Optomechanical entanglement between a movable mirror and a cavity field

Macroscopic entanglement between ferrimagnetic magnons and atoms via crossed optical cavities

We consider a two-dimensional opto-magnomechanical (OMM) system including two optical cavity modes, a magnon mode, a phonon mode, and a collection of two-level atoms. We show how the stationary entanglement between two-level atoms and magnons can be achieved. The presence of two optical cavities leads the atom-magnon entanglement to be achieved in a wide parameter regime. Furthermore, it is shown that one optical cavity can get entangled with magnons, phonons, and the other optical cavity. The entanglement is robust against thermal noise. The work may find applications in building hybrid quantum networks and quantum information processing.

Exploring regenerative coupling in phononic crystals for room temperature quantum optomechanics

Quantum technologies play a pivotal role in driving transformative advancements across diverse fields, surpassing classical approaches and empowering us to address complex challenges more effectively; however, the need for ultra-low temperatures limits the use of these technologies to particular fields. This work comes to alleviate this problem. We present a way of phononic bandgap engineering using FEM by which the radiative mechanical energy dissipation of a nanomechanical oscillator can be significantly suppressed through coupling with a complementary oscillating mode of a defect of the surrounding phononic crystal (PnC). Applied to an optomechanically coupled nanobeam resonator in the megahertz regime, we find a mechanical quality factor improvement of up to four orders of magnitude compared to conventional PnC designs. As this method is based on geometrical optimization of the PnC and frequency matching of the resonator and defect mode, it is applicable to a wide range of resonator types and frequency ranges. Taking advantage of the, hereinafter referred to as, "regenerative coupling" in phononic crystals, the presented device is capable of reaching f × Q products exceeding 10E16 Hz with only two rows of PnC shield. Thus, stable quantum states with mechanical decoherence times up to 700 μs at room temperature can be obtained, offering new opportunities for the optimization of mechanical resonator performance and advancing the room temperature quantum field across diverse applications.

Entanglement and quantum coherence of two YIG spheres in a hybrid Laguerre-Gaussian cavity optomechanics

We theoretically investigate continuous variable entanglement and macroscopic quantum coherence in the hybrid L-G rotational cavity optomechanical system containing two YIG spheres. In this system, a single L-G cavity mode and both magnon modes (which are due to the collective excitation of spins in two YIG spheres) are coupled through the magnetic dipole interaction whereas the L-G cavity mode can also exchange orbital angular momentum (OAM) with the rotating mirror (RM). We study in detail the effects of various physical parameters like cavity and both magnon detunings, environment temperature, optorotational and magnon coupling strengths on the bipartite entanglement and the macroscopic quantum coherence as well. We also explore parameter regimes to achieve maximum values for both of these quantum correlations. We also observed that the parameters regime for achieving maximum bipartite entanglement is completely different from macroscopic quantum coherence. So, our present study shall provide a method to control various nonclassical quantum correlations of macroscopic objects in the hybrid L-G rotational cavity optomechanical system and have potential applications in quantum sensing, quantum meteorology, and quantum information science.

Steady motional entanglement between two distant levitated nanoparticles

Quantum entanglement in macroscopic systems is not only essential for practical quantum information processing, but also valuable for the study of the boundary between quantum and the classical world. However, it is very challenging to achieve the steady remote entanglement between distant macroscopic systems. We consider two distant nanoparticles, both of which are optically trapped in two cavities. Based on the coherent scattering mechanism, we find that the ultrastrong optomechanical coupling between the cavity modes and the motion of the levitated nanoparticles could be achieved. The large and steady entanglement between the filtered output cavity modes and the motion of nanoparticles can be generated if the trapping laser is under the red sideband. Then through entanglement swapping, the steady motional entanglement between the distant nanoparticles can be realized. We numerically simulate and find that the two nanoparticles with 10 km distance can be entangled for the experimentally feasible parameters, even in room temperature environments. The generated continuous variable multipartite entanglement is the key to realizing the quantum enhanced sensor network and the sensitivity beyond the standard quantum limit.

Nonreciprocal strong mechanical squeezing based on the Sagnac effect and two-tone driving

We propose a scheme for generating nonreciprocal strong mechanical squeezing by using two-tone lasers to drive a spinning optomechanical system. For given driving frequencies, strong mechanical squeezing of the breathing mode in the spinning resonator can be achieved in a chosen driving direction but not in the other. The nonreciprocity originates from the Sagnac effect caused by the resonator's spinning. We also find the classical nonreciprocity and the quantum nonreciprocity can be switched by simply changing the angular velocity of the spinning resonator. We show that the scheme is robust to the system's dissipations and the mechanical thermal noise. This work may be meaningful for the study of nonreciprocal device and quantum precision measurement.

Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model

In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.

