Squeezing is a resource that enables precision enhancements in quantum metrology and can be used as a basis for the generation of entanglement by linear optics. While strong squeezing is challenging to generate in optical fields, here we present simple periodic modulation protocols in optomechanical systems that can generate large squeezing of their mechanical degrees of freedom for realistic system parameters. We then proceed to show how such protocols can serve to improve the measurement precision of weak forces and enhance the generation of entanglement between test masses that are subject to any kind of weak interaction. Moreover, these protocols can be reverted to reduce the amount of injected energy, while preserving the generated entanglement and making it more resilient to noise. We present the principle at work, discuss its application in a variety of physical settings, including levitated and tethered mechanical harmonic oscillators, and present example applications to Casimir and gravitational forces.
We study the effect of laser phase noise on the generation of stationary entanglement between an intracavity optical mode and a mechanical resonator in a generic cavity optomechanical system. We show that one can realize robust stationary optomechanical entanglement even in the presence of non-negligible laser phase noise. We also show that the explicit form of the laser phase noise spectrum is relevant, and discuss its effect on both optomechanical entanglement and ground state cooling of the mechanical resonator.
A growing number of experimental set-ups in cavity optomechanics exploit periodically driven fields. However, such set-ups are not amenable to analysis using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a new method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators (ii) Floquet and (iii) iterati…
Entanglement is often the key element in quantum information protocols. Here, we present schemes to generate robust photon entanglement in optomechanical interfaces via quantum interference. The schemes explore the excitation of the Bogoliubov dark mode and the destructive quantum interference between the bright modes of the interface, similar to electromagnetically induced transparency, to eliminate leading-order effects of the mechanical noise. Both continuous-variable and discrete-state entanglements that are robust against the mechanical noise can be achieved.
We provide an argument to infer stationary entanglement between light and a mechanical oscillator based on continuous measurement of light only. We propose an experimentally realizable scheme involving an optomechanical cavity driven by a resonant, continuous-wave field operating in the non-sideband-resolved regime. This corresponds to the conventional configuration of an optomechanical position or force sensor. We show analytically that entanglement between the mechanical oscillator and the output field of the optomechanical cavity can be inferred from the measurement of squeezing in (general…
We propose here a setup to generate and evaluate the entanglement between two mechanical resonators in a cavity optomechanical setting. As in previous proposals, our scheme includes two driving pumps allowing for the generation of two-mode mechanical squeezing. In addition, we include here four additional probing tones, which allow for the separate evaluation of the collective mechanical quadratures required to estimate the Duan quantity, thus allowing us to infer whether the mechanical resonators are entangled.
A pulsed scheme for generating robust optical entanglement via the coupling of two optical modes to a mechanical oscillator is proposed. This scheme is inspired by the Sørensen-Mølmer approach for entangling trapped ions in a thermal environment and is based on the use of optical driving pulses that are slightly detuned from the respective sideband resonance. We show that for certain pulse durations, the optomechanical interaction can return the mechanical oscillator to its initial state. The corresponding entanglement generation is robust against thermal mechanical noise in the weak as well a…
Although superconducting systems provide a promising platform for quantum computing, their networking poses a challenge as they cannot be interfaced to light---the medium used to send quantum signals through channels at room temperature. We show that mechanical oscillators can mediated such coupling and light can be used to measure the joint state of two distant qubits. The measurement provides information on the total spin of the two qubits such that entangled qubit states can be postselected. Entanglement generation is possible without ground-state cooling of the mechanical oscillators for s…
Quantum entanglement not only plays an important role in the study of the fundamentals of quantum theory, but also is considered as a crucial resource in quantum information science. The generation of macroscopic entanglement involving multiple optical and mechanical modes is a desired task in cavity optomechanics. However, the dark-mode effect is a critical obstacle against the generation of quantum entanglement in multimode optomechanical systems consisting of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity mode. Here we propose an auxiliary-cavity-mode met…
We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually through an optical fiber or a phonon tunneling. The cavities are filled with Kerr-type nonlinear medium. It is found that, no matter which the coupling and periodically modulation we choose, both of the quantum synchronization of nonlinear optomechanical system are more appealing than the linear optomechanical system. It is easier to observe greatly enhanced qua…
We study entanglement dynamics in dispersive optomechanical systems consisting of two optical modes and a mechanical oscillator inside an optical cavity. The two optical modes interact with the mechanical oscillator, but not directly with each other. The appearance of optical entanglement witnesses non-classicality of the oscillator. We study the dependence of the entanglement dynamics with the optomechanical coupling, the mean photon number in the cavity and the oscillator temperature. An experimental realization with ultracold atomic ensembles is proposed.
