Normal mode splitting and ground state cooling in a Fabry-Perot optical cavity and transmission line resonator

Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.     

Qubit-assisted squeezing of mirror motion in a dissipative cavity optomechanical system

In this study, we investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with perturbative oscillator-qubit coupling. Such a system is generally very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the master equation and covariance matrix approaches, we discuss in detail the respective squeezing effects. We also determine that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is very effective. In the master equation approach, we find that the squeezing is a resulting effect of the cooling process and is robust against thermal fluctuations of the mechanical mode. In the covariance matrix approach, we can approximately obtain the analytical result of the steady-state mechanical position variance from the reduced dynamical equation. Finally, we compare the two approaches and observe that they are completely equivalent for the stationary dynamics. Moreover, the scheme may be useful for possible ultraprecise quantum measurement that involves mechanical squeezing.     

Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime

The study of optomechanical systems has attracted much attention, most of which are concentrated in the physics in the smallamplitude regime. While in this article, we focus on optomechanics in the extremely-large-amplitude regime and consider both classical and quantum dynamics. Firstly, we study classical dynamics in a membrane-in-the-middle optomechanical system in which a partially reflecting and flexible membrane is suspended inside an optical cavity. We show that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, we study the dynamics of the quantum fluctuations around the classical orbits. By using the logarithmic negativity, we calculate the evolution of the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation. We show that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.     

Optomechanical dynamics in detuned whispering-gallery modes cavity

The dynamics of a microresonator in detuned whispering-gallery modes (WGM) cavity opto-mechanical system are investigated by the quantum Langevin equation. A WGM cavity coupling to two parallel waveguides is devised to study the transmission and reflection of this system. In single mode WGM cavity, without optomechanical coupling, both the transmission and reflection of the cavity present a Lorentzian dip and peak. When the coupling between the cavity mode and mechanical mode is considered, the transmission and reflection of the optomechanical cavity show “W” and “M” shape mode splitting. Moreover, under the action of a controlling and a probe laser, the output field at the probe frequency presents electromagnetically induced transparency (EIT)-like spectrum in the system. We give the physical origin of EIT-like and the pump-probe response for the WGM shares all the features of the Λ system in atoms. Further, due to backscattering, the two traveling waves in WGM are coupled with a rate γ. The transmission and reflection of the optomechanical cavity display three modes splitting in the spectra with optomechanical coupling between the two cavity modes and the mechanical mode.     

强耦合光机械腔中的简正模式分裂和冷却

研究由辐射压力与驱动Fabry-Perot光学腔相耦合而产生的腔光机械动力学行为. 通过量子朗之万方程具体研究了机械振子的涨落光谱、机械阻尼与共振频移和基态冷却. 随着输入激光功率的增加,振子的涨落光谱呈现简正模式分裂的现象,并且数值模拟结果和实验结果相符合. 同时推导了有效机械阻尼和共振频移. 红移边带导致了机械模的冷却,蓝移边带引起了机械模的放大. 此外,引入一种近似机制来研究振子的基态冷却,并且考虑在解析边带机制下简正模式分裂对机械振子冷却的影响. 最后,数值讨论了初始浴温度、输入激光功率和机械品质因数这三个因素对机械振子冷却的影响. 关键词： 腔光机械 辐射压力 简正模式分裂 冷却     

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.     

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 nonreciprocally 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.     

腔光力学系统中的量子测量

腔光力学系统近年来迅猛发展, 在精密测量、量子传感等方面已展现出重要的应用价值. 特别是与微纳技术和冷原子技术结合后, 这一系统正发展成为研究量子测量与量子操控的理想平台. 本文首先综述腔光力学在量子测量, 尤其是量子测量基础理论研究方面的进展; 然后分析腔光力学系统中的量子测量原理; 最后介绍我们近来在这方面的研究进展, 并通过我们设计的一系列新颖的基于腔光力学系统的量子测量方案来具体展示该系统在量子测量、量子操控等方面的潜在应用.     

Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime.We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su-Schrieffer Heeger(SSH)model via designing the effective optomechanical coupling.Especially,the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the opto mechanical coupling.We stress that the to pological phase transition is mainly induced by the decay of the cavity field,which is counter-intuitive since the dissipation is usually detrimental to the system.Also,we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice.We find that the quantum st ate transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields.Our scheme provides the fundamental and the insightful explanations towards the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform.     

Normal Mode Splitting in a Cavity Optomechanical System with a Cubic Anharmonic Oscillator

The strong coupling between a macroscopic mechanical oscillator and a cavity field is essential for many quantum phenomena in a cavity optomechanical system. In this work, we discuss the normal mode splitting in a cavity optomechanical system with a cubic nonlinear movable mirror. We study how the mechanical nonlinearity affects the normal-mode splitting behavior of the movable mirror and the output field. We find that the mechanical nonlinearity can increase the peak separation in the spectra of the movable mirror and the output field. We also find that the heights and linewidths of the two peaks are very sensitive to the mechanical nonlinearity.

     

非线性光学腔中的相位调制光机械动力学

研究了Fabry-Perot光学腔中包含一个光学参量放大器来增强腔场与机械振子之间的耦合的光机械动力学行为.在解析边带机制下用量子郞之万方程具体研究了振子的涨落光谱、光学多稳态行为、机械阻尼与修正共振频移和基态冷却.通过数值解讨论了辐射压力诱导机械振子和腔场的稳态振幅所展现的光学多稳态行为,同时也分析了辐射压力引起的修正共振频移和机械阻尼与参量增益、输入激光功率和参量相位这三个因素的关系.此外,随着调节泵浦场的参量相位,振子的涨落光谱呈现简正模式分裂.通过精确求解最终有效声子数论证了基态冷却.结果表明,机械振子的冷却由初始浴温度、机械品质因数和参量相位这个三个因素控制.参量相提供一个新的方法来操控非线性光机械动力学.     

Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

In this paper,we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system.In the scheme,when the driving bichromatic laser beam is adjusted to the off-resonant j-order red-and blue-sideband,the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model.Moreover,we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system.As a typical example,we theoretically analyze the two-phonon resonance quantum Rabi model,and derive an effective Hamiltonian of the six-phonon coupling.Finally,we present a method of six-phonon generation based on adiabatic passage across the resonance.Numerical simulations confirm the validity of the proposed scheme.Theoretically,the proposed scheme can be extended to the realization of 3j-phonon state.     

Nonlocal nonreciprocal optomechanical circulator

A nonlocal circulator protocol is proposed in a hybrid optomechanical system. By analogy with quantum communication, using the input-output relationship, we establish the quantum channel between two optical modes with long-range. The three-body nonlocal interaction between the cavity and the two oscillators is obtained by eliminating the optomechanical cavity mode and verifying the Bell-CHSH inequality of continuous variables. By introducing the phase accumulation between cyclic interactions, the unidirectional transmission of quantum state between the optical mode and two mechanical modes is achieved. The results show that nonreciprocal transmissions are achieved as long as the accumulated phase reaches a certain value. In addition, the effective interaction parameters in our system are amplified, which reduces the difficulty of the implementation of our protocol. Our research can provide potential applications for nonlocal manipulation and transmission control of quantum platforms.     

Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions

Recently, cavity optomechanics has become a rapidly developing research field exploring the coupling between the optical field and mechanical oscillation. Cavity optomechanical systems were predicted to exhibit rich and nontrivial effects due to the nonlinear optomechanical interaction. However, most progress during the past years have focused on the linearization of the optomechanical interaction, which ignored the intrinsic nonlinear nature of the optomechanical coupling. Exploring nonlinear optomechanical interaction is of growing interest in both classical and quantum mechanisms, and nonlinear optomechanical interaction has emerged as an important new frontier in cavity optomechanics. It enables many applications ranging from single-photon sources to generation of nonclassical states. Here, we give a brief review of these developments and discuss some of the current challenges in this field.     