Simultaneously enhanced magnomechanical cooling and entanglement assisted by an auxiliary microwave cavity

We propose a mechanism to simultaneously enhance quantum cooling and entanglement via coupling an auxiliary microwave cavity to a magnomechanical cavity. The auxiliary cavity acts as a dissipative cold reservoir that can efficiently cool multiple localized modes in the primary system via beam-splitter interactions, which enables us to obtain strong quantum cooling and entanglement. We analyze the stability of the system and determine the optimal parameter regime for cooling and entanglement under the auxiliary-microwave-cavity-assisted (AMCA) scheme. The maximum cooling enhancement rate of the magnon mode can reach 98.53%, which clearly reveals that the magnomechanical cooling is significantly improved in the presence of the AMCA. More importantly, the dual-mode entanglement of the system can also be significantly enhanced by AMCA in the full parameter region, where the initial magnon-phonon entanglement can be maximally enhanced by a factor of about 11. Another important result of the AMCA is that it also increases the robustness of the entanglement against temperature. Our approach provides a promising platform for the experimental realization of entanglement and quantum information processing based on cavity magnomechanics.

Quantum squeezing-induced quantum entanglement and EPR steering in a coupled optomechanical system

We propose a theoretical project in which quantum squeezing induces quantum entanglement and Einstein-Podolsky-Rosen steering in a coupled whispering-gallery-mode optomechanical system. Through pumping the χ(2)-nonlinear resonator with the phase matching condition, the generated squeezed resonator mode and the mechanical mode of the optomechanical resonator can generate strong quantum entanglement and EPR steering, where the squeezing of the nonlinear resonator plays the vital role. The transitions from zero entanglement to strong entanglement and one-way steering to two-way steering can be realized by adjusting the system parameters appropriately. The photon-photon entanglement and steering between the two resonators can also be obtained by deducing the amplitude of the driving laser. Our project does not need an extraordinarily squeezed field, and it is convenient to manipulate and provides a novel and flexible avenue for diverse applications in quantum technology dependent on both optomechanical and photon-photon entanglement and steering.

Multi-field-driven optomechanical entanglement

Cavity optomechanical (COM) entanglement, playing an essential role in building quantum networks and enhancing quantum sensors, is usually weak and easily destroyed by noises. As feasible and effective ways to overcome this obstacle, optical or mechanical parametric modulations have been used to improve the quality of quantum squeezing or entanglement in various COM systems. However, the possibility of combining these powerful means to enhance COM entanglement has yet to be explored. Here, we fill this gap by studying a COM system containing an intra-cavity optical parametric amplifier (OPA), driven optically and mechanically. By tuning the relative strength and the frequency mismatch of optical and mechanical driving fields, we find that constructive interference can emerge and significantly improve the strength of COM entanglement and its robustness to thermal noises. This work sheds what we believe to be a new light on preparing and protecting quantum states with multi-field driven COM systems for diverse applications.

Phase-Controlled Tunable Unconventional Photon Blockade in a Single-Atom-Cavity System

In the past few years, cavity optomechanical systems have received extensive attention and research and have achieved rapid development both theoretically and experimentally. The systems play an important role in many fields, such as quantum information processing, optomechanical storage, high-precision measurement, macroscopic entanglement, ultrasensitive sensors and so on. Photon manipulation has always been one of the key tasks in quantum information science and technology. Photon blockade is an important way to realize single photon sources and plays an important role in the field of quantum information. Due to the nonlinear coupling of the optical force system, the energy level is not harmonic, resulting in a photon blockade effect. In this paper, we study the phase-controlled tunable unconventional photon blockade in a single-atom-cavity system, and the second-order nonlinear crystals are attached to the cavity. The cavity interacts with squeezed light, which results in a nonlinear process. The system is driven by a complex pulsed laser, and the strength of the coherent driving contains the phase. We want to study the effect of squeezed light and phase. We use the second-order correlation function to numerically and theoretically analyze the photon blockade effect. We show that quantum interference of two-photon excitation between three different transition pathways can cause a photon blockade effect. When there is no squeezed light, the interference pathways becomes two, but there are still photon blockade effects. We explore the influence of the tunable phase and second-order nonlinear strength on the photon blockade effect. We calculate the correlation function and compare the numerical results with the analytical results under certain parameters and find that the agreement is better.

Feedback Control of Quantum Correlations in a Cavity Magnomechanical System with Magnon Squeezing

We suggest a method to improve quantum correlations in cavity magnomechanics, through the use of a coherent feedback loop and magnon squeezing. The entanglement of three bipartition subsystems: photon-phonon, photon-magnon, and phonon-magnon, is significantly improved by the coherent feedback-control method that has been proposed. In addition, we investigate Einstein-Podolsky-Rosen steering under thermal effects in each of the subsystems. We also evaluate the scheme's performance and sensitivity to magnon squeezing. Furthermore, we study the comparison between entanglement and Gaussian quantum discord in both steady and dynamical states.