Output entanglement is a key element in quantum information processing. Here, we show how to obtain optimal entanglement between two filtered output fields in a three-mode optomechanical system. First, we obtain the key analytical expression of optimal time delay between the two filtered output fields, from which we can obtain the optimal coupling for output entanglement without time delay. In this case, our linearized analysis predicts that the entanglement saturates to an optimal value as the optomechanical coupling is increased. Furthermore, we obtain the optimal output entanglement with ti…
We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the tra…
We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature.
The radiation pressure induced coupling between an optical cavity field and a mechanical oscillator can create entanglement between them. In previous works this entanglement was treated as that of the quantum fluctuations of the cavity and mechanical modes around their classical mean values. Here we provide a fully quantum approach to optomechanical entanglement, which goes beyond the approximation of classical mean motion plus quantum fluctuation, and applies to arbitrary cavity drive. We illustrate the real-time evolution of optomechanical entanglement under drive of arbitrary detuning to sh…
Cooling and Entanglement in optomechanical systems coupled through radiation pressure and photothermal force is studied. To develop the photothermal model, we derive an expression for deformation constant of the force. Exploiting linearized quantum Langevin equations we investigate dynamics of such systems. According to our analysis, in addition to separate action of radiation pressure and photothermal force, their cross correlation effect plays an important role in dynamics of the system. We also achieve an exact relation for the phonon number of the mechanical resonator in such systems, and …
We examine the entanglement properties of a system that represents two driven microwave cavities each optomechanically coupled to two separate driven optical cavities which are connected by a single-mode optical fiber. The results suggest that it may be possible to achieve near-maximal entanglement of the microwave cavities, thus allowing a teleportation scheme to enable interactions for hybrid quantum computing of superconducting qubits with optical interconnects.
Entangled continuous variable (CV) Gaussian states with different wavelengths plays a central role in recent CV-based approaches to quantum network, quantum information processing and quantum metrology. Typically, experiments demonstrating CV entanglement exploit the optical parametric frequency down conversion. Due to the probabilistic nature of photon pair generation, the entanglement involving the post-selection of photonic qubits is limited to at most three colors. Here We theoretically present a scheme for the deterministic generation of entanglement among bright multicolor CV Gaussian st…
The cavity-optomechanical radiation pressure interaction provides the means to create entanglement between a mechanical oscillator and an electromagnetic field interacting with it. Here we show how we can utilize this entanglement within the framework of time-continuous quantum control, in order to engineer the quantum state of the mechanical system. Specifically, we analyze how to prepare a low-entropy mechanical state by (measurement-based) feedback cooling operated in the blue detuned regime, the creation of bipartite mechanical entanglement via time-continuous entanglement swapping, and pr…
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 demonstrate a complete, probabilistic quantum dynamical simulation of the standard nonlinear Hamiltonian of optomechanics, including decoherence at finite temperatures. Robust entanglement of an optical pulse with the oscillator is predicted, as well as strong quantum steering between the optical and mechanical systems. Importantly, our probabilistic quantum simulation method uses the positive-P technique, which is scalable to large Hilbert spaces.
