We study occurrence of chaos in a four-mirror optomechanical cavity with mechanical drives externally interacting with two transversely located moving-end mirrors of the cavity. The strong cavity mode, driven by the pump laser, excites mechanical oscillations in both moving-end mirrors with its radiation pressure. These radiation-pressure-induced mechanical effects then lead to the indirect coupling between two transverse mirrors, where intra-cavity field mimics as a spring between two mechanical objects. By computing Poincaré surface of sections for both mirrors over a wide interval of initial conditions, we illustrate the transition from stable to mixed -- containing stable islands and chaotic seas -- Poincaré surface of sections with external mechanical drives. To further explore the occurrence of chaos with mechanical drives, we measure the spatio-temporal responses of moving-end mirrors initially located in mixed Poincaré sections. We find that both of the mirrors follow chaotic temporal evolution with external mechanical drives, even in the absence of any one of the mechanical drives. To quantitatively measure the occurrence of chaos, we computed the possible Lyapunov exponents and collective Kolmogorov-Sinai Entropy of the system. We find that the largest Lyapunov exponent, and corresponding Kolmogorov-Sinai Entropy, not only gains positive values with increase in external drives but also crucially depends on the initial conditions chosen from the Poincaré surface of sections. Furthermore, we show the enhancement in chaotic dynamics of mirrors in the presence of mechanical damping rates associated with the oscillatory motion of the mirrors.
We demonstrate a $\mathcal{PT}$-symmetry-breaking chaos in optomechanical system (OMS), which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in $\mathcal{PT}$-symmetry-breaking phase ($\mathcal{PT}$BP). Moreover, this chaos is switchable by tuning the system parameters so that a $\mathcal{PT}$-symmetry phase transiti…
We demonstrate coherent control of optomechanically induced transparency and Fano resonances in a four mirror macroscopic optomechanical cavity, with two movable mirrors, each driven by an external mechanical pump. The variable control of the amplitude and phase of the coherent mechanical pumps provides a means of tuning the shape and nature of the Fano profiles. Further, our scheme shows the occurrence of tunable optomechanical features, even at very low mechanical driving field amplitudes, in macroscopic optomechanical cavities.
Proposing an optomechanical cavity modulated periodically, we study the modulation synchronization of mechanical modes of the mirrors. A periodic modulation is applied to one of the mirrors, where the second mirror has the capability of oscillation, without any modulation for that. As a result, we find a phase-locking synchronization between the mechanical modes of the mirrors and enhancement of quantum synchronization by having the periodic modulation. Using the fact that, periodic modulation can make the squeezed states, we show that there is a robust synchronization of periodic modulation b…
We show how stationary entanglement between an optical cavity field mode and a macroscopic vibrating mirror can be generated by means of radiation pressure. We also show how the generated optomechanical entanglement can be quantified and we suggest an experimental readout-scheme to fully characterize the entangled state. Surprisingly, such optomechanical entanglement is shown to persist for environment temperatures above 20K using state-of-the-art experimental parameters.
In this paper we describe a scheme for state transfer between a trapped atomic Bose condensate and an optomechanical end-mirror mediated by a cavity field. Coupling between the mirror and the cold gas arises from the fact that the cavity field can produce density oscillations in the gas which in turn acts as an internal Bragg mirror for the field. After adiabatic elimination of the cavity field we find that the hybrid system of the gas and mirror is described by a beam splitter Hamiltonian that allows for state transfer, but only if the quantum nature of the cavity field is retained.
We investigate the response of a harmonically confined mirror to an optical pulse in cavity optomechanics. We show that when the pulsed coupling strength takes the form of a chirped pulse, thermal fluctuations of the mirror can be significantly transferred to the cavity field. In addition, the frequency modulation of the pulse could enable a better cooling performance by suppressing the sensitivity of the dependence of detuning and pulse areas. Using numerical investigations, we find that the pulsed-cooling is mainly limited by the cavity-field decay rate.