Entanglement enhancement and EPR steering based on a PT-symmetric-like cavity-opto-magnomechanical hybrid system

We investigate the enhancement of entanglement and EPR steering in a parity-time(PT-) symmetric-like cavity-opto-magnomechanical system. The system consists of an optical cavity, a magnon mode in a ferromagnetic crystal, a phonon mode, and a microwave cavity. Our findings demonstrate that microwave-cavity gain significantly boosts distant quantum entanglement and greatly improves the robustness of bipartite entanglement against environment temperature. Additionally, we observe an enhancement of tripartite entanglement within the system and uncover the phenomenon of entanglement transfer. Notably, we also achieve one-way steering and two-way asymmetric steering in the system. This study offers insights into the integration of traditional optomechanics and cavity magnomechanics, presenting a novel approach to manipulate asymmetric quantum steering between two distant macroscopic objects. The implications of our research extend to the fields of quantum state preparation and quantum information.

Entanglement generation and steering implementation in a double-cavity-magnon hybrid system

We demonstrate a scheme for the generation of bipartite and tripartite entanglement, as well as he implementation of stable and controllable long-distance one-way and asymmetric two-way steering in a cavity-magnon hybrid system. This system consists of a magnon mode and two coupled microwave cavities. The first cavity is driven by a flux-driven Josephson parametric amplifier, which generates squeezed vacuum fields, and is coupled to the other cavity through optical tunneling interaction. The second cavity and magnon mode are coupled through magnetic dipole interaction. We find that under weak coupling between the two cavities, and strong coupling between the second cavity and magnon mode, remote controllable one-way steering and tripartite entanglement can be achieved. Our scheme may have potential applications in quantum information.

Dephasing-assisted preparation of asymmetric steering in coupled quantum wells

It is shown that the dephasing rates are usually harmful for quantum correlations in various systems. Nevertheless, we explore that the dephasing rates in the coupled quantum wells (QWs), as a major contribution of the decay processes, can assist to generate one-way Einstein-Podolsky-Rosen (EPR) steering. By applying two strong fields to drive two dipole-allowed transitions while the other transitions are coupled with two quantized modes, the asymmetric EPR steering is possible to obtain at steady state through a single-pathway dissipation in the three-well system. According to dressed-state and Bogoliubov mode transformation, we find that the dephasing rates play a role in modifying the dressed-state populations and the dissipation rate through multiple quantum interference mechanisms. The positive effect of the dephasing rates from a nanostructure on quantum correlation is expected to find potential applications in quantum information processing.

High-efficiency entanglement of microwave fields in cavity opto-magnomechanical systems

We demonstrate a scheme to realize high-efficiency entanglement of two microwave fields in a dual opto-magnomechanical system. The magnon mode simultaneously couples with the microwave cavity mode and phonon mode via magnetic dipole interaction and magnetostrictive interaction, respectively. Meanwhile, the phonon mode couples with the optical cavity mode via radiation pressure. Each magnon mode and optical cavity mode adopts a strong red detuning driving field to activate the beam splitter interaction. Therefore, the entangled state generated by the injected two-mode squeezed light in optical cavities can be eventually transferred into two microwave cavities. A stationary entanglement E a 1 a 2 =0.54 is obtained when the input two-mode squeezed optical field has a squeezing parameter r = 1. The entanglement E a 1 a 2 increases as the squeezing parameter r increases, and it shows the flexible tunability of the system. Meanwhile, the entanglement survives up to an environmental temperature about 385 mK, which shows high robustness of the scheme. The proposed scheme provides a new mechanism to generate entangled microwave fields via magnons, which enables the degree of the prepared microwave entanglement to a more massive scale. Our result is useful for applications which require high entanglement of microwave fields like quantum radar, quantum navigation, quantum teleportation, quantum wireless fidelity (Wi-Fi) network, etc.

Quantum correlation in a nano-electro-optomechanical system enhanced by an optical parametric amplifier and Coulomb-type interaction

In this paper, we investigated the quantum correlation of nano-electro-optomechanical system enhanced by an optical parametric amplifier (OPA) and Coulomb-type interaction. In particular, we consider a hybrid system consisting of a cavity and two charged mechanical oscillators with an OPA, where the optical cavity mode is coupled with a charged mechanical oscillator via radiation pressure, and the two charged mechanical oscillators are coupled through a Coulomb interaction. We use logarithmic negativity to quantify quantum entanglement, and quantum discord to measure the quantumness correlation between the two mechanical oscillators. We characterize quantum steering using the steerability between the two mechanical oscillators. Our results show that the presence of OPA and strong Coulomb coupling enhances the quantum correlations between the two mechanical oscillators. In addition, Coulomb interactions are more prominent in quantum correlations. Besides, in the presence of OPA, the maximum amount of quantum entanglement, quantum steering, and quantum discord were achieved between the two mechanical oscillators is greater than in the absence of OPA. Moreover, a proper phase choice of the optical field driving the OPA enhances quantum correlations under suitable conditions. We obtain quantum entanglement confines quantum steering and quantum discord beyond entanglement. Furthermore, quantum entanglement, quantum steering, and quantum discord decrease rapidly with increasing temperature as a result of decoherence. In addition, quantum discord persists at higher temperature values, although the quantum entanglement between the systems also vanishes completely. Our proposed scheme enhances quantum correlation and proves robust against fluctuations in the bath environment. We believe that the present scheme of quantum correlation provides a promising platform for the realization of continuous variable quantum information processing.