Displaced single-photon entanglement is a simple form of optical entanglement, obtained by sending a photon on a beamsplitter and subsequently applying a displacement operation. We show that it can generate, through a momentum transfer in the pulsed regime, an optomechanical entangled state involving macroscopically distinct mechanical components, even if the optomechanical system operates in the single-photon weak coupling regime. We discuss the experimental feasibility of this approach and show that it might open up a way for testing unconventional decoherence models.
We consider the distribution of entanglement from a multi-mode optical driving source to a network of remote and independent optomechanical systems. By focusing on the tripartite case, we analyse the effects that the features of the optical input states have on the degree and sharing-structure of the distributed, fully mechanical, entanglement. This study, which is conducted looking at the mechanical steady-state, highlights the structure of the entanglement distributed among the nodes and determines the relative efficiency between bipartite and tripartite entanglement transfer. We discuss a f…
We study the simplest optomechanical system with a focus on the bistable regime. The covariance matrix formalism allows us to study both cooling and entanglement in a unified framework. We identify two key factors governing entanglement, namely the bistability parameter, i.e. the distance from the end of a stable branch in the bistable regime, and the effective detuning, and we describe the optimum regime where entanglement is greatest. We also show that in general entanglement is a non-monotonic function of optomechanical coupling. This is especially important in understanding the optomechani…
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 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…
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 …
Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement…
We propose a protocol how to generate and verify bipartite Gaussian entanglement between two mechanical modes coupled to a single optical cavity, by means of short optical pulses and measurement. Our protocol requires neither the resolved sideband regime, nor low thermal phonon occupancy, and allows the generation and verification of quantum entanglement in less than a mechanical period of motion. Entanglement is generated via effective two-mode mechanical squeezing through conditioning position measurements. We study the robustness of entanglement to experimental deviations in mechanical freq…
A potential experimental system, based on the Silicon Nitride (SiN) material, is proposed to generate steady-state room-temperature optomechanical entanglement. In the proposed structure, the nanostring interacts dispersively and reactively with the microdisk cavity via the evanescent field. We study the role of both dispersive and reactive coupling in generating optomechanical entanglement, and show that the room-temperature entanglement can be effectively obtained through the dispersive couplings within the reasonable experimental parameters. In particular, we find, in the high Temperature (…
Entanglement generation at a macroscopic scale offers an exciting avenue to develop new quantum technologies and study fundamental physics on a tabletop. Cavity quantum optomechanics provides an ideal platform to generate and exploit such phenomena owing to the precision of quantum optics combined with recent experimental advances in optomechanical devices. In this work, we propose schemes operating outside the resolved-sideband regime, to prepare and verify both optical-mechanical and mechanical-mechanical entanglement. Our schemes employ pulsed interactions with a duration much less than the…
Stationary entanglement in a four-mode optomechanical system, especially under roomtemperature, is discussed. In this scheme, when the coupling strengths between the two target modes and the mechanical resonator are equal, the results cannot be explained by the Bogoliubov mode- based scheme. This is related to the idea of quantum-mechanics-free subspace, which plays an important role when the thermal noise of the mechanical modes is considered. Significantly prominent steady-state entanglement can be available under room-temperature.
We propose an optomechanical dissipation engineering scheme by introducing an ancillary mechanical mode with a large decay rate to control the density of states of the optical mode. The effective linewidth of the optical mode can be reduced or broadened, manifesting the dissipation engineering. To prove the ability of our scheme in improving the performances of the optomechanical system, we studied optomechanical entanglement and phonon cooling. It is demonstrated that the optomechanical entanglement overwhelmed by thermal phonon excitations could be restored via dissipation engineering. For t…
We study entanglement of the cavity modes in a double-cavity optomechanical system in strong-coupling regime. The system consists of two optomechanical systems coupled by a single photon hopping between them. With the radiation pressure of the photon, entanglement of the cavity modes can be generated. The concurrence between the cavity modes is at least twice larger than that between the mechanical modes. Moreover, when we change the ratio between coupling strength and resonant frequency of mechanical modes, the entanglement in cavity and mechanical modes are influenced differently.