The present paper illustrates the realization of an atom-optomechanical system where an atomic ensemble is confined in a ring optomechanical cavity consisting of a fixed mirror and two movable ones. An analysis of the dynamics and the linearization of the equations allows to derive the multimode covariance matrix. Under realistic experimental conditions, we numerically simulate the steady-state bipartite and tripartite continuous variable entanglement using the logarithmic negativity, and analyze the shared entanglement in the multimode system. The introduction of the atomic medium allows to o…
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient cha…
We perform a theoretical study on quantum correlations in an optomechanical system where the mechanical mirror is perturbatively coupled to an auxiliary qubit. In our study, we consider logarithmic negativity to quantify the degree of stationary entanglement between the cavity field and mechanical mirror, and, Gaussian quantum discord as an witness of the quantumness of the correlation beyond entanglement. Utilizing experimentally feasible parameters, we show that both entanglement and quantum discord enhance significantly with increase in mirror-qubit coupling. Moreover, we find that in prese…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling bifurcations that leads to chaos, and state the experimentally observable signatures in the optical spectrum. In addition to the semi-classical dynamics we analyze the possibility of chaotic motion in the quantum regime. We find that quantum mechanics protects the optomechanical system against irregular dynamics, such that simple periodic orbits reappear and repl…
We present an experimental study of the internal mechanical vibration modes of a mirror. We determine the frequency repartition of acoustic resonances via a spectral analysis of the Brownian motion of the mirror, and the spatial profile of the acoustic modes by monitoring their mechanical response to a resonant radiation pressure force swept across the mirror surface. We have applied this technique to mirrors with cylindrical and plano-convex geometries, and compared the experimental results to theoretical predictions. We have in particular observed the gaussian modes predicted for plano-conve…
We investigate a double cavity optomechanical system(OMS) generating single and double Fano resonance(multi Fano). By altering a single parameter, the tunneling rate $g$ of the middle mirror, we are able to switch between single and double Fano line shapes. The first spectral line shape is stronger in the case of multi Fano than in the case of single Fano. Also the behaviour of steady state value of the displacement of the middle mirror with respect to $g$, heavily influences the behaviour of double Fano lines in our scheme. This tunability along-with using a single pump and signal/probe laser…
We propose a method to generate quadrature squeezed states of a moving mirror in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the cavity is driven by an external field with a large detuning, the moving mirror behaves as a parametric oscillator. We show that parametric resonance can be reached approximately by modulating the driving field amplitude at a frequency matching the frequency shift of the mirror. The parametric resonance leads to an efficient generation of squeezing, which is limited by the thermal noise of the environment.
The dominant hurdle to the operation of optomechanical systems in the quantum regime is the coupling of the vibrating element to a thermal reservoir via mechanical supports. Here we propose a scheme that uses an optical spring to replace the mechanical support. We show that the resolved-sideband regime of cooling can be reached in a configuration using a high-reflectivity disk mirror held by an optical tweezer as one of the end-mirrors of a Fabry-Perot cavity. We find a final phonon occupation number of the trapped mirror ${\bar n}$= 0.14 for reasonable parameters, well within the quantum regi…
We investigate the optical behavior of a single Laguerre-Gaussian cavity optomechanical system consisting of two mechanically rotating mirrors. We explore the effects of various physical parameters on the double optomechanically induced transparency (OMIT) of the system and provide a detailed explanation of the underlying physical mechanism. We show that the momentum is not the cause of the current double-OMIT phenomena; rather, it results from the orbital angular momentum between the optical field and the rotating mirrors. Additionally, the double-OMIT is simply produced using a single Laguer…
In this paper, firstly, we consider bipartite entanglement between each part of an optomechanical cavity composed of one dimensional Bose-Einstein condensate (BEC). we investigate atomic collision on the behavior of the BEC in the week photon-atom coupling constant, and use Bogoliubov approximation for the BEC. Secondly under above condition, we propose a scheme for entanglement swapping protocol wich involves tripartite systems. In our investigation, we consider a scenario where BECs, moving mirrors, and optical cavity modes are given in a Gaussian state with a covariance matrix (CM). By appl…
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10$^{-5}$mbar and with feedback engaged the pressure is reduced to 10$^{-6}$mbar. Modifications to the …
We consider a hybrid optomechanical system which is composed of the atomic ensemble and a standard optomechanical cavity driven by the periodically modulated external laser field. We investigate the asymptotic behaviors of Heisenberg operator first moments and clearly show the approaching process between the exact numerical results and analytical solutions. Based on the specific modulation forms of external driving and effective optomechanical coupling, we discuss in detail the atom-mirror entanglement enhancement, respectively. Compared with the constant driving regime, the entanglement can b…
We analyze a scheme to entangle the movable mirrors of two spatially separated nanoresonators via a broadband squeezed light. We show that it is possible to transfer the EPR-type continuous-variable entanglement from the squeezed light to the mechanical motion of the movable mirrors. An optimal entanglement transfer is achieved when the nanoresonators are tuned at resonance with the vibrational frequencies of the movable mirrors and when strong optomechanical coupling is attained. Stationary entanglement of the states of the movable mirrors as strong as that of the input squeezed light can be …
We study the quantum limits in an optomechanical sensor based on a detuned high-finesse cavity with a movable mirror. We show that the radiation pressure exerted on the mirror by the light in the detuned cavity induces a modification of the mirror dynamics and makes the mirror motion sensitive to the signal. This leads to an amplification of the signal by the mirror dynamics, and to an improvement of the sensor sensitivity beyond the standard quantum limit, up to an ultimate quantum limit only related to the mechanical dissipation of the mirror. This improvement is somewhat similar to the one …
We investigate the squeezing for a movable mirror in the dissipative optomechanics in which the oscillating mirror modulates both the resonance frequency and the linewidth of the cavity mode. Via feeding a much weaker broadband squeezed vacuum light accompanying the coherent driving laser field into the cavity, the master equation for the cavity-mirror system is derived by following the general reservoir theory based on the density operator in which the reservoir variables are adiabatically eliminated by using the reduced density operator for the system in the interaction picture. When the mir…
Cavity Optomechanical system is speedily approaching the regime where the radiation pressure of a single photon displaces the moving mirror. In this paper, we consider a cavity optomechanical system where the cavity field is driven by an external field. In the limit of weak mirror-cavity couplings, we calculate analytically the reflection and transmission rates for cavity field and discuss the effects of mirror-cavity coupling on the reflection and transmission.
