Recent experimental progress in table-top experiments or gravitational-wave interferometers has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers. The appearance of such optomechanical instabilities is the result of the nonlinear interplay between the motion of the mirrors and the optical field dynamics. In a detuned cavity indeed, the displacements of the mirror are coupled to intensity fluctuations, which modifies the effective dynamics of the mirror. Such "optical spring" effects have already been demonstrated on the mechanical damping of an electromagnetic waveguide with a moving wall, on the resonance frequency of a specially designed flexure oscillator, and through the optomechanical instability of a silica micro-toroidal resonator. We present here an experiment where a micro-mechanical resonator is used as a mirror in a very high-finesse optical cavity and its displacements monitored with an unprecedented sensitivity. By detuning the cavity, we have observed a drastic cooling of the micro-resonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator, either by passive or active cooling techniques.
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.
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…
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 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…
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…
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.
We propose a scheme for the creation of robust entanglement between a movable mirror and atomic ensemble at the macroscopic level in coupled optomechanical system. In experimentally accessible parameter regimes, we show that critical temperature of the bipartite continuous variable entanglement in our scheme can be raised from previous 24 K [Vitali {\it et al.}, Phys. Rev. Lett. \textbf{98}, 030405 (2007)] and 20 K [Genes {\it et al.}, Phys. Rev. A \textbf{77}, 050307(R) (2008)] to 32 K. We also investigate the entanglement transfer based on this coupled system. The scheme can be used for the …
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 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 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…
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…
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 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 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 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 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…
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 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…
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 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.
We discuss the dynamics of moving end mirror of an optomechanical system that consists of a Fabry-Perot cavity loaded with dilute condensate and driven by a single mode optical field. It is shown that quantum mechanical phenomenon of dynamical localization occurs both in position and momentum space for moving end mirror in the system. The parametric dependencies of dynamical localization are discussed. We also provide a set of parameters which makes this phenomenon experimentally feasible.
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.
Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of a two level BEC with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portrait of the system. The rich phase portrait generated by analytic arguments displays two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in ach…
In a hybrid optomechanical setup consisting of a two-level atom in a cavity with a pendular end-mirror, the interplay between the light field's radiation pressure on the mirror and the dipole interaction with the atom can lead to a blockade effect, which manifests itself in a suppression of Rabi oscillations in the atomic population. This effect is present when the system is in the single photon strong coupling regime and has an analogy in the photon blockade of optomechanics.
We investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with the perturbative oscillator-qubit coupling. It is shown that such a hybrid system is very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the approaches of master equation and covariance matrix, we discuss the respective squeezing effects in detail and find that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is …
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 theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that by suitably driving $Λ$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Such process allows us to manipulate the heating and cooling effects. Particularly, we develop an optomecha…
We present a closed-form analytical solution to the eigenvalue problem of the Liouville operator generating the dissipative dynamics of the standard optomechanical system. The corresponding Lindblad master equation describes the dynamics of a single-mode field inside an optical cavity coupled by radiation pressure to its moving mirror. The optical field and the mirror are in contact with separate environments, which are assumed at zero and finite temperature, respectively. The optomechanical damping basis refers to the exact set of eigenvectors of the generator that, together with the exact ei…
We study the detection of weak coherent forces by means of an optomechanical device formed by a highly reflecting isolated mirror shined by an intense and highly monochromatic laser field. Radiation pressure excites a vibrational mode of the mirror, inducing sidebands of the incident field, which are then measured by heterodyne detection. We determine the sensitivity of such a scheme and show that the use of an entangled input state of the two sideband modes improves the detection, even in the presence of damping and noise acting on the mechanical mode.
Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system's vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field, in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror, based on our effective Hamiltonian …
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.
