Quantum control with Lyapunov function and bang–bang solution in the optomechanics system

We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero as t → ∞ while the quantum system is driven to the target state. Such an evolution makes no limit on the initial state and one needs not manipulate the laser pulses during the evolution. To prove the effectiveness of the scheme, we show two useful applications in the optomechanics system: one is the cooling of nanomechanical resonator and the other is the quantum fluctuation transfer between membranes. Numerical simulation demonstrates that the perfect and fast cooling of nanomechanical resonator and quantum fluctuation transfer between membranes can be rapidly achieved. Besides, some optimizations are made on the traditional Lyapunov control waveform and the optimized bang–bang control fields makes Lyapunov function V decrease faster. The optimized quantum control scheme can achieve the same goal with greater efficiency. Hence, we hope that this work may open a new avenue of the experimental realization of cooling mechanical oscillator, quantum fluctuations transfer between membranes and other quantum optomechanics tasks and become an alternative candidate for quantum manipulation of macroscopic mechanical devices in the near future.     

On the Interaction of Massive Photons and Mechanical Oscillators in Cavity Optomechanics: Basic Model and Quantization

This study investigates the theoretical aspects of the interaction between photons with mass and a mechanical oscillator as drawn within the framework of cavity optomechanics. The study employs Proca theory as the mathematical framework to initially describe the dynamics of massive photons in a Fabry-Perot cavity with a movable mass, both in classical and quantum scenarios. It quantifies the modifications induced by the nonzero photon mass, considering first- and second-order effects, and derives expressions for the amplification of radiation pressure resulting from the presence of nonzero photon mass. Additionally, it derives the Hamiltonian of the quantum optomechanical system, incorporating the effects of photon mass at first and second order. It anticipates that experimental realization of massive optomechanics can be achieved by utilizing Proca material, which is a spatio-temporally dispersive material that exhibits behavior equivalent to Proca theory in a vacuum, thus enabling the study of the interaction between massive photons and mechanical systems in cavity-based optomechanical setups (referred to as massive cavity optomechanics). The study presented here caters to a diverse audience with an interest in the analysis and measurement of interactions among massive objects at the quantum scale.     

Photon blockade effect in optomechanical systems

We analyze the photon statistics of a weakly driven optomechanical system and discuss the effect of photon blockade under single-photon strong coupling conditions. We present an intuitive interpretation of this effect in terms of displaced oscillator states and derive analytic expressions for the cavity excitation spectrum and the two-photon correlation function g(2)(0). Our results predict the appearance of nonclassical photon correlations in the combined strong coupling and sideband resolved regime and provide a first detailed understanding of photon-photon interactions in strong coupling optomechanics.     

三机械薄膜腔光力系统相互作用的研究

本文主要研究了利用传输矩阵理论和共振透射条件详细地推导光腔中均匀放置三个机械薄膜构成的腔光力系统中系统本征模式随机械运动的色散关系.计算结果发现系统的光学本征模式由一组四个的本征能级构成,且不同的能级随不同的机械运动模式的变化曲线各不相同,进而导致不同光学模式与不同机械运动模式之间的耦合也不相同.此外,利用微扰理论求解了当机械运动振幅远小于腔模波长、机械振子处于平衡位置附近时,各种光学模式与不同机械振动模式间相互作用耦合强度的解析表达式.研究结果能够为理论和实验上研究多模腔光力系统提供一定的参考.     

边界振动的微腔中的二能级原子

采用全量子理论，对注入腔内的二能级原子、单模腔场和振动边界(视为频率为ω_m的量子谐振子)构成的系统，在相互作用绘景中，求解了该系统的态函数随时间的演化关系，在此基础上得到了原子布居数随时间的演化关系，结果显示布居数在初始值附近振荡，这说明边界的振动是周期性的，它对原子布居数的影响也是周期性的. 关键词： 边界振动的微腔 二能级原子 布居数     

Single-photon optomechanics

Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady states of the mechanical oscillator when multiphoton transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.     

Dissipative optomechanics in a Michelson-Sagnac interferometer

Dissipative optomechanics studies the coupling of the motion of an optical element to the decay rate of a cavity. We propose and theoretically explore a realization of this system in the optical domain, using a combined Michelson-Sagnac interferometer, which enables a strong and tunable dissipative coupling. Quantum interference in such a setup results in the suppression of the lower motional sideband, leading to strongly enhanced cooling in the non-sideband-resolved regime. With state-of-the-art parameters, ground-state cooling and low-power quantum-limited position transduction are both possible. The possibility of a strong, tunable dissipative coupling opens up a new route towards observation of such fundamental optomechanical effects as nonlinear dynamics. Beyond optomechanics, the suggested method can be readily transferred to other setups involving nonlinear media, atomic ensembles, or single atoms.     

Approach to statistical equilibrium in a soluble model

The soluble model of an oscillator coupled to a scalar field is used to describe the Brownian motion of an oscillator in a thermal bath. The approach to equilibrium is shown by studying the generating functional that corresponds to a non-equilibrium situation fixed as an initial condition. It is shown how this functional goes over into the functional associated with the equilibrium situation. The solution of the functional equations is discussed.     

Picosecond laser for performance of efficient nonlinear spectroscopy from 10 to 21 microm

Laser tunability from 10 to 21 microm is obtained by use of an optical parametric oscillator based on a KTP crystal followed by a difference-frequency stage with a CdSe crystal. An all-solid-state picosecond Nd:YAG oscillator mode locked by a frequency-doubling nonlinear mirror is used for synchronous pumping.     

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.