An interferometric scheme for the creation of momentum superposition states of mechanical oscillators, using a quantum mirror kicked by free photons is analyzed. The scheme features ultra-fast preparation with immediate detection and should allow for the observation of signatures of momentum superpositions in a massive macroscopic system at non-zero temperatures. It is robust against thermalized initial states, displacement and movement, mirror imperfections, and the measurements' back-actions.
We study how an oscillating mirror affects the electromagnetically induced transparency (EIT) of an atomic ensemble, which is confined in a gas cell placed inside a micro-cavity with an oscillating mirror in one end. The oscillating mirror is modeled as a quantum mechanical harmonic oscillator. The cavity field acts as a probe light of the EIT system and also produces a light pressure on the oscillating mirror. The back-action from the mirror to the cavity field results in several (from one to five) steady-states for this atom-assisted optomechanical cavity, producing a complex structure in it…
We study a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end-mirror. The intracavity light field has a dual role: it excites a momentum side-mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate …
We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.}, arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effe…
We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon spectrum reveals resonances that depend on how many phonons are created as well as on the strength of the mirror-photon interaction. A dressed-state picture is used to explain positions and relative strengths of those resonances. The time-dependent spectrum shows how the resonances are built up over time by the photon interacting with the moving mirror.
We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should wor…
Experiments in the field of optomechanics do not yet fully exploit the photon polarization degree of freedom. Here experimental results for an optomechanical interaction in a polarization nondegenerate system are presented and schemes are proposed for how to use this interaction to perform accurate side-band thermometry and to create novel forms of photon-phonon entanglement. The experimental system utilizes the compressive force in the mirror attached to a mechanical resonator to create a micro-mirror with two radii of curvature which leads, when combined with a second mirror, to a significan…
A cavity optomechanical system is initiated by a radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as cooling its effective temperature. Here we show that by properly engineering the spectral density of a thermal heat bath that interacts with a quantum system, the evolution of the quantum system can be effectively turned on and off. Inside a cavity optomechanical system, when the heat bath is realized by a multi-mode oscillator modeling of the mirror, this …
We theoretically study an optomechanical system, which consists of a two-sided cavity and a mechanical membrane that is placed outside of it. The membrane is positioned close to one of its mirrors, and the cavity is coupled to the external light field through the other mirror. Our study is focused on the regime where the dispersive optomechanical coupling in the system vanishes. Such a regime is found to be possible if the membrane is less reflecting than the adjacent mirror, yielding a potentially very strong dissipative optomechanical coupling. Specifically, if the absolute values of amplitu…
We experimentally study a fiber-based optical ring cavity integrated with a mechanical resonator mirror and an optical amplifier. The device exhibits a variety of intriguing nonlinear effects including synchronization and self-excited oscillation. Passively generated optical pulses are observed when the frequency of the optical ring cavity is tuned very close to the mechanical frequency of the suspended mirror. The optical power at the threshold of this process of mechanical mode locking is found to be related to quantum noise of the optical amplifier.
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and highe…
We review recent progress in the field of optomechanics, where one studies the effects of radiation on mechanical motion. The paradigmatic example is an optical cavity with a movable mirror, where the radiation pressure can induce cooling, amplification and nonlinear dynamics of the mirror.
