Mechanical systems in the quantum regime

Mechanical systems are ideal candidates for studying quantum behavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter includes sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto- and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems is bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum mechanics.     

Dynamics of a bistable Mott insulator to superfluid phase transition in cavity optomechanics

We study the dynamics of the many-body state of ultracold bosons trapped in a bistable optical lattice in an optomechanical resonator controlled by a time-dependent input field. We focus on the dynamics of the many-body system following discontinuous jumps of the intracavity field. We identify experimentally realizable parameters for the bistable quantum phase transition between Mott insulator and superfluid.     

Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics

We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a $1/f$ thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, $?=4.5?{10}^{?6}$, agrees well with the quality factor (Q) of the fundamental beam mode ($?=Q^{?1}$). In conjunction with Q measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such “structural damping” on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.     

Optomechanical soft metamaterials

We present a new type of optomechanical soft metamaterials, which is different from conventional mechan-ical 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 con-stitutive 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 con-sidered. A theoretical model is formulated to characterize the resulting optomechanical behavior of the thin sheet by com-bining 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 simula-tions 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.     

Ultra-low dissipation resonators for improving the sensitivity of gravitational wave detectors

Broadband enhancement of the sensitivity of gravitational wave detectors can be achieved by the use of negative dispersion filters to create white light signal recycling cavities. This filter should have mechanical frequency of 300 kHz or higher and $T/Q_{\mathrm{m}}～6\times {10}^{?10}$ K, in order to achieve appreciable sensitivity enhancement in the range of 1–2 kHz. This paper investigates the possibility of using optical dilution of GaAs/AlGaAs-coated Si and GaAs “cat-flap” micro-resonators to achieve such performance. We analyse the loss contributions to such resonators, particularly thermoelastic loss, suspension loss and acceleration loss. Sufficient reduction of thermoelastic loss is possible when operating near the zero thermal expansion point with temperature control of ～1 K for both materials. Acceleration loss and suspension losses can be minimised in the frequency range ${10}^4\text{–}{10}^5\text{Hz}$, allowing Q-factors in the range ${10}^{11}\text{–}{10}^{12}$, but these are reduced at the target 400 kHz frequency. Results are subject to assumptions regarding material losses. Fabrication techniques for creating GaAs and SiN_x suspended silicon cat-flap resonators are presented.     

Phoxonic crystals and cavity optomechanics

Phoxonic crystals are dual phononic/photonic crystals exhibiting simultaneously band gaps for both types of excitations. Therefore, they have the ability to confine phonons and photons in the same cavity and in turn allow the enhancement of their interaction. In this paper, we review some of our theoretical works on cavity optomechanical interactions in different types of phoxonic crystals, including two-dimensional, slab, and nanobeam structures. Two mechanisms are behind the phonon–photon interaction, namely the photoelastic and the moving interface effects. Coupling rates of a few MHz are obtained with high-frequency phonons of a few GHz. Finally, we give some preliminary results about the optomechanical interaction when a metallic nanoparticle is introduced into the cavity, giving rise to coupled photon–plasmon modes or, in the case of very small particles, to an enhancement of the electric field at the position of the particle.     

激光干扰扩束系统光机结构设计

针对常规红外干扰技术存在的能量无法集中、隐蔽性差且无法进行变倍切换等实际问题,提出一种离轴双反射式激光干扰扩束系统的设计方案,并对离轴双反射镜组,转向平面反射镜及支撑固定机构等主要组成部分进行了光机结构设计.为实现扩束比的变倍切换功能,采用新型离轴副镜组件设计;为减小镜面变形,离轴主副镜组均采用微应力设计.分析结果表明,在-20~+60℃温度范围内,主副镜组轴向最大位移小于等于0.01mm,主副镜组的反射镜面形误差小于等于71.9nm;系统一阶固有频率108.3Hz,其支撑结构应力响应远小于材料的屈服极限.实际测试发现,系统可实现1:10.02(19.92,25.02)扩束比,满足设计技术指标要求.分析及试验结果表明,系统光机结构设计合理,完全满足实际应用要求.