     

Compensation of fluctuational back action and detection of mechanical squeezing in the regime of strongly detuned pumping of an optical displacement sensor

Measurement of the position of an oscillator by means of a Fabry-Perot resonator with one moving mirror (oscillator mass) pumped by a laser in the regime of strongly detuned pumping is analyzed. Compensation of fluctuational back action in the reflected wave is demonstrated. However, this does not allow overcoming the standard quantum limit due to the dynamic back action. Additionally, the possibility of detecting mechanical squeezing under parametric action on a mechanical oscillator is analyzed.     

FTIR光谱仪中基于定镜调整的动镜运动控制研究

动镜是FTIR光谱仪中唯一不断运动的部件,动镜的匀速运动性能以及动镜与定镜的准直性好坏影响干涉效果和光谱图质量,直接制约着仪器的精度和分辨率,对仪器整体指标起着重要作用。文章围绕FTIR光谱仪中干涉仪动镜运动的匀速性以及其与定镜的准直性展开研究,使用相位检测技术对定镜的姿态作出动态调整以补偿动镜与定镜间的倾斜夹角,并且设计了具有磁悬浮特点的动镜支撑系统。文章采用改进的模糊PID控制算法实现动镜运动速度的精确调节,对该控制方案从硬件设计和算法上实现。结果表明所研发的动镜运动控制系统具有足够的精度和实时性,能够保证FTIR光谱仪中干涉仪所需的准直性及动镜匀速性的要求。     

Spatially-temporal dynamics of a passively Q-switched Raman-active solid-state oscillator

The spatially-temporal model of an all-solid-state passively Q-switched oscillator with an active medium providing the stimulated Raman scattering is presented. The model does not presume a Gaussian shape of the cylindrically symmetric modes at both fundamental and Stokes wavelengths. It is found, that the highly-nontrivial spatially-temporal dynamics can be regularized by an optimal choice of oscillator parameters, viz. initial transmission of a saturable absorber, curvature of a spherical mirror, and output mirror transmission at the fundamental and Stokes wavelengths. As a result, the pulse can be substantially temporally squeezed and spatially broadened at both fundamental and Stokes wavelengths.     

Quantum optomechanics of a Bose-Einstein antiferromagnet

We investigate the cavity optomechanical properties of an antiferromagnetic Bose-Einstein condensate, where the role of the mechanical element is played by spin-wave excitations. We show how this system can be described by a single rotor that can be prepared deep in the quantum regime under realizable experimental conditions. This system provides a bottom-up realization of dispersive rotational optomechanics, and opens the door to the direct observation of quantum spin fluctuations.     

Ehrenfest Time at the Transition from Integrable Motion to Chaotic Motion

Ehrenfest time depends differently on the Planck constant in integrable motion and chaotic motion. We study how its dependence on the Planck constant changes when there is a continuous transition from regular motion to chaotic motion. We find that the dependence is a weighted compromise between its two distinct dependences in regular and chaotic motions. The study is carried out with the system of periodically driven anharmonic oscillator. As the system is quite typical, the result may apply generally.     

Optomechanical effects in superfluid properties of BEC in an optical lattice

We investigate the effects of a movable mirror (cantilever) of an optical cavity on the superfluid properties and the Mott phase boundary of a Bose-Einstein condensate (BEC) in an optical lattice. The Bloch energy, effective mass, Bogoliubov energy and the superfluid fraction are modified due to the mirror motion. The mirror motion is also found to modify the Mott-superfluid phase boundaries. This study reveals that the mirror emerges as a new handle to coherently control the superfluid properties of the BEC.     

Cavity optomechanics with cold atomic gas

We present a tutorial review on the topics related to current development in cavity optomechanics, with special emphasis on cavity optomechanical effects with ultracold gases, Bose-Einstein condensates, and spinor Bose-Einstein condensates. Topics including the quantum model and nonlinearity of the cavity optomechanics, the principles of optomechanical cooling, radiation-pressure-induced nonlinear states, the chaotic dynamics in a condensate-mirror-hybrid optomechanical setup, and the spin-mixing dynamics controlled by optical cavities are covered.     

Towards quantum superpositions of a mirror

We propose an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.     

Improvement of extraction efficiency by regenerative amplification in an Nd: YAG-MOPA with a phase-conjugating SBS cell

A regenerative amplifier consisting of a conventional mirror as the output coupler and a phase-conjugating SBS cell as the high-reflectivity mirror was seeded with a single longitudinal and transverse mode oscillator with pulse durations of 10 ns and pulse energies up to 5.3 mJ. The output energy, temporal characteristics and beam-quality were measured as a function of pump energy, input energy and the reflectivity of the feedback mirror. Output energies up to 180 mJ were obtained for oscillator input energies of only 0.3 mJ. The beam quality was 2.5 times the diffraction limit. The results are compared with those for simple double-pass amplification.     

Normal mode splitting in hybrid BEC-optomechanical system

We consider an opto-mechanical cavity system consisting of Bose-Einstein condensate (BEC), trapped inside the optical cavity and driven by single mode laser field. The intracavity field acts as nonlinear spring which couples the condensate mode with moving end mirror of the cavity. We study the occurrence of normal mode splitting in the position spectra of the mechanical oscillator and condensate mode as a consequence of hybridization of the fluctuations of intracavity field, mechanical mode and condensate mode. We also discuss the modification in the dynamics of the mechanical oscillator due to frequency of the collective oscillations of cold atoms and the back action of the atoms on the mechanical mirror. Moreover, we investigate the normal mode splitting in the transmission spectrum of cavity field.