In this paper we discuss how red-sideband cooling is modified in the single-photon strong-coupling regime of cavity optomechanics where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. Using Fermi's Golden rule we calculate the transition rates induced by the optical drive without linearizing the optomechanical interaction. In the resolved-sideband limit we find multiple-phonon cooling resonances for strong single-photon coupling that lead to non-thermal steady states including the possibility of phonon anti-bunching. Our study generalizes the standard linear cooling theory.
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 d…
We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red-detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong las…
Multimode optomechanical systems are an emerging platform for studying fundamental aspects of matter near the quantum ground state and are useful in sensitive sensing and measurement applications. We study optomechanical cooling in a system where two nearly degenerate mechanical oscillators are coupled to a single microwave cavity. Due to an optically mediated coupling the two oscillators hybridize into a bright mode with strong optomechanical cooling rate and a dark mode nearly decoupled from the system. We find that at high coupling, sideband cooling of the dark mode is strongly suppressed. …
We study the effect of laser phase noise on the generation of stationary entanglement between an intracavity optical mode and a mechanical resonator in a generic cavity optomechanical system. We show that one can realize robust stationary optomechanical entanglement even in the presence of non-negligible laser phase noise. We also show that the explicit form of the laser phase noise spectrum is relevant, and discuss its effect on both optomechanical entanglement and ground state cooling of the mechanical resonator.
In cavity optomechanics, light is used to control mechanical motion. A central goal of the field is achieving single-photon strong coupling, which would enable the creation of quantum superposition states of motion. Reaching this limit requires significant improvements in optomechanical coupling and cavity coherence. Here we introduce an optomechanical architecture consisting of a silicon nitride membrane coupled to a three-dimensional superconducting microwave cavity. Exploiting their large quality factors, we achieve an optomechanical cooperativity of 146,000 and perform sideband cooling of …
We study the effect of cavity damping asymmetries on backaction in a "membrane-in-the-middle" optomechanical system, where a mechanical mode modulates the coupling between two photonic modes. We show that in the adiabatic limit, this system generically realizes a dissipative optomechanical coupling, with an effective position-dependent photonic damping rate. The resulting quantum noise interference can be used to ground-state cool a mechanical resonator in the unresolved sideband regime. We explicitly demonstrate how quantum noise interference controls linear backaction effects, and show that …
Cavity optomechanical phenomena, such as cooling, amplification or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically-induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compare…
We study entanglement of the cavity modes in a double-cavity optomechanical system in strong-coupling regime. The system consists of two optomechanical systems coupled by a single photon hopping between them. With the radiation pressure of the photon, entanglement of the cavity modes can be generated. The concurrence between the cavity modes is at least twice larger than that between the mechanical modes. Moreover, when we change the ratio between coupling strength and resonant frequency of mechanical modes, the entanglement in cavity and mechanical modes are influenced differently.
We study the cavity mode frequencies of a Fabry-Pérot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membrane…
We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output …
We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes, and show that ground state cooling of th…
Surface acoustic waves (SAWs) are a versatile tool for coherently interfacing with a variety of solid-state quantum systems spanning microwave to optical frequencies, including superconducting qubits, spins, and quantum emitters. Here, we demonstrate SAW cavity optomechanics with quantum emitters in 2D materials, specifically monolayer WSe$_2$, on a planar lithium niobate SAW resonator driven by superconducting electronics. Using steady-state photoluminescence spectroscopy and time-resolved single-photon counting, we map the temporal dynamics of modulated 2D emitters under coupling to differen…
The mechanical properties of light have found widespread use in the manipulation of gas-phase atoms and ions, helping create new states of matter and realize complex quantum interactions. The field of cavity-optomechanics strives to scale this interaction to much larger, even human-sized mechanical objects. Going beyond the canonical Fabry-Perot cavity with a movable mirror, here we explore a new paradigm in which multiple cavity-optomechanical elements are wired together to form optomechanical circuits. Using a pair of optomechanical cavities coupled together via a phonon waveguide we demonst…
Optomechanical arrays made of structured flexible dielectrics are a promising system for exploring quantum and many-body optomechanical phenomena. We generalize investigations of the optomechanical properties of periodic arrays of one-dimensional scatterers in optical resonators to the case of vibrating membranes whose thickness is not necessarily small with respect to the optical wavelength of interest. The array optical transmission spectrum and its optomechanical coupling with a linear Fabry-Perot cavity field are investigated both analytically and numerically.