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 study theoretically nonlinear effects arising from the presence of a Kerr-down conversion nonlinear crystal inside an optomechanical cavity. For this system we investigate the influences of the two nonlinearities, i.e., the Kerr nonlinearity and the parametric gain, on the dynamics of the oscillating mirror, the intensity and the squeezing spectra of the transmitted field, and the steady-state mirror-field entanglement. We show that in comparison with a bare optomechanical cavity, the combination of the cavity energy shift due to the Kerr nonlinearity and increase in the intracavity photon …
In this paper, we study theoretically the bipartite and tripartite continuous variable entanglement as well as the normal-mode splitting in a single-atom cavity optomechanical system with intensity-dependent coupling. The system under consideration is formed by a Fabry-Perot cavity with a thin vibrating end mirror and a two-level atom in the Gaussian standing-wave of the cavity mode. We first derive the general form of Hamiltonian describing the tripartite intensity-dependent atom-field-mirror coupling due to the presence of cavity mode structure. We then restrict our treatment to the first vi…
Thermal noise of a mirror can be reduced by cold damping. The displacement is measured with a high-finesse cavity and controlled with the radiation pressure of a modulated light beam. We establish the general quantum limits of noise in cold damping mechanisms and we show that the optomechanical system allows to reach these limits. Displacement noise can be arbitrarily reduced in a narrow frequency band. In a wide-band analysis we show that thermal fluctuations are reduced as with classical damping whereas quantum zero-point fluctuations are left unchanged. The only limit of cold damping is the…
According to quantum mechanics, if we keep observing a continuous variable we generally disturb its evolution. For a class of observables, however, it is possible to implement a so-called quantum nondemolition measurement: by confining the perturbation to the conjugate variable, the observable is estimated with arbitrary accuracy, or prepared in a well-known state. For instance, when the light bounces on a movable mirror, its intensity is not perturbed (the effect is just seen on the phase of the radiation), but the radiation pressure allows to trace back its fluctuations by observing the mirr…
We study the optomechanical coupling of a oscillating effective mirror with a Rydberg atomic gas, mediated by the dynamical atom-mirror Casimir-Polder force. This coupling may produce a near-field resonant atomic excitation whose probability scales as $\propto (d^2\;a\;n^4\;t)^2/z_0^8$, where $z_0$ is the average atom-surface distance, $d$ the atomic dipole moment, $a$ the mirror's effective oscillation amplitude, $n$ the initial principal quantum number, and $t$ the time. We propose an experimental configuration to realize this system with a cold atom gas trapped at a distance $\sim 2\cdot10 …
Enforcing a non-classical behavior in mesoscopic systems is important for the study of the boundaries between quantum and classical world. Recent experiments have shown that optomechanical devices are promising candidates to pursue such investigations. Here we consider two different setups where the indirect coupling between a three-level atom and the movable mirrors of a cavity is achieved. The resulting dynamics is able to conditionally prepare a non-classical state of the mirrors by means of projective measurements operated over a pure state of the atomic system. The non-classical features …
In 1909 Einstein described the thermalization of a mirror within a blackbody cavity by collisions with thermal photons. While the time to thermalize the motion of even a microscale or nanoscale object is so long that it is not feasible, we show that it is using the high intensity light from an amplified thermal light source with a well-defined chemical potential. We predict damping of the center-of mass motion due to this effect on times scales of seconds for small optomechanical systems, such as levitated nanoparticles, allowing experimental observation.
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 multi-partite entanglement, the generation of EPR states and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beamsplitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuat…
Optomechanical systems have been attracting intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it, and impos…
In most optomechanical systems a movable mirror is a part of an optical cavity, and its oscillation modulates either the resonance frequency of the cavity, or its coupling to the environment. There exists the third option -- which we call a "coherent coupling" -- when the mechanical oscillation couples several non-degenerate optical modes supported by the cavity. Identifying the nature of the coupling can be an important step in designing the setup for a specific application. In order to unambiguously distinguish between different optomechanical couplings, we develop a general framework based …
The hopping mechanism plays a key role in collective phenomena emerging in many-body physics. The ability to create and control systems that display this feature is important for next generation quantum technologies. Here we study two cavities separated by a vibrating two-sided perfect mirror and show that, within currently available experimental parameters, this system displays photon-pair hopping between the two electromagnetic resonators. In particular, the two-photon hopping is not due to tunneling, but rather to higher order resonant processes. Starting from the classical problem, where t…
We investigate the dynamics of an optomechanical system where a cavity with a movable mirror involves a degenerate optical parametric amplifier and is driven by a periodically modulated laser field. Our results show that the cooperation between the parametric driving and periodically modulated cavity driving results in a two-fold squeezing on the movable cavity mirror that acts as a mechanical oscillator. This allows the fluctuation of the mechanical oscillator in one quadrature (momentum or position) to be reduced to a level that cannot be reached by solely applying either of these two drivin…
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 study the quantum dynamics of a Michelson interferometer with Fabry-Perot cavity arms and one movable end mirror, and driven by a single photon --- an optomechanical device previously studied by Marshall et al. as a device that searches for gravity decoherence. We obtain an exact analytical solution for the system's quantum mechanical equations of motion, including details about the exchange of the single photon between the cavity mode and the external continuum. The resulting time evolution of the interferometer's fringe visibility displays interesting new features when the incoming photon…
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 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.
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…