Optomechanical entanglement affected by exceptional point in a WGM resonator system

Entanglement of optical mode and mechanical mode plays a significant role for quantum information processing and memory. This type of optomechanical entanglement is always be suppressed by the mechanically dark-mode (DM) effect. However, the reason of the DM generation and how to control the bright-mode (BM) effect flexibly are still not resolved. In this letter, we demonstrate that the DM effect occurs at the exceptional point (EP) and it can be broken by changing the relative phase angle (RPA) between the nano scatters. We find that the optical mode and mechanical mode are separable at EPs but entangled when the RPA is tuned away from the EPs. Remarkably, the DM effect will be broken if the RPA away from EPs, resulting in the ground-state cooling of the mechanical mode. In addition, we prove that the chirality of the system can also influence the optomechanical entanglement. Our scheme can control the entanglement flexible merely depend on the relative phase angle, which is continuously adjustable and experimentally more feasible.

Optomechanical force sensor operating over wide detection range

A detector with both broad operation range and high sensitivity is desirable in the measurement of weak periodic forces. Based on a nonlinear dynamical mechanism of locking the mechanical oscillation amplitude in optomechanical systems, we propose a force sensor that realizes the detection through the cavity field sidebands modified by an unknown external periodic force. Under the mechanical amplitude locking condition, the unknown external force happens to modify the locked oscillation amplitude linearly to its magnitude, thus achieving a linear scaling between the sideband changes read by the sensor and the magnitude of the force to be measured. This linear scaling range is found to be comparable to the applied pump drive amplitude, so the sensor can measure a wide range of force magnitude. Because the locked mechanical oscillation is rather robust against thermal perturbation, the sensor works well at room temperature. In addition to weak periodic forces, the same setup can as well detect static forces, though the detection ranges are much narrower.

Enhancement of magnon-photon-phonon entanglement in a cavity magnomechanics with coherent feedback loop

In this paper, we present a coherent feedback loop scheme to enhance the magnon-photon-phonon entanglement in cavity magnomechanics. We provide a proof that the steady state and dynamical state of the system form a genuine tripartite entanglement state. To quantify the entanglement in the bipartite subsystem and the genuine tripartite entanglement, we use the logarithmic negativity and the minimum residual contangle, respectively, in both the steady and dynamical regimes. We demonstrate the feasibility of our proposal by implementing it with experimentally realizable parameters to achieve the tripartite entanglement. We also show that the entanglement can be significantly improved with coherent feedback by appropriately tuning the reflective parameter of the beam splitter and that it is resistant to environmental thermalization. Our findings pave the way for enhancing entanglement in magnon-photon-phonon systems and may have potential applications in quantum information.

Generation of robust optical entanglement in cavity optomagnonics

We propose a scheme to realize robust optical entanglement in cavity optomagnonics, where two optical whispering gallery modes (WGMs) couple to a magnon mode in a yttrium iron garnet (YIG) sphere. The beam-splitter-like and two-mode squeezing magnon-photon interactions can be realized simultaneously when the two optical WGMs are driven by external fields. Entanglement between the two optical modes is then generated via their coupling with magnons. By exploiting the destructive quantum interference between the bright modes of the interface, the effects of initial thermal occupations of magnons can be eliminated. Moreover, the excitation of the Bogoliubov dark mode is capable of protecting the optical entanglement from thermal heating effects. Therefore, the generated optical entanglement is robust against thermal noise and the requirement of cooling the magnon mode is relaxed. Our scheme may find applications in the study of magnon-based quantum information processing.

Mechanical squeezing in an active-passive-coupled double-cavity optomechanical system via pump modulation

We focus on the generation of mechanical squeezing by using periodically amplitude-modulated laser to drive an active-passive-coupled double-cavity optomechanical system, where the coupled gain cavity and loss cavity can form into a parity-time (P T)-symmetry system. The numerical analysis of the system stability shows that the system is more likely to be stable in the unbroken-P T-symmetry regime than in the broken-P T-symmetry regime. The mechanical squeezing in the active-passive system exhibits stronger robustness against the thermal noise than that in the passive-passive system, and the so-called 3 dB limit can be broken in the resolved-sideband regime. Furthermore, it is also found that the mechanical squeezing obtained in the unbroken-P T-symmetry region is stronger than that in the broken-P T-symmetry region. This work may be meaningful for the quantum state engineering in the gain-loss quantum system that contributes to the study of P T-symmetric physics in the quantum regime.