Using carefully designed hybrid metal-dielectric resonators, we study molecular optomechanics in the strong coupling regime ($g_{\rm }^2/ω_m {>} κ$), which manifests in anharmonic emission lines in the sideband-resolved region of the cavity-emitted spectrum ($κ{<}ω_m$). This nonlinear optomechanical strong coupling regime is enabled through a metal-dielectric cavity system that yields not only deep sub-wavelength plasmonic confinement, but also dielectric-like confinement times that are more than two orders of magnitude larger than those from typical localized plasmon modes. These hybrid metal…
Cavity optomechanical systems are approaching a strong-coupling regime where the coherent dynamics of nanomechanical resonators can be manipulated and controlled by optical fields at the single photon level. Here we propose an interferometric scheme able to detect optomechanical coherent interaction at the single-photon level which is experimentally feasible with state-of-the-art devices.
We propose a versatile, free-space cavity optomechanics platform built from two photonic crystal membranes, one of which is freely suspended, and designed to form a microcavity less than one wavelength long. This cavity features a series of photonic bound states in the continuum that, in principle, trap light forever and can be favorably used together with evanescent coupling for realizing various types of optomechanical couplings, such as linear or quadratic coupling of either dispersive or dissipative type, by tuning the photonic crystal patterning and cavity length. Crucially, this platform…
We present a scheme for ground-state cooling of a mechanical resonator by simultaneously coupling it to a superconducting qubit and a cavity field. The Hamiltonian describing the hybrid system dynamics is systematically derived. The cooling process is driven by a red-detuned ac drive on the qubit and a laser drive on the optomechanical cavity. We have investigated cooling in the weak and the strong coupling regimes for both the individual system, i.e., qubit assisted cooling and optomechanical cooling, and compared them with the effective hybrid cooling. It is shown that hybrid cooling is more…
We present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation trea…
We experimentally study an optomechanical cavity consisting of an oscillating mechanical resonator embedded in a superconducting microwave transmission line cavity. Tunable optomechanical coupling between the mechanical resonator and the microwave cavity is introduced by positioning a niobium-coated single mode optical fiber above the mechanical resonator. The capacitance between the mechanical resonator and the coated fiber gives rise to optomechanical coupling, which can be controlled by varying the fiber-resonator distance. We study radiation pressure induced self-excited oscillations as a …
Electromagnetically induced transparency has great theoretical and experimental importance in many physics subjects, such as atomic physics, quantum optics, and more recent cavity optomechanics. Optical delay is the most prominent feature of electromagnetically induced transparency, and in cavity optomechanics optical delay is limited by mechanical dissipation rate of sideband-resolved mechanical modes. Here we demonstrate a cascaded optical transparency scheme by leveraging the parametric phonon-phonon coupling in a multimode optomechanical system, where a low damping mechanical mode in the u…
We demonstrate highly efficient coupling of light from an optical fiber to a silicon photonic crystal optomechanical cavity. The fiber-to-cavity coupling utilizes a compact (L ~ 25 um) intermediate adiabatic coupler. The optical coupling is lithographically controlled, broadband, relatively insensitive to fiber misalignment, and allows for light to be transferred from an optical fiber to, in principle, any photonic chip with refractive index greater than that of the optical fiber. Here we demonstrate single-sided cavity coupling with a total fiber-to-cavity optical power coupling efficiency of…
We study the optical cooling of the resonator mirror in a cavity-optomechanical system that contains an optical gain medium. We find that the optical damping rate is vanishingly small for an incoherently pumped laser above threshold. In the presence of an external coherent drive however, the optical damping rate can be enhanced substantially with respect to that of a passive cavity. We show that the strength of the incoherent pump provides a conduit to tune the damping rate and the minimum attainable phonon number with the same radiation pressure force, and the latter can be lowered from that …
Laser cooling of mesoscopic mechanical resonators is of great interest for both fundamental studies and practical applications. We provide a general framework to describe the cavity-assisted backaction cooling in the strong coupling regime. By studying the cooling dynamics, we find that the temporal evolution of mean phonon number oscillates as a function of the optomechanical coupling strength depending on frequency mixing. The further analytical result reveals that the optimal cooling limit is obtained when the system eigenmodes satisfy the frequency matching condition. The reduced instantan…
