Cavity optomechanics： Manipulating photons and phonons towards the single-photon strong coupling

Cavity optomechanical systems provide powerful platforms to manipulate photons and phonons, open potential ap- plications for modern optical communications and precise measurements. With the refrigeration and ground-state cooling technologies, studies of cavity optomechanics are making significant progress towards the quantum regime including non- classical state preparation, quantum state tomography, quantum information processing, and future quantum internet. With further research, it is found that abundant physical phenomena and important applications in both classical and quan- tum regimes appeal as they have a strong optomechanical nonlinearity, which essentially depends on the single-photon optomechanical coupling strength. Thus, engineering the optomechanical interactions and improving the single-photon optomechanical coupling strength become very important subjects. In this article, we first review several mechanisms, theoretically proposed for enhancing optomechanical coupling. Then, we review the experimental progresses on enhancing optomechanical coupling by optimizing its structure and fabrication process. Finally, we review how to use novel structures and materials to enhance the optomechanical coupling strength. The manipulations of the photons and phonons at the level of strong optomechanical coupling are also summarized.

Quantum estimation of rotational speed in optomechanics

We study the quantum Fisher information(QFI)of the angular velocity of rotation in an optomechanical system.Based on the Gaussian measurements method,we derive the explicit form of a single-mode Gaussian QFI,which is valid for arbitrary angular velocity of rotation.The information about the angular velocity to be measured is contained in the optical covariance matrix,which can be experimentally determined via homodyne measurement.We find that QFI increases rapidly when driving the system close to the unstable boundary.This result can be attributed to the strong nonlinearity of the system at the unstable boundary.Our results indicate the possibility of using an optomechanical system for high precision detection of the angular velocity of rotation.

Microscale Crystalline Rare-Earth Doped Resonators for Strain-Coupled Optomechanics

Rare-earth ion doped crystals for hybrid quantum technologies are an area of growing interest in the solid-state physics community. We have earlier theoretically proposed a hybrid scheme of a mechanical resonator which is fabricated out of a rare-earth doped mono-crystalline structure. The rare-earth ion dopants have absorption energies which are sensitive to crystal strain, and it is thus possible to couple the ions to the bending motion of the crystal cantilever. This type of resonator can be useful for either investigating the laws of quantum physics with material objects or for applications such as sensitive force-sensors. Here, we present the design and fabrication method based on focused-ion-beam etching techniques which we have successfully employed in order to create such microscale resonators, as well as the design of the environment which will allow studying the quantum behavior of the resonators.

Nonlinearly induced entanglement in dissipatively coupled optomechanical system

Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system.Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently,a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.

Nonreciprocal mechanical entanglement in a spinning optomechanical system

Quantum entanglement between distant massive mechanical oscillators is an important resource in sensitive measurements and quantum information processing.We achieve the nonreciprocal mechanical entanglement in a compound optomechanical device consisting of two mechanical oscillators and a spinning whispering-gallery mode(WGM)optical microresonator.It is found that obvious nonreciprocal mechanical entanglement emerges in this system in the presence of the Sagnac effect which is induced by the rotation of the WGM resonator,and the nonreciprocal region can be controlled by tuning the angular velocity of the rotation.The nonreciprocity originates from the breaking of the time-reversal symmetry of this multimode system due to the presence of the Sagnac effect.The optomechanical coupling and the mechanical interaction provide cooling channels for the first and second mechanical oscillators,respectively.Two mechanical oscillators can be cooled simultaneously.The simultaneous cooling and the mechanical coupling of two mechanical oscillators ensure the generation of mechanical entanglement.Furthermore,an optimal mechanical entanglement can be achieved when the moderate optical frequency detuning and the driving power are chosen.The thermal noise of the mechanical environment has a negative effect on mechanical entanglement.Our scheme provides promising opportunities for research of quantum information processing based on phonons and sensitive measurements.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation.Essentially,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum correlation.Nonetheless,this indistinguishability is no longer holds for mixed states.To contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum correlations.Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping process.this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes.The key ingredient in analyzing quantum correlation in this system is the global covariance matrix.It forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,respectively.Our study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.

半导体量子点分子-腔光机械耦合系统中光学双稳及多稳态的形成及调控

本研究探讨了外部磁场对半导体量子点分子与腔光机械耦合系统中光学双稳态行为的影响.研究结果显示,外部磁场、量子点之间的隧穿耦合以及探测光单光子的失谐可以有效地调控系统的光学双稳态.在弱隧穿和弱磁场条件下,系统的光学双稳态阈值和磁滞回线宽度随着外部磁场和点间隧穿耦合强度的增加而增大.随着磁场强度和隧穿耦合强度的进一步增加,系统的双稳态将演变为多稳态.有趣的是,在强隧穿和强磁场作用下,系统的光学双稳态阈值和磁滞回线宽度随着外部磁场和点间隧穿耦合强度的增加而减小.这种对耦合腔光机械系统中光学双稳态的灵活调控将在可控光开关方面具有潜在的广泛应用前景.