Simultaneous ground-state cooling of multiple degenerate mechanical modes through the cross-Kerr effect

Simultaneous ground-state cooling of multiple degenerate mechanical modes is a difficult issue in optomechanical systems, owing to the existence of the dark mode effect. Here we propose a universal and scalable method to break the dark mode effect of two degenerate mechanical modes by introducing cross-Kerr (CK) nonlinearity. At most, four stable steady states can be achieved in our scheme in the presence of the CK effect, unlike the bistable behavior of the standard optomechanical system. Under a constant input laser power, the effective detuning and mechanical resonant frequency can be modulated by the CK nonlinearity, resulting in an optimal CK coupling strength for cooling. Similarly, there will be an optimal input laser power for cooling when the CK coupling strength stays fixed. Our scheme can be extended to break the dark mode effect of multiple degenerate mechanical modes by introducing more than one CK effect. To fulfill the requirement of the simultaneous ground-state cooling of N multiple degenerate mechanical modes, N - 1 CK effects with different strengths are needed. Our proposal provides new, to the best of our knowledge. insights into dark mode control and might pave the way to manipulating multiple quantum states in a macroscopic system.

Mechanical Bistability in Kerr-modified Cavity Magnomechanics

Bistable mechanical vibration is observed in a cavity magnomechanical system, which consists of a microwave cavity mode, a magnon mode, and a mechanical vibration mode of a ferrimagnetic yttrium-iron-garnet sphere. The bistability manifests itself in both the mechanical frequency and linewidth under a strong microwave drive field, which simultaneously activates three different kinds of nonlinearities, namely, magnetostriction, magnon self-Kerr, and magnon-phonon cross-Kerr nonlinearities. The magnon-phonon cross-Kerr nonlinearity is first predicted and measured in magnomechanics. The system enters a regime where Kerr-type nonlinearities strongly modify the conventional cavity magnomechanics that possesses only a radiation-pressure-like magnomechanical coupling. Three different kinds of nonlinearities are identified and distinguished in the experiment. Our Letter demonstrates a new mechanism for achieving mechanical bistability by combining magnetostriction and Kerr-type nonlinearities, and indicates that such Kerr-modified cavity magnomechanics provides a unique platform for studying many distinct nonlinearities in a single experiment.

Magnon-atom-optical photon entanglement via the microwave photon-mediated Raman interaction

We show that it is possible to generate magnon-atom-optical photon tripartite entanglement via the microwave photon-mediated Raman interaction. Magnons in a macroscopic ferromagnet and optical photons in a cavity are induced into a Raman interaction with an atomic spin ensemble when a microwave field couples the magnons to one Raman wing. The controllable magnon-atom entanglement, magnon-optical photon entanglement, and even genuine magnon-atom-optical photon tripartite entanglement can be generated simultaneously. In addition, these bipartite and tripartite entanglements are robust against the environment temperature. Our scheme paves the way for exploring a quantum interface bridging the microwave and optical domains, and may provide a promising building block for hybrid quantum networks.

Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism

Entanglement of light and multiple vibrations is a key resource for multichannel 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 DM breaking induced by synthetic magnetism. We find that at nonzero temperature, light and vibrations are separable in the DM-unbreaking regime but entangled in the DM-breaking regime. Remarkably, the threshold thermal phonon number for preserving entanglement in our simulations has been observed to be up to 3 orders of magnitude stronger than that in the DM-unbreaking regime. The application of the DM-breaking mechanism to optomechanical networks can make noise-tolerant entanglement networks feasible. These results are quite general and can initiate advances in quantum resources with immunity against both dark modes and thermal noise.

Cooling Effect and Cooling Speed for a Membrane-in-Middle Optomechanical System

Optomechanical systems are suitable for realizing the ground-state cooling of macroscopic objects. Based on a dynamical approach that goes beyond the validity of the standard linearization approach, we simulate the detailed cooling processes for a membrane-in-middle optomechanical system. In addition to the cooling results, we especially study the cooling speed, which is indicated by how soon the first minimum thermal phonon number is reached. Their relevance to the system parameters provides essential knowledge about how to achieve the best and/or fastest cooling under various combinations of different driving fields.

