We show that the closed-loop control obtained by feeding back the derivative of the signal from the homodyne measurement of one mode of the light exiting a two-mode optical cavity interacting with a mechanical resonator permits us to control and increase optical output entanglement. In particular, the proposed feedback-enhanced setup allows us to achieve a fidelity of coherent-state teleportation greater than the threshold value of 2/3 for secure teleportation and two-way steering between the two cavities' output modes down the line in the presence of loss, which otherwise would not be possible without feedback.
We show that the closed-loop control obtained by feeding back the derivative of the signal from the homodyne measurement of one mode of the light exiting a two-mode optical cavity interacting with a mechanical resonator permits us to control and increase optical output entanglement. In particular, the proposed feedback-enhanced setup allows us to achieve a fidelity of coherent-state teleportation greater than the threshold value of 2/3 for secure teleportation and two-way steering between the two cavities' output modes down the line in the presence of loss, which otherwise would not be possible without feedback.
We propose a scheme to enhance entanglement and asymmetric steering between two mechanical oscillators in an optomechanical system with coherent feedback control. In the system, an optical cavity interacts with two mechanical oscillators and an auxiliary cavity whose output field is fed back into the input port of the optical cavity via a feedback loop. Due to the coherence between the auxiliary cavity and feedback, we derive the effective decay rate and a nonzero frequency shift of the optical cavity. Consequently, the induced beam-splitter-type and parametric-type interactions between the two mechanical oscillators are modulated, which leads to the enhancement of entanglement and the generation of asymmetric steering even if the two mechanical oscillators possess identical decoherence properties. And the direction of asymmetric steering can be controlled by tuning the jumping phase between two cavities and optimizing the ratio of drive asymmetry. In contrast to the method of adding losses or noises to one subsystem at the cost of reducing steerability, this scheme provides an active way to achieve enhanced asymmetric steering. Furthermore, the steady-state and dynamical entanglement and asymmetric steering can be generated in the unresolved-sideband regime, which is friendly for experimental implementation.
The theory of phase control of coherence, entanglement and quantum steering is developed for an optomechanical system composed of a single mode cavity containing a partially transmitting dielectric membrane and driven by short laser pulses. The membrane divides the cavity into two mutually coupled optomechanical cavities resulting in an effective three-mode closed loop system, two field modes of the two cavities and a mechanical mode representing the oscillating membrane. The closed loop in the coupling creates interfering channels which depend on the relative phase of the coupling strengths of the field modes to the mechanical mode. Populations and correlations of the output modes are calculated analytically and show several interesting phase dependent effects such as reversible population transfer from one field mode to the other, creation of collective modes, and induced coherence without induced emission. We find that these effects result from perfect mutual coherence between the field modes which is preserved even if one of the modes is not populated. The inseparability criterion for the output modes is also investigated and we find that entanglement may occur only between the field modes and the mechanical mode. We show that depending on the phase, the field modes can act on the mechanical mode collectively or individually resulting, respectively, in tripartite or bipartite entanglement. In addition, we examine the phase sensitivity of quantum steering of the mechanical mode by the field modes. Deterministic phase transfer of the steering from bipartite to collective is predicted and optimum steering corresponding to perfect EPR state can be achieved. These different types of quantum steering can be distinguished experimentally by measuring the coincidence rate between two detectors adjusted to collect photons of the output cavity modes. In particular, we find that the minima of the interference pattern of the coincidence rate signal the bipartite steering, while the maxima signal the collective steering.
We propose a coherent control scheme for engineering quantum correlations in a cavity optomechanical (COM) system consisting of a driven optical cavity with an embedded nonlinear medium and a membrane, assisted by a coherent feedback loop. The nonlinear medium and the membrane are pumped to implement optical and mechanical parametric amplifications with controllable modulation frequencies and pump amplitudes. Within the stable regime identified by Floquet analysis, the feedback-induced enhancement of optomechanical entanglement persists when the period-averaged mean-field intracavity photon number is matched, showing that the enhancement cannot be attributed simply to an increase in this quantity. A systematic comparison of the four configurations further reveals a nonadditive interplay between dual parametric amplification and coherent feedback. Varying the amplitude reflectivity of the beam splitter and the feedback loop phase enables effective control of optomechanical entanglement and directional EPR steering, including a transition from one-way to two-way steering. The combined scheme also improves the robustness of both correlations against thermal noise, providing a potential route toward robust quantum-state engineering in COM systems.
Abstract In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein–Podolsky–Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can only be prepared in steady weakly entangled states which however do not display EPR steering and Bell nonlocality, due to the so-called 3 dB limit. But when the feedback is present, it is found that the mechanical entanglement is considerably enhanced such that strong mechanical steering and Bell nonlocality can be obtained in the steady-state regime. We analytically reveal that this is because the feedback drives the mechanical oscillators into a steady approximate two-mode squeezed vacuum state, with arbitrary squeezing in principle. It is shown that the feedback can also obviously improve the purity of the nonclassical mechanical states. The dependences of the mechanical quantum nonlocality on the feedback strength and thermal fluctuations are studied, and it is found that Bell nonlocality is much more vulnerable to thermal noise than EPR steerable nonlocality.
In this paper, we investigate the dynamics of quantum correlations for the continuous-variable bipartite optomechanical system in the presence of homodyne mediated quantum feedback. The system is constructed using the Fabry–Perot cavity and a mechanical oscillator. In detail, we have studied the quantum entanglement via logarithmic negativity, quantum discord, and quantum steering between the optical and mechanical modes. The results show that the maximum entanglement between the optical and mechanical modes occurred out of the resonance frequency at the steady-state region due to the presence of the optical feedback. We also employ quantum steering to see the steerability between the modes. It is observed that the quantum entanglement increases when the effective detuning frequency increases, however, the quantum discord and steering decrease when the effective detuning frequency increases for a given quantum feedback strength with other parameters of the system are to be fixed. Moreover, the presence of quantum feedback has an enhancement effect on the quantum correlations.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.