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…
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…
Entangling a mechanical oscillator with an optical mode is an enticing and yet a very challenging goal in cavity optomechanics. Here we consider a pulsed scheme to create Einstein-Podolsky-Rosen-type entanglement between a traveling-wave light pulse and a mechanical oscillator. The entanglement can be verified unambiguously by a pump-probe sequence of pulses. In contrast to schemes that work in a steady-state regime under a continuous-wave drive, this protocol is not subject to stability requirements that normally limit the strength of achievable entanglement. We investigate the protocol's per…
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement …
We propose how to achieve significantly enhanced quantum refrigeration and entanglement by coupling a pumped auxiliary cavity to an optomechanical cavity. We obtain both analytical and numerical results, and find optimal-refrigeration and -entanglement conditions under the auxiliary-cavity-assisted (ACA) mechanism. Our method leads to a giant amplification in the net refrigeration rate, and reveals that the ACA entanglement has a much stronger noise-tolerant ability in comparison with the unassisted case. By appropriately designing the ACA mechanism, an effective mechanical susceptibility can …
Low dissipation, tunable coupling to other quantum systems, and unique features of phonons in the aspects of propagation, detection and others suggest the applications of quantized mechanical resonators in phonon-based quantum information processing (QIP) in a way different from their photonic counterpart. In this paper, we propose the first protocol of entanglement concentration for nonlocal phonons from quantized mechanical vibration. We combine the optomechanical cross-Kerr interaction with the Mach-Zehnder interferometer and, by means of twice optomechanical interactions and the photon ana…
We study theoretically a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. By using two-tone (i.e. amplitude-modulated) driving of the cavity, it is possible to couple the cavity to a single collective quadrature of the mechanical oscillators. In such a way, a back-action-evading measurement of the collective mechanical quadrature is possible. We discuss how this can allow one to measure both quadratures of a mechanical force beyond the full quantum limit, paying close attention to the role of dissipation and experimental imperfections. We a…
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…
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed lig…
Quantum networking based on optical Gaussian states, although promising in terms of scalability, is hindered by the fact that their entanglement cannot be distilled via Gaussian operations. We show that optomechanics, integrable (on-chip) availability, and particularly the scope to measure the mechanical degree of freedom, can address this problem. Here, one of the optical modes of a two-mode squeezed vacuum is injected into a single-sided Fabry-Pérot cavity and non-linearly coupled to a mechanical oscillator. Afterward, the position of the oscillator is measured using pulsed optomechanics and…
A standard model is suggested to explore correlation features of two spatially separated optomechanical cavities. The cavities are coupled through the photon-hopping process. In particular, we investigate the generation of entanglement between mechanical resonators in the strong coupling regime and the two cavities are assumed to be driven by a coherent laser field. In order to quantify entanglement we use the logarithmic negativity. The analytical solutions are presented for the system in a parameter regime very close to the current experimental results. We show that in the presence of the ph…
We study steady-state continuous variable entanglement in a three-mode optomechanical system consisting of an active optical cavity (gain) coupled to a passive optical cavity (loss) supporting a mechanical mode. For a driving laser which is blue-detuned, we show that coupling between optical and mechanical modes is enhanced in the unbroken-$\mathcal{PT}$-symmetry regime. We analyze the stability and this shows that steady-state solutions are more stable in the gain and loss systems. We use these stable solutions to generate distant entanglement between the mechanical mode and the optical field…
Distribution of the entangled state of trapped atomic ions to long distance using quantum repeater protocol is considered. Indeed, the long distance is divided into short parts, and then using entanglement generation and entanglement swapping techniques in optomechanical cavities, the entanglement is distributed. To do the task, we perform interaction between trapped atomic ions in optomechanical cavities, operate proper measurements on trapped ions and also make Bell state measurement as a well-known way to swap the entanglement. Accordingly, the entanglement is distributed between target ion…