Dissipation-driven entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system

The generation and manipulation of highly pure and strongly entangled steady state in a quantum system are vital tasks in the standard continuous-variable teleportation protocol. Especially, the manipulation implemented in integrated devices is even more crucial in practical quantum information applications. Here we propose an effective approach for creating steady-state entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system. The entanglement can be achieved by combining the processes of three beam-splitter interactions and two parametric-amplifier interactions. Due to the dissipation-driven and cavity cooling processes, the entanglement obtained can go far beyond the entanglement limit based on coherent parametric coupling. Moreover, our proposal allows the engineered bath to cool both Bogoliubov modes almost simultaneously. In this way, a highly pure and strongly entangled steady state of two microwave modes is obtained. Our finding may be significant for using the hybrid opto-electro-mechanical system fabricated on chips in various quantum tasks, where the strong and pure entanglement is an important resource.

Quantum entanglement and one-way steering in a cavity magnomechanical system via a squeezed vacuum field

We propose a simple scheme to generate quantum entanglement and one-way steering between distinct mode pairs in a generic cavity magnomechanical system, which is composed of a microwave cavity and a yttrium iron garnet sphere supporting magnon and phonon modes. The microwave cavity is pumped by a weak squeezed vacuum field, which plays an important role for establishing quantum entanglement and steering. It is found that when the magnon mode is driven by the red-detuned laser, the maximum entanglement between cavity mode and phonon mode and the maximum phonon-to-photon one-way steering can be effectively generated via adjusting the ratio of two coupling rates. While under the much weaker magnomechanical coupling, the quantum entanglement and one-way steering between cavity mode and magnon mode can be achieved, where the steering direction is determined merely by the relative dissipation strength of the cavity to the magnon mode. More interestingly, we reveal that the robustness to the temperature for entanglement and steering between any mode pairs can be evidently enhanced by selecting the squeezing parameter appropriately.

Squeezed vacuum interaction with an optomechanical cavity containing a quantum well

We investigate a hybrid system consisting of an optomechanical resonator and an optical cavity containing a quantum well. The system is coupled to a squeezed vacuum reservoir. We analyze the effect of the injection of squeezed photons inside the cavity on the intensity spectrum. The system reaches a regime of hybrid resonance where mechanical, excitonic and cavity modes are intermixed. Despite that the optomechanical interaction is the source of the nonlinearity in the system, the optimum squeezing is obtained at the hybrid resonance frequencies. However, when the squeezed vacuum is applied, at these frequencies the minimum squeezing is realized as well as an increase of fluctuations is observed. We show that the squeezed vacuum transforms the coherent states into highly squeezed states of light, and offers a great flexibility to obtain maximal squeezing. Furthermore, a perfect squeezing is predicted.

Squeezing Light via Levitated Cavity Optomechanics

Squeezing light is a critical resource in both fundamental physics and precision measurement. Squeezing light has been generated through optical-parametric amplification inside an optical resonator. However, preparing the squeezing light in an optomechanical system is still a challenge for the thermal noise inevitably coupled to the system. We consider an optically levitated nano-particle in a bichromatic cavity, in which two cavity modes could be excited by the scattering photons of the dual tweezers, respectively. Based on the coherent scattering mechanism, the ultra-strong coupling between the cavity field and the torsional motion of nano-particle could be achieved for the current experimental conditions. With the back-action of the optically levitated nano-particle, the broad single-mode squeezing light can be realized in the bad cavity regime. Even at room temperature, the single-mode light can be squeezed for more than 17 dB, which is far beyond the 3 dB limit. The two-mode squeezing light can also be generated, if the optical tweezers contain two frequencies, one is on the red sideband of the cavity mode, the other is on the blue sideband. The two-mode squeezing can be maximized near the boundary of the system stable regime and is sensitive to both the cavity decay rate and the power of the optical tweezers.

Force Dependent Quantum Phase Transition in the Hybrid Optomechanical System

The optomechanics shows a great potential in quantum control and precise measurement due to appropriate mechanical control. Here we theoretically study the quantum phase transition in a hybrid atom-optomechanical cavity with an external force. Our study shows, in the thermodynamic limit, the critical value of quantum phase transition between the normal phase and super-radiant phase can be controlled and modified by the external force via the tunable frequency of optomechanics, then a force dependent quantum phase transition can be achieved in our system. Moreover, this force dependent quantum phase transition can be employed to detect the external force variation. In addition, our numerical simulations illustrate the sensitivity of the external force measurement can be improved by the squeezing properties of the quantum phase transition.

Strong single-photon optomechanical coupling in a hybrid quantum system

Engineering strong single-photon optomechanical couplings is crucial for optomechanical systems. Here, we propose a hybrid quantum system consisting of a nanobeam (phonons) coupled to a spin ensemble and a cavity (photons) to overcome it. Utilizing the critical property of the lower-branch polariton (LBP) formed by the ensemble-phonon interaction, the LBP-cavity coupling can be greatly enhanced by three orders magnitude of the original one, while the upper-branch polariton (UBP)-cavity coupling is fully suppressed. Our proposal breaks through the condition of the coupling strength less than the critical value in previous schemes using two harmonic oscillators. Also, strong Kerr effect can be induced in our proposal. This shows our proposed approach can be used to study quantum nonlinear and nonclassical effects in weakly coupled optomechanical systems.

