Entanglement is fundamental to quantum information science and technology, yet controlling and manipulating entanglement -- so-called entanglement engineering -- for arbitrary quantum systems remains a formidable challenge. There are two difficulties: the fragility of quantum entanglement and its experimental characterization. We develop a model-free deep reinforcement-learning (RL) approach to entanglement engineering, in which feedback control together with weak continuous measurement and partial state observation is exploited to generate and maintain desired entanglement. We employ quantum optomechanical systems with linear or nonlinear photon-phonon interactions to demonstrate the workings of our machine-learning-based entanglement engineering protocol. In particular, the RL agent sequentially interacts with one or multiple parallel quantum optomechanical environments, collects trajectories, and updates the policy to maximize the accumulated reward to create and stabilize quantum entanglement over an arbitrary amount of time. The machine-learning-based model-free control principle is applicable to the entanglement engineering of experimental quantum systems in general.
The polarizations of optical fields, besides field intensities, provide more degrees of freedom to manipulate coherent light-matter interactions. Here we propose how to achieve a coherent switch of optomechanical entanglement in a polarized-light-driven cavity system. We show that by tuning the polarizations of the driving field, the effective optomechanical coupling can be well controlled and, as a result, quantum entanglement between the mechanical oscillator and the optical transverse electric (TE) mode can be coherently and reversibly switched to that between the same phonon mode and the o…
Quantum entanglement is the key to many applications like quantum key distribution, quantum teleportation, and quantum sensing. However, reliably generating quantum entanglement in macroscopic systems has proved to be a challenge. Here, we present a detailed analysis of ponderomotive entanglement generation which utilizes optomechanical interactions to create quantum correlations. We numerically calculate an entanglement measure -- the logarithmic negativity -- for the quantitative assessment of the entanglement. Experimental limitations, including thermal noise and optical loss, from measurem…
In this paper, firstly, we consider bipartite entanglement between each part of an optomechanical cavity composed of one dimensional Bose-Einstein condensate (BEC). we investigate atomic collision on the behavior of the BEC in the week photon-atom coupling constant, and use Bogoliubov approximation for the BEC. Secondly under above condition, we propose a scheme for entanglement swapping protocol wich involves tripartite systems. In our investigation, we consider a scenario where BECs, moving mirrors, and optical cavity modes are given in a Gaussian state with a covariance matrix (CM). By appl…
Quantum entanglement plays a key role in both understanding the fundamental aspects of quantum physics and realizing various quantum devices for practical applications. Here we propose how to achieve coherent switch of optomechanical entanglement in an optical whispering-gallery-mode resonator, by tuning the phase difference of the driving lasers. We find that the optomechanical entanglement and the associated two-mode quantum squeezing can be well tuned in a highly asymmetric way, providing an efficient way to protect and enhance quantum entanglement against optical backscattering, in compari…
In this work, we theoretically study the quantum correlations present in an optomechanical system by invoking an additional cross-Kerr coupling between the optical and mechanical mode. Under experimentally achievable conditions, we first show that a significant enhancement of the steady-state entanglement could be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature. Then, we employ Gaussian quantum discord as a witness of the genuine quantumness of the correlation present in the system and discuss its de…
We report a study of optomechanical entanglement under the drive of one or a series of laser pulses with arbitrary detuning and different pulse shapes. Because of the non-existence of system steady state under pulsed driving field, we adopt a different approach from the standard treatment to optomechanical entanglement. The situation of the entanglement evolution in high temperature is also discussed.