Review of cavity optomechanical cooling

Quantum manipulation of macroscopic mechanical systems is of great interest in both fundamental physics and ap- plications ranging from high-precision metrology to quantum information processing. For these purposes, a crucial step is to cool the mechanical system to its quantum ground state. In this review, we focus on the cavity optomechanical cooling, which exploits the cavity enhanced interaction between optical field and mechanical motion to reduce the thermal noise. Recent remarkable theoretical and experimental efforts in this field have taken a major step forward in preparing the mo- tional quantum ground state of mesoscopic mechanical systems. This review first describes the quantum theory of cavity optomechanical cooling, including quantum noise approach and covariance approach; then, the up-to-date experimental progresses are introduced. Finally, new cooling approaches are discussed along the directions of cooling in the strong coupling regime and cooling beyond the resolved sideband limit.

The optical nonreciprocal response based on a four-mode optomechanical system

We propose a scheme for realizing the optical nonreciprocal response based a four-mode optomechanical system,consisting of two charged mechanical modes and two linearly coupled optical modes. Two charged mechanical modes are coupled by Coulomb interaction, and two optical modes are coupled to one of mechanical modes by radiation pressure. We numerically evaluate the transmission probability of the probe field to obtain the optimum optical nonreciprocal response parameters. Also, we show that the optical nonreciprocal response is caused by the quantum interference between the optomechanical couplings and the linearly coupled interaction that breaks the time-reversal symmetry.

Tunable ponderomotive squeezing induced by Coulomb interaction in an optomechanical system

We investigate the properties of the ponderomotive squeezing in an optomechanical system coupled to a charged nanomecbanical oscillator （NMO） nearby via Coulomb force. We find that the introduction of Coulomb interaction allows the generation of squeezed output light from this system. Our numerical results show that the degree of squeezing can be tuned by the Coulomb coupling strength, the power of laser, and the frequencies of NMOs. Furthermore, the squeezing generated in our approach can be used to measure the Coulomb coupling strength.

Optomechanical soft metamaterials

We present a new type of optomechanical soft metamaterials, which is different from conventional mechanical metamaterials, in that they are simple isotropic and homogenous materials without resorting to any complex nano/microstructures. This metamaterial is unique in the sense that its responses to uniaxial forcing can be tailored by programmed laser inputs to manifest different nonlinear constitutive behaviors, such as monotonic, S-shape, plateau, and non-monotonic snapping performance. To demonstrate the novel metamaterial, a thin sheet of soft material impinged by two counterpropagating lasers along its thickness direction and stretched by an in-plane tensile mechanical force is considered. A theoretical model is formulated to characterize the resulting optomechanical behavior of the thin sheet by combining the nonlinear elasticity theory of soft materials and the optical radiation stress theory. The optical radiation stresses predicted by the proposed model are validated by simulations based on the method of finite elements. Programmed optomechanical behaviors are subsequently explored using the validated model under different initial sheet thicknesses and different optical inputs, and the first- and second-order tangential stiffness of the metamaterial are used to plot the phase diagram of its nonlinear constitutive behaviors. The proposed optomechanical soft metamaterial shows great potential in biological medicine, microfluidic manipulation, and other fields.

Enhancing stationary optomechanical entanglement with the Kerr medium

We theoretically investigate the stationary entanglement of a optomechanical system with an additional Kerr medium in the cavity. There are two kinds of interactions in the system, photon-mirror interaction and photon-photon interaction. The optomechanical entanglement created by the former interaction can be effectively controlled by the latter one. We find that the optomechanical entanglement is suppressed by Kerr interaction due to photon blockage. We also find that the Kerr interaction can create the stationary entanglement and induce the resonance of entanglement in the small detuning regime. These results show that the Kerr interaction is an effective control for the optomechanical system.

Entangling two oscillating mirrors in an optomechanical system via a flying atom

We propose a novel scheme for generating the entanglement of two oscillating mirrors in an optomechanical system via a flying atom. In this scheme, a two-level atom, in an arbitrary superposition state, passes through an optomechanical system with two oscillating cavity-mirrors, and then its states are detected. In this way, we can generate the entangled states of the two oscillating mirrors. We derive the analytical expressions of the entangled states and make numerical calculations. We find that the entanglement of the two oscillating mirrors can be controlled by the initial state of the atom, the optomechanical coupling strength, and the coupling strength between the atom and the cavity field. We investigate the dynamics of the system with dissipations and discuss the experimental feasibility.

Controlling the entanglement of mechanical oscillators in composite optomechanical system

A controllable entanglement scheme of two mechanical oscillators is proposed in a composite optomechanical system.In the case of strong driving and high dissipation,the dynamics of the movable mirror of the optomechanical cavity is characterized by an effective frequency in the long-time evolution of the system.Considering the classical nonlinear effects in an optomechanical system,we investigate the relationship between the effective frequency of the movable mirror and the adjustable parameters of the cavity.It shows that the effective frequency of the movable mirror can be adjusted ranging fromωm（the resonance frequency of the coupling oscillator） to-ωm.Under the condition of experimental realization,we can generate and control steady-state entanglement between two oscillators by adjusting the effective frequency of the movable mirror and reducing the effective dissipation by selecting the parameter of the cavity driving laser appropriately.Our scheme provides a promising platform to control the steady-state behavior of solid-state qubits using classical manipulation,which is significant for quantum information processing and fundamental research.