Quantum simulation of tunable and ultrastrong mixed-optomechanics

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.

Impact of the central frequency of environment on non-Markovian dynamics in piezoelectric optomechanical devices

The piezoelectric optomechanical devices supply a promising experimental platform to realize the coherent and effective control and measurement of optical circuits working in Terahertz (THz) frequencies via superconducting electron devices typically working in Radio (MHz) frequencies. However, quantum fluctuations are unavoidable when the size of mechanical oscillators enter into the nanoscale. The consequences of the noisy environment are still challenging due to the lack of analytical tools. In this paper, a semi-classical and full-quantum model of piezoelectric optomechanical systems coupled to a noisy bosonic quantum environment are introduced and solved in terms of quantum-state diffusion (QSD) trajectories in the non-Markovian regime. We show that the noisy environment, particularly the central frequency of the environment, can enhance the entanglement generation between optical cavities and LC circuits in some parameter regimes. Moreover, we observe the critical points in the coefficient functions, which can lead the different behaviors in the system. Besides, we also witness the entanglement transfers between macroscopic objects due to the memory effect of the environment. Our work can be applied in the fields of electric/ optical switches, and long-distance distribution in a large-scale quantum network.

Approximate Evolution for A Hybrid System-An Optomechanical Jaynes-Cummings Model

In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with U^(t) to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.

Optical Bistability in an Optomechanical System with N-Type Atoms under Nonresonant Conditions

In this paper, the phenomenon of the optical bistability of a cavity field is theoretically investigated in an optomechanical system containing an N-type atomic ensemble. In this hybrid optomechanical system, the atoms are coupled with two controlling light fields besides coupling with the cavity field. Under the nonresonant condition, we analyze the influences of the coupling strength between cavity and atoms, Rabi frequencies of the controlling light field, the detuning between the controlling light field and atoms, and pump field power on the optical bistable behavior of mean intracavity photon number. The nonlinear distribution of the mean intracavity photon number has a potential application in field optical switches and optical bistable devices.

Nonreciprocal Optomechanical Entanglement against Backscattering Losses

We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to protect and engineer quantum resources by utilizing diverse nonreciprocal devices, for building noise-tolerant quantum processors, realizing chiral networks, and backaction-immune quantum sensors.

Spontaneous phase locking of mechanical multimodes in anti-parity-time optomechanics

We propose a system for observing the spontaneous phase locking of two frequency separate mechanical modes in an anti-parity-time symmetric optomechanical system. In our approach, a common optical cavity mode mediates the coupling between two phonon modes, leading to the phase locking of the coupled mechanical modes to a common frequency in the symmetry unbroken regime. We furthermore observe the change of quantum correlation near the exceptional point. Our results are also directly relevant to numerous other physical platforms, such as atomic ensembles in cavity quantum electrodynamics (QED) systems and spin interaction mediated by collective motional mode in trapped ions.

Spectrometric detection of weak forces in cavity optomechanics

We propose a spectrometric method to detect a classical weak force acting upon the moving end mirror in a cavity optomechanical system. The force changes the equilibrium position of the end mirror, and thus the resonance frequency of the cavity field depends on the force to be detected. As a result, the magnitude of the force can be inferred by analyzing the single-photon emission and scattering spectra of the optomechanical cavity. Since the emission and scattering processes are much faster than the characteristic mechanical dissipation, the influence of the mechanical thermal noise is negligible in this spectrometric detection scheme. We also extent this spectrometric method to detect a monochromatic oscillating force by utilizing an optomechanical coupling modulated at the same frequency as the force.

Magnetostrictively Induced Stationary Entanglement between Two Microwave Fields

We present a scheme to entangle two microwave fields by using the nonlinear magnetostrictive interaction in a ferrimagnet. The magnetostrictive interaction enables the coupling between a magnon mode (spin wave) and a mechanical mode in the ferrimagnet, and the magnon mode simultaneously couples to two microwave cavity fields via the magnetic dipole interaction. The magnon-phonon coupling is enhanced by directly driving the ferrimagnet with a strong red-detuned microwave field, and the driving photons are scattered onto two sidebands induced by the mechanical motion. We show that two cavity fields can be prepared in a stationary entangled state if they are, respectively, resonant with two mechanical sidebands. The present scheme illustrates a new mechanism for creating entangled states of optical fields and enables potential applications in quantum information science and quantum tasks that require entangled microwave fields.