We consider an optomechanical cavity made by two moving mirrors which contains a Kerr-down conversion nonlinear crystal. We show that the coherent oscillations of the two mechanical oscil- lators can lead to splitting in the electromagnetically induced transparency (EIT) resonance, and appearance of an absorption peak within the transparency window. In this configuration the coher- ent induced splitting of EIT is similar to driving a hyperfine transition in an atomic Lambda-type three-level system by a radio-frequency or microwave field. Also, we show that the presence of non- linearity provid…
We investigate the effects of atomic collisions as well as optomechanical mirror-field coupling on the optical bistability in a hybrid system consisting of a Bose-Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mi…
We theoretically study a cavity filled with atoms, which provides the optical-mechanical interaction between the modified cavity photonic field and a movable mirror at one end. We show that the cavity field ``dresses'' these atoms, producing two types of polaritons, effectively enhancing the radiation pressure of the cavity field upon the end mirror, as well as establishing an additional squeezing mode of the end mirror. This squeezing produces an adiabatic entanglement, which is absent in usual vacuum cavities, between the oscillating mirror and the rest of the system. We analyze the entangle…
The multiphonon quantum dynamics in laser-pumped cavity optomechanical samples containing a vibrating mirror is investigated. Especially, we focus on dispersive interaction regimes where the externally applied coherent field frequency detuning from the optical resonator frequency is not equal to the mirror's oscillating frequency or to its multiples. As a result, for moderately strong couplings among the involved subsystems, the quantum dynamics of this complex system is described by multiphonon absorption or emission processes, respectively. Particularly, we demonstrate efficient ways to moni…
We theoretically investigate the dispersive interaction of a Bose-Einstein condensate (BEC) trapped inside an optomechanical cavity with a moving end mirror in the presence of the laser phase noise (LPN) as well as the atomic collisions. We assume that the effective frequency of the optical mode is much greater than those of the mechanical and the Bogoliubov modes of the movable mirror and the BEC . In the adiabatic approximation where the damping rate of the cavity is faster than those of the other modes, the system behaves as an effective two-mode model in which the atomic and mechanical mod…
We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulation. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, th…
We experimentally study an optomechanical cavity that is formed between a mechanical resonator, which serves as a movable mirror, and a stationary on-fiber dielectric mirror. A significant change in the behavior of the system is observed when the distance between the fiber's tip and the mechanical resonator is made smaller than about 1 micrometer. The observed effects are attributed to the combined influence of Casimir force, Coulomb interaction due to trapped charges, and optomechanical coupling. The comparison between experimental results and theory yields a partial agreement.
We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force. The atoms are intrinsically two-level systems that can absorb or emit photons, but the dynamics of their position and momentum are treated classically. On the other hand, the membrane, the cavity field, and the intrinsic two-level atoms are treated quantum mechanically. We show that the mean excitation of the three systems can be stable, periodically oscillating, or in a chaotic state depending on the strength of the coupling between…
The Fano line profiles, originally discovered in the context of photoionization, have been found to occur in a large class of systems like resonators, metamaterials, plasmonics. We demonstrate the existence of such resonances in cavity optomechanics by identifying the interfering contributions to the fields generated at antiStokes and Stokes frequencies. Unlike the atomic systems, the optomechanical systems provide great flexibility as the width of the resonance is controlled by the coupling field. We further show how the double cavities coupled by a single optomechanical mirror can lead to th…
We use a microscopic model, the Mirror-Oscillator-Field (MOF) model proposed by Galley, Behunin and Hu [Phys. Rev. A 87, 043832 (2013)], to describe the quantum entanglement between a mirror's center of mass (CoM) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's CoM, the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is t…
We theoretically investigate the optical and mechanical properties of a double cavity optomechanical system with one stationary and two harmonically bound mirrors. We show that it is possible for the mechanical mirrors in this system to posses negative effective mass. Working within the strong coupling and the resolved sideband regime, we show that the displacement of the middle resonator is multistable under certain constrains. We also point to the existence of optomechanically induced absorption (OMIA) and Fano resonance. Owing to the negative effective mass, our scheme can be exploited in t…
We discuss how the optomechanical coupling provided by radiation pressure can be used to cool macroscopic collective degrees of freedom, as vibrational modes of movable mirrors. Cooling is achieved using a phase-sensitive feedback-loop which effectively overdamps the mirrors motion without increasing the thermal noise. Feedback results able to bring macroscopic objects down to the quantum limit. In particular, it is possible to achieve squeezing and entanglement.
Cavity-optomechanics, a rapidly developing area of research, has made a remarkable progress. A stunning manifestation of optomechanical phenomena is in exploiting the mechanical effects of light to couple the optical degree of freedom with mechanical degree of freedom. In this report, we investigate the controlled bistable dynamics of such hybrid optomechanical system composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside high-finesse optical cavity with one moving-end mirror and is driven by a single mode optical field. The numerical results provide evidence for controlled opt…
We describe and demonstrate a method to control a detuned movable-mirror Fabry-Perot cavity using radiation pressure in the presence of a strong optical spring. At frequencies below the optical spring resonance, self-locking of the cavity is achieved intrinsically by the optomechanical (OM) interaction between the cavity field and the movable end mirror. The OM interaction results in a high rigidity and reduced susceptibility of the mirror to external forces. However, due to a finite delay time in the cavity, this enhanced rigidity is accompanied by an anti-damping force, which destabilizes th…
We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