Three-mode optomechanical system for angular velocity detection

We propose a scheme for measuring the angular velocity of absolute rotation using a three-mode optomechanical system in which one mode of the two-dimensional （2D） mechanical resonator is coupled to an optical cavity. When the total system rotates, the Coriolis force acting on the 2D mechanical resonator due to the absolute rotation will affect the mechanical motion and thus change the phase of the output field from the cavity. The angular velocity of the absolute rotation can be estimated by monitoring the spectrum of the output field from the cavity via homodyne measurement. The minimum measurable angular velocity, which is determined by the noise spectrum, is calculated. The working range of the gyroscope for measuring angular velocity is discussed.

Electromagnetically induced transparency in a three-mode optomechanical system

We study a three-mode double-cavity optomechanical system in which an oscillating membrane of perfect reflection is inserted between two fixed mirrors of partial transmission. We find that electromagnetically induced transparency （EIT） can be realized and controlled in this optomechanical system by adjusting the relative intensity and the relative phase between left-hand and right-hand input （probe and coupling） fields. In particular, one perfect EIT window is seen to occur when the two probe fields are exactly out of phase and the EIT window＇s width is very sensitive to the relative intensity of two coupling fields. Our numerical findings may be extended to achieve optomechanical storage and switching schemes applicable in quantum information processing.

Optomechanical-organized multipulse dynamics in ultrafast fiber laser

A novel organized multipulse pattern and its birth dynamics under strong optomechanical effect in microfiber-assisted ultrafast fiber laser are investigated in this work.The background pulses are observed to obviously exhibit selectively amplifying self-organized process of evolving into quasi-stable equidistant clusters.The radio frequency spectrum of the multipulse pattern displays a harmonic mode-locking-like behavior with a repetition rate of 2.0138 GHz,corresponding to the frequency of torsional-radial(TR_(2m))acoustic mode in microfiber.The results show the evidence of optomechanical effect in dominating the birth dynamics and pattern of multipulse.

Optomechanically induced transparency with Bose-Einstein condensate in double-cavity optomechanical system

We propose a novel technique of generating multiple optomechanically induced transparency(OMIT)of a weak probe field in hybrid optomechanical system.This system consists of a cigar-shaped Bose-Einstein condensate(BEC),trapped inside each high finesse Fabry-P6rot cavity.In the resolved sideband regime,the analytic solutions of the absorption and the dispersion spectrum are given.The tunneling strength of the two resonators and the coupling parameters of the each BEC in combination with the cavity field have the appearance of three distinct OMIT windows in the absorption spectrum.Furthermore,whether there is BEC in each cavity is a key factor in the number of OMIT windows determination.The technique presented may have potential applications in quantum engineering and quantum information networks.

Tunable optomechanically induced transparency and fast-slow light in a loop-coupled optomechanical system

We theoretically explore the tunability of optomechanically induced transparency(OMIT)phenomenon and fast-slow light effect in a loop-coupled hybrid optomechanical system in which two optical modes are coupled to a common mechanical mode.In the probe output spectrum,we find that the interference phenomena OMIT caused by the optomechanical interactions and the normal mode splitting(NMS)induced by the strong tunnel coupling between the cavities can be observed.We further observe that the tunnel interaction will affect the distance and the heights of the sideband absorption peaks.The results also show that the switch from absorption to amplification can be realized by tuning the driving strength because of the existence of stability condition.Except from modulating the tunnel interaction,the conversion between slow light and fast light also can be achieved by adjusting the optomechanical interaction in the output field.This study may provide a potential application in the fields of high precision measurement and quantum information processing.

Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system

We investigate the quantum entanglement in a double-cavity optomechanical system consisting of an optomechanical cavity and an auxiliary cavity,where the optomechanical cavity mode couples with the mechanical mode via radiation-pressure interaction,and simultaneously couples with the auxiliary cavity mode via nonreciprocal coupling.We study the entanglement between the mechanical oscillator and the cavity modes when the two cavities are reciprocally or non-reciprocally coupled.The logarithmic negativity E_(n)^((1))(E_(n)^((2)))is adopted to describe the entanglement degree between the mechanical mode and the optomechanical cavity mode(the auxiliary cavity mode).We find that both E_(n)^((1))and E_(n)^((2))have maximum values in the case of reciprocal coupling.By using nonreciprocal coupling,E_(n)^((1))and E_(n)^((2))can exceed those maximum values,and a wider detuning region where the entanglement exists can be obtained.Moreover,the entanglement robustness with respect to the environment temperature is also effectively enhanced.