).pdf

Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor

A large increase in atomic absorption due to coherent interaction with resonant radiation is predicted for a closed transition between two degenerate atomic levels verifying $0l{F}_{g}l{F}_{e}{(F}_{g}$ and ${F}_{e}$ are the total angular momentum of the ground and the excited levels, respectively). In good agreement with the theoretical prediction, a total absorption enhancement by a factor 1.7 was obtained on the ${D}_{2}$ line of ${}^{85}\mathrm{Rb}\mathrm{}$ in a vapor cell experiment.

https://researchbank.swinburne.edu.au/file/5e0ba619-1251-475e-853b-2a95ef4db094/1/PDF (Published version).pdf

Electromagnetically induced absorption

Steep dispersion of opposite signs in driven degenerate two-level atomic transitions have been predicted and observed on the ${D}_{2}$ line of ${}^{87}\mathrm{Rb}$ in an optically thin vapor cell. The intensity dependence of the anomalous dispersion has been studied. The maximum observed value of anomalous dispersion ( $\mathrm{dn}/d\ensuremath{\nu}\ensuremath{\simeq}\ensuremath{-}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}{\mathrm{Hz}}^{\ensuremath{-}1}$) corresponds to a negative group velocity ${V}_{g}\ensuremath{\simeq}\ensuremath{-}c/23000$.

Steep Anomalous Dispersion in Coherently Prepared Rb Vapor

The absorption properties of degenerate two-level atomic systems tested by a weak probe field in the presence of an intense pump field have been analyzed. The theoretical model previously presented in Phys. Rev. A 61, 013801 (1999) that appears to be suitable for arbitrary choices of the pump intensity, level angular momenta, and pump and probe polarizations, was used for the calculation of the spectra for several basic configurations. Experimental absorption spectra obtained on a Rb atomic beam for different pump and probe field polarizations show good agreement with the calculation. The spectra are in general essentially different from and more complex than the classical Mollow absorption triplet.

Absorption spectra of driven degenerate two-level atomic systems

Spectroscopic features revealing the coherent interaction of a degenerate two-level atomic system with two optical fields are examined. A model for the numerical calculation of the response of a degenerate two-level system to the action of an arbitrarily intense resonant pump field and a weak probe in the presence of a magnetic field is presented. The model is valid for arbitrary values of the total angular momentum of the lower and upper levels and for any choice of the polarizations of the optical waves. Closed and open degenerate two-level systems are considered. Predictions for probe absorption and dispersion, field generation by four-wave-mixing, population modulation and Zeeman optical pumping are derived. On all these observables, sub-natural-width coherence resonances are predicted and their spectroscopic features are discussed. Experimental spectra for probe absorption and excited state population modulation in the D2 line of Rb vapor are presented in good agreement with the calculations.

S. Barreiro

Papers

Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor

Electromagnetically induced absorption

Steep Anomalous Dispersion in Coherently Prepared Rb Vapor

Absorption spectra of driven degenerate two-level atomic systems

Coherent two-field spectroscopy of degenerate two-level systems