Single-crystal diamond cavity optomechanical devices are a promising example of a hybrid quantum system: by coupling mechanical resonances to both light and electron spins, they can enable new ways for photons to control solid state qubits. However, realizing cavity optomechanical devices from high quality diamond chips has been an outstanding challenge. Here we demonstrate single-crystal diamond cavity optomechanical devices that can enable photon-phonon-spin coupling. Cavity optomechanical coupling to $2\,\text{GHz}$ frequency ($f_\text{m}$) mechanical resonances is observed. In room tempera…
Quantum manipulation of macroscopic mechanical systems is of great interest in both fundamental physics and applications ranging from high-precision metrology to quantum information processing. A crucial goal is to cool the mechanical system to its quantum ground state. In this review, we focus on the cavity optomechanical cooling, which exploits the cavity enhanced interaction between optical field and mechanical motion to reduce the thermal noise. Recent remarkable theoretical and experimental efforts in this field have taken a major step forward in preparing the motional quantum ground stat…
Polariton-mediated light-sound interaction is investigated through resonant Brillouin experiments in GaAs/AlAs multiple-quantum wells. Photoelastic coupling enhancement at exciton-polariton resonance reaches 105 at 30 K as compared to a typical bulk solid room temperature transparency value. When applied to GaAs based cavity optomechanical nanodevices, this result opens the path to huge displacement sensitivities and to novel ultrastrong-coupling cavity phenomena with optomechanical couplings g0 in the range of 100 THz.
We describe a cryogenic cavity-optomechanical system that combines Si3N4 membranes with a mechanically-rigid Fabry-Perot cavity. The extremely high quality-factor frequency products of the membranes allow us to cool a MHz mechanical mode to a phonon occupation of less than 10, starting at a bath temperature of 5 kelvin. We show that even at cold temperatures thermally-occupied mechanical modes of the cavity elements can be a limitation, and we discuss methods to reduce these effects sufficiently to achieve ground state cooling. This promising new platform should have versatile uses for hybrid …
Resonant photoelastic coupling in semiconductor nanostructures opens new perspectives for strongly enhanced light-sound interaction in optomechanical resonators. One potential problem, however, is the reduction of the cavity Q-factor induced by dissipation when the resonance is approached. We show in this letter that cavity-polariton mediation in the light-matter process overcomes this limitation allowing for a strongly enhanced photon-phonon coupling without significant lifetime reduction in the strongly-coupled regime. Huge optomechanical coupling factors in the PetaHz/nm range are envisaged…
We report a development of an electro-optomechanical system based on a surface acoustic wave (SAW), where a piezoelectric material with a large optoelastic susceptibility is used for the coupling of both a radio wave and optical light to the SAW. In the optical domain, we exploit a tensorial nature of the optoelastic effect to show a polarization dependence of the photon-SAW interaction. We discuss the construction of two-dimensional SAW focusing circuits for the coupling enhancement and the optical cavity enhanced photon-phonon scattering. We estimate an optomechanical coupling rate $g_0$ of …
We consider feedback cooling in a cavityless levitated optomechanics setup, and we investigate the possibility to improve the feedback implementation. We apply optimal control theory to derive the optimal feedback signal both for quadratic (parametric) and linear (electric) feedback. We numerically compare optimal feedback against the typical feedback implementation used for experiments. In order to do so, we implement a tracking scheme that takes into account the modulation of the laser intensity. We show that such a tracking implementation allows us to increase the feedback strength, leading…
In an optomechanical setup, the coupling between cavity and resonator can be increased by tuning them to the same frequency. We study this interaction between a carbon nanotube resonator and a radio-frequency circuit. In this resonant regime, the vacuum optomechanical coupling is enhanced by the DC voltage coupling the cavity and the mechanical resonator. Using the cavity to detect the nanotube's motion, we observe and simulate interference between mechanical and electrical oscillations. We measure the mechanical ring-down and show that further improvements to the system could enable measureme…
Recent experimental progress in cavity optomechanics has allowed cooling of mesoscopic mechanical oscillators via dynamic backaction provided by the parametric coupling to either an optical or an electrical resonator. Here we analyze the occurrence of normal-mode splitting in backaction cooling at high input power. We find that a hybridization of the oscillator's motion with the fluctuations of the driving field occurs and leads to a splitting of the mechanical and optical fluctuation spectra. Moreover, we find that cooling experiences a classical limitation through the cavity lifetime.