Quantum coherence transfer between an optical cavity and mechanical resonators

This study highlights the theoretical investigation of quantum coherence in mechanical oscillators and its transfer between the cavity and mechanical modes of an optomechanical system comprising an optical cavity and two mechanical oscillators that,in this study, were simultaneously coupled to the optical cavity at different optomechanical coupling strengths. The quantum coherence transfer between the optical and mechanical modes is found to depend strongly on the relative magnitude of the two optomechanical couplings. The laser power, decay rates of the cavity and mechanical oscillators, environmental temperature, and frequency of the mechanical oscillator are observed to significantly influence the investigated quantum coherences. Moreover,quantum coherence generation in the optomechanical system is restricted by the system's stability condition, which helps sustain high and stable quantum coherence in the optomechanical system.     

Reservoir-engineered entanglement in an unresolved-sideband optomechanical system

We study theoretically the generation of strong entanglement of two mechanical oscillators in an unresolved-sideband optomechanical cavity, using a reservoir engineering approach. In our proposal, the effect of unwanted counter-rotating terms is suppressed via destructive quantum interference by the optical field of two auxiliary cavities. For arbitrary values of the optomechanical interaction, the entanglement is obtained numerically. In the weak-coupling regime, we derive an analytical expression for the entanglement of the two mechanical oscillators based on an effective master equation, and obtain the optimal parameters to achieve strong entanglement. Our analytical results are in accord with numerical simulations.     

Generation of Optical and Mechanical Squeezing in the Linear‐and‐Quadratic Optomechanics

Generation of strong stationary optical and mechanical squeezing is proposed for the linear‐and‐quadratic optomechanical system, where two cavity modes induce linear and quadratic optomechanical couplings, respectively. Through the linearization treatment, linearized coupling between cavity mode and mechanical mode and the mechanical parametric amplification process are achievable and controllable by independent driving lasers. Optical and mechanical squeezing are generated following different mechanisms. Optical squeezing works in the strong coupling regime, and mechanical amplification would push the system close to instability threshold, which could deeply improve ponderomotive squeezing even significantly beyond the 3 dB squeezing limit. Mechanical squeezing is generated based on the reservoir engineering method, where parametric amplification induces the squeezing transformation of mechanical mode; and linearized coupling, which operates in the red‐sideband and weak coupling limits, induces the ground‐state cooling of transformed mechanical mode. Finally, the original mechanical mode would be squeezed, which could also exceed 3 dB limit.     

Indirect strong coupling regime between a quantum emitter and a cavity mediated by a mechanical resonator

Achieving strong coupling between light and matter is usually a challenge in Cavity Quantum Electrodynamics (cQED), especially in solid state systems. For this reason is useful taking advantage of alternative approaches to reach this regime, and then, generate reliable quantum polaritons. In this work we study a system composed of a quantized single mode of a mechanical resonator interacting linearly with both a single mode cavity and a quantum two-level system. In particular, we focus on the behavior of the indirect light-matter interaction when the phonon mode interfaces both parts. By diagonalization of the Hamiltonian and computing the density matrix in a master equation approach, we evidence several features of strong coupling between photons and matter excitations. For large energy detuning between the cavity and the mechanical resonator it is obtained a phonon-dispersive effective Hamiltonian which is able to retrieve much of the physics of the conventional Jaynes–Cummings model (JCM). In order to characterize this mediated coupling, we make a quantitative comparison between both models and analyze light-matter entanglement and purity of the system leading to similar results in cQED.     

腔光力系统制备微波非经典态研究进展

腔光力系统作为一种新型的混合量子系统,因其超强耦合度、低温超导条件下极低的噪声、较长的相干时间等优势而成为被广受关注的量子实验平台.本文简要介绍腔光力学及腔光力系统基本原理,对常见腔光力系统进行分类,详细介绍利用广义腔光力系统进行微波非经典量子态制备的相关进展,对其性能优势和待解决问题进行分析,最后总结相关应用场景并对未来的潜在应用领域进行了展望.     

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 applications 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 nonclassical 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 quantum 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.