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arXiv:2108.08586 · Journal of Physics A Mathematical and Theoretical

Dynamics of a hybrid optomechanical system in the framework of the generalized linear response theory

Behrouz Askari, Ali Dalafi

Published Dec 7, 2021• 3 citations
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Abstract

Abstract In this article, the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Bose–Einstein condensate to an external time-dependent perturbation is studied in the framework of the generalized linear response theory (GLRT). It is shown that the Stokes and anti-Stokes amplitudes of the optical and atomic modes of the system can be obtained through the solutions to the equations of motion of the open quantum system Green’s function predicted by the GLRT. In this way, interesting phenomena like anti-resonance and Fano resonance are described and it is shown how the atom–atom interaction affects them. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the optical spectral function and self-energy.

DOI
10.1088/1751-8121/ac40e2

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Abstract In this article, the linear response of a driven-dissipative hybrid optomechanical system consisting of an interacting one-dimensional Bose–Einstein condensate to an external time-dependent perturbation is studied in the framework of the generalized linear response theory (GLRT). It is shown that the Stokes and anti-Stokes amplitudes of the optical and atomic modes of the system can be obtained through the solutions to the equations of motion of the open quantum system Green’s function predicted by the GLRT. In this way, interesting phenomena like anti-resonance and Fano resonance are described and it is shown how the atom–atom interaction affects them. Furthermore, an interpretation of the anti-resonance phenomenon is presented based on the optical spectral function and self-energy.
Abstract In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green’s function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.
Abstract Closed-form expressions for the average amplitude of the optical field in optomechanical systems are obtained, in which, in addition to the linear interaction, quadratic and cubic interactions of the vibrational mode of the mechanical resonator with the mode of the optical resonator are considered. In the framework of the non-secular perturbation theory, using the Bogoliubov averaging method, it is shown that the effects of photon blockade, collapse and revival of optical oscillations in such systems can be realized. The main contribution to the formation of revivals is provided by the Kerr self-action of the optical mode and the cross-Kerr interaction of the fourth degree in optical and mechanical amplitudes. The cross-Kerr interactions of the sixth and eighth orders reduce the amplitude of revivals. The influence of these cross-Kerr nonlinearities decreases with an increase in the decay rate of the optical mode. It is shown that the asymmetry of the spectral line of the optical field intensity in the cavity is most pronounced with an increase in the degree and magnitude of nonlinearity and is explained by Fano interference.
We study the emergence of dynamical phases of a Bose-Einstein condensate that is optomechanically coupled to a dissipative cavity mode and transversally driven by a laser. We focus on the regime close to the optomechanical resonance, where the atoms' refractive index shifts the cavity into resonance, assuming fast cavity relaxation. We derive an effective model for the atomic motion, where the cavity degrees of freedom are eliminated using perturbation theory in the atom-cavity coupling and benchmark its predictions using numerical simulations based on the full model. Away from the optomechanical resonance, perturbation theory in the lowest order (adiabatic elimination) reliably describes the dynamics and predicts chaotic phases with unstable oscillations. Interestingly, the dynamics close to the optomechanical resonance are qualitatively captured only by including the corrections to next order (nonadiabatic corrections). In this regime we find limit-cycle phases that describe stable oscillations of the density with a well-defined frequency. We further show that such limit-cycle solutions are metastable configurations of the adiabatic model. Our work sheds light on the mechanisms that are required to observe dynamical phases and predict their existence in atom-cavity systems where a substantial timescale separation is present.
Abstract We study the pump-probe response in an optomechanical cavity accommodating an ensemble of two-level atoms interacting with a cavity mode, which is pumped by a strong driving field and probed by a weak signal field. The atomic excitation is examined without taking any approximations and may be in any regimes ranging from the low limit to the high limit for a given collective coupling constant between the atomic ensemble and the cavity mode. This then results in different absorption and dispersion spectra (such as optomechanically induced transparency, Fano-resonance, normal-mode splitting) when the excitation transfer from cavity mode to atomic ensemble is controlled to change from ineffective to effective. This indicates that a hybrid optomechanical response is indeed determined by the excitation of the atomic ensemble embedded in the optomechanical cavity. It is also of interest that the output signal component and the inside atomic polarization show either synchronous or asynchronous behaviors depending on how the atom-field detuning is chosen, i.e. equal to the mechanical resonator frequency or its negative. Such features may open up an effective avenue in coherently manipulating the internal atomic polarization via the external signal field, and vice versa.
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 optical bistability in optomechanics using transverse optical field which directly interacts with atoms causing the coupling of transverse field with momentum side modes, exited by intra-cavity field. This technique of transverse field coupling is also used to control bistable dynamics of both moving-end mirror and BEC. The report provides an understanding of temporal dynamics of moving-end mirror and BEC with respect to transverse field. Moreover, dependence of effective potential of the system on transverse field has also been discussed. To observe this phenomena in laboratory, we have suggested a certain set of experimental parameters. These findings provide a platform to investigate the tunable behavior of novel phenomenon like electromagnetically induced transparency and entanglement in hybrid systems.
We consider a hybrid atom-optomechanical system consisting of a mechanical membrane inside an optical cavity and an atomic Bose-Einstein condensate outside the cavity. The condensate is confined in an optical lattice potential formed by a traveling laser beam reflected off one cavity mirror. We derive the cavity-mediated effective atom-atom interaction potential and find that it is nonuniform, site-dependent, and does not decay as the interatomic distance increases. We show that the presence of this effective interaction breaks the Z2{Z}_{2}Z2​ symmetry of the system and gives rise to new quantum phases and phase transitions. When the long-range interaction dominates, the condensate breaks the translation symmetry and turns into a novel self-organized latticelike state with increasing particle densities for sites farther away from the cavity. We present the phase diagram of the system and investigate the stabilities of different phases by calculating their respective excitation spectra. The system can serve as a platform to explore various self-organized phenomena induced by the long-range interactions.