Entanglement of propagating optical modes via a mechanical interface

Many applications of quantum information processing (QIP) require distribution of quantum states in networks, both within and between distant nodes. Optical quantum states are uniquely suited for this purpose, as they propagate with ultralow attenuation and are resilient to ubiquitous thermal noise. Mechanical systems are then envisioned as versatile interfaces between photons and a variety of solid-state QIP platforms. Here, we demonstrate a key step towards this vision, and generate entanglement between two propagating optical modes, by coupling them to the same, cryogenic mechanical system. The entanglement persists at room temperature, where we verify the inseparability of the bipartite state and fully characterize its logarithmic negativity by homodyne tomography. We detect, without any corrections, correlations corresponding to a logarithmic negativity of EN = 0.35. Combined with quantum interfaces between mechanical systems and solid-state qubit processors, this paves the way for mechanical systems enabling long-distance quantum information networking over optical fiber networks.

Transparency and tunable slow-fast light in a hybrid cavity optomechanical system

We theoretically investigate the optomechanically induced transparency (OMIT) phenomenon in a hybrid optomechanical system composing of an optomechanical cavity and a traditional one. A Kerr medium is inserted in the optomechanical cavity and the other traps the atomic ensemble. We demonstrate the appearance of electromagnetically and optomechanically induced transparency when there is only Kerr medium or atoms in the system. We give an explicit explanation for the mechanism of the transparency. Moreover, we set up new scheme for the measurement of Kerr coefficient and the single atom-photon coupling strength. It is shown that Kerr nonlinearity can inhibit the normal mode splitting (NMS) when the tunnel strength is strong coupling. Furthermore, in the output field, slow light and fast light are converted to realize the tunable switch from slow light to fast light. This study has some important guiding significance in the fields of the high precision measurement and quantum information processing.

Fifty Years of the Dynamical Casimir Effect

This is a digest of the main achievements in the wide area, called the Dynamical Casimir Effect nowadays, for the past 50 years, with the emphasis on results obtained after 2010.

Nonreciprocal interference and coherent photon routing in a three-port optomechanical system

We study the interference between different weak signals in a three-port optomechanical system, which is achieved by coupling three cavity modes to the same mechanical mode. If one cavity serves as a control port and is perturbed continuously by a control signal, nonreciprocal interference can be observed when another signal is injected upon different target ports. In particular, we exhibit frequency-independent perfect blockade induced by the completely destructive interference over the full frequency domain. Moreover, coherent photon routing can be realized by perturbing all ports simultaneously, with which the synthetic signal only outputs from the desired port. We also reveal that the routing scheme can be extended to more-port optomechanical systems. The results in this paper may have potential applications for controlling light transport and quantum information processing.

Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling

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 can be achieved, meanwhile a strong mechanical squeezing is also realized. Moreover, we study the environment-induced decoherence and dissipation, and find that they can be mitigated by increasing the number of photons. This work provides an effective way to manipulate entanglement and quantum squeezing and to suppress decoherence in the cavity quantum electrodynamics with a quadratic optomechanics.

Force sensing beyond standard quantum limit with optomechanical "soft" mode induced by nonlinear interaction

We consider an optomechanical (OM) system that consists of a mechanical and an optical mode interacting through linear and quadratic OM dispersive couplings. The system is operated in unresolved sideband limit with a high quality factor mechanical resonator. Such a system acts as a parametrically driven oscillator, giving access to an intensity-assisted tunability of the spring constant. This enables the operation of the OM system in its "soft mode," wherein the mechanical spring softens and responds with a lower resonance frequency. We show that this soft mode can be exploited to nonlinearize backaction noise, which yields higher force sensitivity beyond the conventional standard quantum limit.

Improving macroscopic entanglement with nonlocal mechanical squeezing

We report an efficient mechanism to generate mechanical entanglement in a two-cascaded cavity optomechanical system with optical parametric amplifiers (OPAs) inside the two coupled cavities. We use the especially tuned OPAs to squeeze the hybrid mode composed of two mechanical modes, leading to strong macroscopic entanglement between the two movable mirrors. The squeezing parameter as well as the effective mechanical damping are both modulated by the OPA gains. The optimal degree of mechanical entanglement therefore depends on the balanced process between coherent hybrid mode squeezing and dissipation engineering. The mechanical entanglement is robust to strong cavity decay, going beyond simply resolved sideband regime, and is resistant to reasonable high thermal noise. The scheme provides an alternative way for generating strong macroscopic entanglement in cascaded optomechanical systems.

Entanglement of two rotating mirrors coupled to a single Laguerre-Gaussian cavity mode

We theoretically investigate the entanglement between two macroscopic rotating mirrors in a Laguerre-Gaussian (L-G) cavity, in which they exchange orbital angular momentum with a same L-G cavity mode, and we examine the influence of various factors such as angular frequencies of two mirrors, effective detuning, temperature and orbital angular momentum of L-G cavity mode on the entanglement. The results show that in some range of mirrors' angular frequencies the entanglement will appear and has strong robustness. And we also study the range of effective detuning and the minimum orbital angular momentum of the L-G cavity mode required to generate entanglement.