Optomechanical coupling between a light field and the motion of a cavity mirror via radiation pressure plays an important role for the exploration of macroscopic quantum physics and for the detection of gravitational waves (GWs). It has been used to cool mechanical oscillators into their quantum ground states and has been considered to boost the sensitivity of GW detectors, e.g. via the optical spring effect. Here, we present the experimental characterization of generalized, that is, dispersive and dissipative optomechanical coupling, with a macroscopic (1.5mm)^2-sized silicon nitride (SiN) me…
We report narrow linewidth optomechanical oscillation of a silica microsphere immersed in a buffer solution. Through a novel optomechanical transduction sensing approach, single 10-nm-radius silica beads and Bovine serum albumin (BSA) protein molecules with a molecular weight of 66 kDalton were detected. This approach predicts the detection of 3.9 kDalton single molecules at a signal-to-noise ration above unity.
Electronic resonances can significantly enhance the photon-phonon coupling in cavity optomechanics, but are normally avoided due to absorption losses and dephasing by inhomogeneous broadening. We experimentally demonstrate that exciton-polaritons in semiconductor microcavities enable GHz optomechanics with single-particle resonant couplings reaching record values in the 10s of MHz range. Moreover, this resonant enhancement is protected from inhomogeneous broadening by the Rabi gap. Single-polariton non-linearities and the optomechanical strong-coupling regime become accessible in this platform…
So far, Brillouin scattering and cavity optomechanics were mostly disconnected branches of research -- although both deal with photon-phonon coupling. This begs for the development of a broader theory that contains both fields. Here, we derive the dynamics of optomechanical cavities from that of Brillouin-active waveguides. This explicit transition elucidates the link between phenomena such as Brillouin amplification and electromagnetically induced transparency. It proves that effects familiar from cavity optomechanics all have traveling-wave partners, but not vice versa. We reveal a close con…
A III-V compound semiconductor nanowire is an attractive material for a novel hybrid quantum interface that interconnects photons, electrons, and phonons through a wavelength-tunable quantum structure embedded in its free-standing structure. In such a nanomechanical element, however, a challenge is how to detect and manipulate a small number of phonons via its tiny mechanical motion. A solution would be to couple an optical cavity to a nanowire by introducing the ``cavity optomechanics'' framework, but the typical size difference between them becomes a barrier to achieving this. Here, we demon…
We study a hybrid system formed from an optomechanical resonator and a cavity mode strongly coupled to an excitonic transition inside a quantum well. We show that due to the mixing of cavity photon and exciton states, the emergent quasiparticles - polaritons - possess coupling to the mechanical mode of both dispersive and dissipative nature. We calculate the occupancies of polariton modes and reveal bistable behavior, which deviates from conventional Kerr nonlinearity or dispersive coupling cases due to the dissipative coupling. The described system serves as a good candidate for future polari…
Confining photons in cavities enhances the interactions between light and matter. In cavity optomechanics, this enables a wealth of phenomena ranging from optomechanically induced transparency to macroscopic objects cooled to their motional ground state. Previous work in cavity optomechanics employed devices where ubiquitous structural disorder played no role beyond perturbing resonance frequencies and quality factors. More generally, the interplay between disorder, which must be described by statistical physics, and optomechanical effects has thus far been unexplored. Here, we demonstrate how…
