We describe a scheme for entangling mechanical resonators which is efficient beyond the resolved sideband regime. It employs the radiation pressure force of the squeezed light produced by a degenerate optical parametric oscillator, which acts as a reservoir of quantum correlations (squeezed reservoir), and it is effective when the spectral bandwidth of the reservoir and the field frequencies are appropriately selected. It allows for the steady-state preparation of mechanical resonators in entangled Einstein-Podolsky-Rosen states and can be extended to the preparation of many entangled pairs of resonators which interact with the same light field, in a situation in which the optomechanical system realizes a starlike harmonic network.
We describe a scheme for entangling mechanical resonators which is efficient beyond the resolved sideband regime. It employs the radiation pressure force of the squeezed light produced by a degenerate optical parametric oscillator, which acts as a reservoir of quantum correlations (squeezed reservoir), and it is effective when the spectral bandwidth of the reservoir and the field frequencies are appropriately selected. It allows for the steady-state preparation of mechanical resonators in entangled Einstein-Podolsky-Rosen states and can be extended to the preparation of many entangled pairs of resonators which interact with the same light field, in a situation in which the optomechanical system realizes a starlike harmonic network.
Einstein–Podolski–Rosen (EPR) entanglement state is achievable by combining two single-mode position and momentum squeezed states at a 50:50 beam-splitter (BS). We investigate the generation of the EPR entangled state of two vibrating membranes in a ring resonator, where clockwise (CW) and counter-clockwise (CCW) travelling-wave modes are driven by lasers and finite-bandwidth squeezed lights. Since the optomechanical coupling depends on the location of the membranes, CW and CCW can couple to the symmetric and antisymmetric combination of mechanical modes for a suitable arrangement, which corresponds to a 50:50 BS mixing. Moreover, by employing the red-detuned driving laser and tuning the central frequency of squeezing field blue detuned from the driving laser with a mechanical frequency, the squeezing property of squeezed light can be perfectly transferred to the mechanical motion in the weak coupling regime. Thus, the BS mixing modes can be position and momentum squeezed by feeding the appropriate squeezed lights respectively, and the EPR entangled mechanical state is obtained. Moreover, cavity-induced mechanical cooling can further suppress the influence of thermal noise on the entangled state.
We propose a scheme for generating two-mode squeezing in high-Q resonators using a beam of atoms with random arrival times, which acts as a reservoir for the field. The scheme is based on four-wave mixing processes leading to emission into two cavity modes, which are resonant with the Rabi sidebands of the atomic dipole transition, driven by a saturating classical field. At steady state the cavity modes are in an Einstein-Podolsky-Rosen state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fluctuations in the atomic beam, does not require atomic detection nor velocity selection, and can be realized by presently available experimental setups with microwave resonators.
In this paper we investigate the squeezing of a finite-bandwidth optical field which may be thought of as originating from Einstein-Podolsky-Rosen- (EPR-) like quantum correlations between the upper and lower sidebands. Ordinarily, when EPR pairs are created from such a resource, the bandwidth is preserved, and the signal-to-noise ratio of the quadrature correlations is reduced. Here we show that by using frequency-dependent beam splitters we may create N EPR pairs from a single finite-bandwidth squeezed beam with no reduction in the correlations's signal-to-noise ratio. However, the bandwidth is reduced by a factor of N relative to the original squeezed beam. Because this transformation is linear it may be inverted to retrieve the single squeezed beam from the corresponding N EPR pairs.
We propose a scheme of an optomechanical system that optimizes entanglement in nanomechanical resonators through quantum state transfer of intracavity squeezing and squeezed reservoir field sources assisted by radiation pressure. The system is driven by red-detuned laser fields, which enable simultaneous cooling of the mechanical resonators and facilitate the quantum state transfer in a weak coupling and good cavity limit. Specifically, the mechanical entanglement is quantified using logarithmic negativity within the bipartite Gaussian states of the two mechanical modes. The results show that several key parameters, including the parametric phase and nonlinear gain of the non-degenerate optical parametric amplifier, the strength of the squeezing reservoir, optomechanical cooperativity, thermal excitation of phonons, and the temperature of mechanical baths, strongly influence the degree of mechanical entanglement. Hence, the findings indicate that careful tuning of the parameters can enable control over the enhancement of entanglement robustness, suggesting that this optomechanical scheme provides a viable pathway for applications in quantum sensing and information processing
Quantum optomechanical systems enable versatile control of non-classical light. We study two-mode squeezed-light generation in a driven optomechanical cavity with parametrically amplified optical modes coupled to mechanical resonator. Coherent driving reveals a rich control landscape where parametric nonlinearity, optomechanical coupling, and reservoir interactions jointly tailor quantum correlations-including two-mode squeezing, entanglement, steering, and discord. Remarkably, mechanical oscillators not only mediate optical entanglement but also act as a squeezing resource, enabling enhancement or suppression of quantum correlations via parameter tuning. We derive steady-state second-order moments and closed-form covariance matrix expressions, quantifying entanglement via logarithmic negativity, steering via Reid criterion, and discord via von Neumann entropy, providing a comprehensive framework for optimized generation of quantum correlations in hybrid quantum systems.
Einstein–Podolski–Rosen (EPR) entanglement states are achievable by combining two single-mode position and momentum squeezed states at a 50:50 beam splitter (BS). To generate the EPR mechanical entanglement, we consider the system consisted of two parametric optomechanical resonators, where two mechanical oscillators are linearly coupled. The linear coupling forms the symmetric and antisymmetric combinations of two mechanical modes, parallel to a 50:50 BS mixing. In the weak optomechanical coupling regime and via applying the opposite phases of parametric interactions, the symmetric and antisymmetric mechanical modes can be position and momentum squeezed, respectively. Therefore, two original mechanical modes are EPR entangled. Moreover, the mechanical thermal noise can decrease the entanglement. But with the parametric interaction enhanced optomechanical cooling, the influence of thermal noise on entanglement can be significantly suppressed, and the mechanical entanglement can be generated under a relatively high temperature. We also discuss the critical thermal occupation where the entanglement disappears, which is proportional to the optomechanical cooperativity parameter.