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 effect of a degenerate optical parametric amplifier (OPA) placed inside an optomechanical cavity on the steady-state entanglement of two cavity modes, which jointly interact with a mechanical resonator. Two cavity modes are respectively driven at the red and blue sideband associated with the mechanical resonator, which generates entanglement between them in the limit of resolved sideband. The OPA gives rise to single-mode squeezing of the cavity fields, which results in significant improvement of the two-mode entanglement. It is found that an optimal nonlinear gain of the OP…
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…
We investigate dynamics of an optomechanical system under the Non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field (called bound state) is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage …
We propose an approach to generate strong quantum entanglement by the controllable four wave mixing mechanism in a single cavity, weak coupling optomechanical system. The optomechanical system is driven by a strong two tone pump field and a weak signal field, simultaneously. The two tone pump field consists of a lower and an upper sideband, which couple with the optical cavity and mechanical resonator, and generate the beam splitter and two mode squeezing interactions under the rotating wave approximation. This interaction mechanism modifies the effective susceptibility of the optomechanical c…
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…
We give a theoretical study of a double-cavity system in which a mechanical resonator beam is coupled to two cavity modes on both sides through radiation pressures. The indirect coupling between the cavities via the resonator sets up a correlation in the optomechanical entanglements between the two cavities with the common resonator. This correlation initiates an entanglement transfer from the intracavity photon-phonon entanglements to an intercavity photon-photon entanglement. Using numerical solutions, we show two distinct regimes of the optomechanical system, in which the indirect entanglem…
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…
In recent development of quantum technologies, a frequency conversion of quantum signals has been studied widely. We investigate the optic-microwave entanglement that is generated by applying an electro-optomechanical frequency conversion scheme to one mode in an optical two-mode squeezed vacuum state. We quantify entanglement of the converted two-mode Gaussian state, where surviving entanglement of the state is analyzed with respect to the parameters of the electro-optomechanical system. Furthermore, we show that there exists an upper bound for the entanglement that survives after the convers…
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…
In this work, we perform a series of phonon counting measurement with different methods in a 3-mode optomechanical system, and we compare the difference of the entanglement after measurement. In this article we focus on the two cases: imperfect measurement and on-off measurement. We find that whatever measurement you take, the entanglement will increase. The size of entanglement enhancement is the largest in perfect measurement, second in the imperfect measurement, and it is not obvious in the on-off measurement. We are sure that the more precise measurement information, the larger entanglemen…
We investigate the stationary bipartite entanglement is a useful hybrid optomechanical system, which is constituted of two coupled-cavity optomechanics through a photon hopping process and both are driven by squeezed light. The transfer of correlations from an entangled light source to optomechanical cavities is explored. It is found that the generation of bipartite entanglement and entanglement transfer depend strongly on photon hopping strength and the matching of the input squeezed modes to the cavity modes. It is revealed that the generated stationary bipartite entanglement due to squeezed…
A strategy for generating entanglement in two separated optomechanical oscillators is analysed, using entangled radiation produced from downconversion and stored in an initiating cavity. We show that the use of pulsed entanglement with optimally shaped temporal modes can efficiently transfer quantum entanglement into a mechanical mode, then remove it after a fixed waiting time for measurement. This protocol could provide new avenues to test for bounds on decoherence in massive systems that are spatially separated, as originally suggested by Wendell Furry [1] not long after the discussion by Ei…
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 propose a scheme for the creation of robust entanglement between a movable mirror and atomic ensemble at the macroscopic level in coupled optomechanical system. In experimentally accessible parameter regimes, we show that critical temperature of the bipartite continuous variable entanglement in our scheme can be raised from previous 24 K [Vitali {\it et al.}, Phys. Rev. Lett. \textbf{98}, 030405 (2007)] and 20 K [Genes {\it et al.}, Phys. Rev. A \textbf{77}, 050307(R) (2008)] to 32 K. We also investigate the entanglement transfer based on this coupled system. The scheme can be used for the …
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive…
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 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…
We investigate the phenomenon of gravity-induced entanglement in optomechanical systems. Assuming photon number conservation and the Newtonian potential expanded up to the quadratic order of the oscillator positions, we exactly solve the dynamics of the optomehcanical systems. Then, we find that the phase difference due to the Newtonian gravity leads to the large entanglement of photons in separated cavities. We clarify the generating mechanism of large gravity-induced entanglements in optomechanical systems in an exact manner. We also determine the characteristic time to generate the maximal …
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 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.
Quantum transduction between microwave and optics can be realized by quantum teleportation if given reliable microwave-optical entanglement, namely entanglement-based quantum transduction. To realize this protocol, an entangled source with high-fidelity between the two frequencies is necessary. In this paper, we study the microwave and optical entanglement generation based on a generic cavity electro-optomechanical system in the strong coupling regime. Splittings are shown in the microwave and optical output spectra and the frequency entanglement between the two modes is quantified. We show th…
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…
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…
We study an optomechanical system in which the mechanical motion of a single trapped ion is coupled to a cavity field for the realization of a strongly quantum correlated two-mode system. We show that for large pump intensities the steady state photon number exhibits bistable behaviour. We further analyze the occurrence of normal mode splitting (NMS) due to mixing of the fluctuations of the cavity field and the fluctuations of the ion motion which indicates a coherent energy exchange. We also find that in the parameter regime where NMS exists, the steady state of the system shows continuous va…
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…
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…
Entanglement of light and multiple vibrations is a key resource for multi-channel quantum information processing and memory. However, entanglement generation is generally suppressed, or even fully destroyed, by the dark-mode (DM) effect induced by the coupling of multiple degenerate or near-degenerate vibrational modes to a common optical mode. Here we propose how to generate optomechanical entanglement via \emph{DM breaking} induced by synthetic magnetism. We find that at nonzero temperature, light and vibrations are \emph{separable} in the DM-unbreaking regime but \emph{entangled} in the DM-…
We present exact solutions for the quantum time evolution of two spatially separated, local inductor-capacitor (LC) oscillators that are coupled optomechanically to a long elastic strip that functions as a quantum thermal acoustic field environment. We show that the optomechanical coupling to the acoustic environment gives rise to causal entanglement dynamics between the two LC oscillators in the absence of resonant photon exchange between them, and that significant entanglement develops regardless of the environment temperature. Such a process establishes that distributed entanglement may be …
