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Quantum correlations beyond quantum entanglement represent vital resources in quantum information processing as well as in quantum computation. In fact, both quantum entanglement and quantum correlation are the same when the quantum system is described by pure states. However, this is not exactly the case when general mixed states are considered. In order to clarify this, a simple model has been proposed for the production and quantification of these quantum correlations between two mechanical resonators that are macroscopic in two Fabry–Pérot cavities optomechanical coupled by the photon hopping process. In this model, we analyze and investigate the quantification of the quantum correlation beyond the entanglement between the mechanical modes. We determine the global covariance matrix of the model from which we derive the expression of the entropy of formation ($E_f$) as well as the Gaussian quantum discord ($G_D$), which quantify the amount of quantum entanglement and quantum correlations, respectively. The analysis based on these two quantum correlations quantifiers shows that quantum discord is more appropriate to characterize the quantum correlations between the mechanical modes in an optomechanical quantum system in the presence of robust photon hopping.

We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this review, we will introduce the current status of optical trapping of dielectric particles in air and vacuum, Brownian motion of an optically trapped particle at room temperature, Feedback cooling and cavity cooling of the Brownian motion. We will also discuss about using optically trapped dielectric particles for studying macroscopic quantum mechanics and ultrasensitive force detection. Applications range from creating macroscopic Schrödinger's cat state, testing objective collapse models of quantum wavefunctions, measuring Casimir force, searching short-range non-Newtonian gravity, to detect gravitational waves.

In this paper, we study the decaying dynamics in the mirror-field interaction by means of the intrinsic decoherence scheme. Factorization of the mirror-field Hamiltonian with the use of displacement operators allows us to calculate the explicit solution to Milburn’s equation for arbitrary initial conditions. We show expectation values, correlations, and Husimi functions for the solutions obtained.

We propose to achieve quantum optical nonreciprocity in a hybrid qubit-optomechanical solid-state system. A two-level system (qubit) is coupled to a mechanically compliant mirror (via the linear Jaynes–Cummings interaction) placed in the middle of a solid-state optical cavity. We show for the first time that the generated optical bistability exhibits a bi-directional photonic switch, making the device a suitable candidate for a duplex communication system. On further exploring the fluctuation dynamics of the system, we found that the proposed device breaks the symmetry between forward and backward propagating optical modes (optical nonreciprocity), which can be controlled by tuning the various system parameters, including the qubit, which emerges as a new handle. The device thus behaves like an optical isolator and hence can store optical data in the acoustic mode, which can be retrieved later.

We analyze an optomechanical system formed by a mechanical mode and the two optical modes of an optomechanical cavity for the realization of a strongly quantum correlated three-mode system. We show that the steady state of the system shows three possible bipartite continuous variable (CV) entanglements in an experimentally accessible parameter regime, which are robust against temperature. We further show that selective entanglement between the mechanical mode and any of the two optical modes is also possible by the proper choice of the system parameters. Such a two-mode optomechanical system can be used for the realization of CV quantum information interfaces and networks.

In this study, we control the quantum correlations existing between a movable mirror and atoms in hybrid atom-optomechanical system using rotating wave approximation (RWA) in adiabatic regime. We use the Mancini criterion to measure the entanglement, the purity to quantify the degree of mixedness and the Gaussian geometric discord (GGD) to characterize the quantum correlations even beyond entanglement. We study the effect of the optomechanical cooling rate and the cooperativity atomic on the transfer of quantum correlations between the movable mirror and atoms under the thermal effect. We also investigate the robustness of the GGD with respect to entanglement by exploiting recent experimental parameters.

In an optomechanical system consisting of two Fabry–Pérot cavities fed by squeezed light and coupled via Coulomb interaction, we respectively use the logarithmic negativity, Gaussian discord and Gaussian coherence to analyze the behavior of three different indicators of nonclassicality, namely the entanglement, quantum discord and quantum coherence. We perform the rotating wave approximation and work in the resolved sideband regime. In two bi-mode states (optical and mechanical), the coherence is generally found to be greater than entanglement and discord. More interestingly, we show that the Coulomb interaction can be used either to degrade or enhance the nonclassical properties of the optical subsystem. In addition, compared with the discord and coherence, the mechanical entanglement is found strongly sensitive to both thermal and Coulomb effects, and it requires a minimum value of cooperativity to be generated. Remarkably, this minimum increases when increasing the Coulomb coupling strength. Finally, we notice that an optimal transfer of quantum correlations between the optical and mechanical subsystems is achieved in the absence of the Coulomb interaction.

In a two-mode Gaussian state ${\widehat{\varrho }}_{AB}$, we report on stationary evolution of three measures of correlations defined via the Rényi-2 entropy, i.e. quantum mutual information (QMI) ${{ℐ}}_{R,2}$, the Gaussian–Rényi-2 entanglement (GR2E) ${{ℰ}}_{R,2}$ and Gaussian quantum steering (GQS) ${𝒢}$. We evaluate analytical expression of the covariance matrix fully describing the state ${\widehat{\varrho }}_{AB}$. Further, we study, under influences of parameters characterizing the state at hand and its environment, the behavior of the three considered measures. We find that quantum steering ${𝒢}$ is always upper bounded by (GR2E) ${{ℰ}}_{R,2}$, which in turn is found always upper bounded by half of the QMI ${{ℐ}}_{R,2}$. This therefore satisfies the hierarchical relation $\frac{1}{2}{{ℐ}}_{R,2}\ge {{ℰ}}_{R,2}\ge {𝒢}$ established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett.117 (2016) 220502]. Importantly, we find that both GR2E ${{ℰ}}_{R,2}$ and GQS ${𝒢}$ are strongly affected by the thermal effects. Remarkably, when the GR2E ${{ℰ}}_{R,2}$ thoroughly vanishes, the GMI ${{ℐ}}_{R,2}$ exhibits a freezing behavior, and seems to be captured within a wide range of temperature.

An important challenge in the field of materials design and synthesis is to deliberately design mesoscopic objects starting from well-defined precursors and inducing directed movements in them to emulate biological processes. Recently, mesoscopic metal-oxide-based soft oxometalates (SOMs) have been synthesized from well-defined molecular precursors transcending the regime of translational periodicity. Here, we show that it is actually possible to controllably move such an asymmetric SOM, with the shape of a "peapod" along complex paths using tailor-made sophisticated optical potentials created by spin–orbit interaction of light due to a tightly focused linearly polarized Gaussian beam propagating through a stratified medium in an optical trap. We demonstrate motion of individual trapped SOMs along circular paths of more than 15 μm in a perfectly controlled manner by simply varying the input polarization of the trapping laser. Such controlled motion can have a wide range of applications starting from catalysis to the construction of dynamic mesoscopic architectures.

Optomechanical devices in which a flexible SiN membrane is placed inside an optical cavity allow for very high finesse and mechanical quality factor in a single device. They also provide fundamentally new functionality: the cavity detuning can be a quadratic function of membrane position. This enables a measurement of "position squared" (x²) and in principle a QND phonon number readout of the membrane. However, the readout achieved using a single transverse cavity mode is not sensitive enough to observe quantum jumps between phonon Fock states.

Here we demonstrate an x²-sensitivity that is orders of magnitude stronger using two transverse cavity modes that are nearly degenerate. We derive a first-order perturbation theory to describe the interactions between nearly-degenerate cavity modes and achieve good agreement with our measurements using realistic parameters. We also demonstrate theoretically that the x²-coupling should be easily tunable over a wide range.