David Vitali, Stefano Mancini, Paolo Tombesi
We show that a cooling scheme and an appropriate quantum nonstationary strategy can be used to improve the signal to noise ratio for the optomechanical detection of weak impulsive forces.
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Optomechanical systems are often used for the measurement of weak forces. Feedback loops can be used in these systems for achieving noise reduction. Here we show that even though feedback is not able to improve the signal to noise ratio of the device in stationary conditions, it is possible to design a nonstationary strategy able to improve the sensitivity.
Optomechanical detectors have reached the standard quantum limit in position and force sensing where measurement backaction noise starts to be the limiting factor for the sensitivity. A strategy to circumvent measurement backaction, and surpass the standard quantum limit, has been suggested by M. Tsang and C. Caves in Phys. Rev. Lett. 105 123601 (2010). We provide a detailed analysis of this method and assess its benefits, requirements, and limitations. We conclude that a proof-of-principle demonstration based on a micro-optomechanical system is demanding, but possible. However, for parameters…
We experimentally study an optomechanical cavity that is formed between a mechanical resonator, which serves as a movable mirror, and a stationary on-fiber dielectric mirror. A significant change in the behavior of the system is observed when the distance between the fiber's tip and the mechanical resonator is made smaller than about 1 micrometer. The observed effects are attributed to the combined influence of Casimir force, Coulomb interaction due to trapped charges, and optomechanical coupling. The comparison between experimental results and theory yields a partial agreement.
We propose to use cavity optomechanical systems in the regime of optical bistability for the detection of weak harmonic forces. Due to the optomechanical coupling an external force on the mechanical oscillator modulates the resonance frequency of the cavity and consequently the switching rates between the two bistable branches. A large difference in the cavity output fields then leads to a strongly amplified homodyne signal. We determine the switching rates as a function of the cavity detuning from extensive numerical simulations of the stochastic master equation as appropriate for continuous …
Cooling and Entanglement in optomechanical systems coupled through radiation pressure and photothermal force is studied. To develop the photothermal model, we derive an expression for deformation constant of the force. Exploiting linearized quantum Langevin equations we investigate dynamics of such systems. According to our analysis, in addition to separate action of radiation pressure and photothermal force, their cross correlation effect plays an important role in dynamics of the system. We also achieve an exact relation for the phonon number of the mechanical resonator in such systems, and …
Mechanical resonators based on low-dimensional materials are promising for force and mass sensing experiments. The force sensitivity in these ultra-light resonators is often limited by the imprecision in the measurement of the vibrations, the fluctuations of the mechanical resonant frequency, and the heating induced by the measurement. Here, we strongly couple multilayer graphene resonators to superconducting cavities in order to achieve a displacement sensitivity of $1.3$ fm Hz$^{-1/2}$. This coupling also allows us to damp the resonator to an average phonon occupation of $7.2$. Our best forc…
Nanomechanical sensor resolving impulsive forces below its zero-point fluctuations
该研究利用光学悬浮纳米颗粒，通过相干放大扰动，实现了分辨低于零点波动的冲击力，展示了单个冲击力的高灵敏度测量。
We consider an optomechanical system that is composed of a mechanical and an optical mode interacting through a linear and quadratic optomechanical dispersive couplings. The system is operated in an unresolved side band limit with a high quality factor mechanical resonator. Such a system then acts as parametrically driven oscillator, giving access to an intensity assisted tunability of the spring constant. This enables the operation of optomechanical 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…
Application of frequency-dependent squeezed vacuum improves the force sensitivity of optomechanical interferometer beyond the standard quantum limit by a factor of $e^{-r}$, where $r$ is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum optical restoring force can enhance the sensitivity beyond the standard quantum limit by a factor of $\sqrt{e^{-2r}ζ/4Δ}$, where $0< ζ/Δ<1$, with $ζ$ as the optomechanical cavity decay rate and $Δ$ as the detuning between cavity eigenfrequency and driving field. The technique described in this article is re…
Controlling photothermal forces and backaction in nano-optomechanical resonators through strain engineering
通过纳米尺度结构设计，实现对纳米光学机械谐振器中光热力和辐射压力力的精确控制，以优化系统性能。
The optomechanical force sensor in non-Markovian environment for a mechanical oscillator is presented. By performing homodyne detection we obtain an generally expression for the output signal. It is shown that the weak force detection is sensitive to the non-Markovian environment. The additional noise can be obviously reduced comparing to the Markovian condition. Moreover, the optimal additional noise can be maintained in a rather low level without using assistant system or squeezing under available experimental condition in unsolved sideband regime. Our results provides a promising platform f…
Control of quality factor of atomic force microscopy cantilever by cavity optomechanical effect
提出在 Fabry-Pérot 干涉仪中利用双激光与光机械力调控 AFM 微悬臂品质因数的方法，可在不影响偏转灵敏度的情况下优化测量，并建模补偿热致频移。
We study the detection of weak coherent forces by means of an optomechanical device formed by a highly reflecting isolated mirror shined by an intense and highly monochromatic laser field. Radiation pressure excites a vibrational mode of the mirror, inducing sidebands of the incident field, which are then measured by heterodyne detection. We determine the sensitivity of such a scheme and show that the use of an entangled input state of the two sideband modes improves the detection, even in the presence of damping and noise acting on the mechanical mode.
Overcoming the Standard Quantum Limit with Electro-Optomechanical Hybrid System for Enhanced Force Sensing
本研究在含OPA、超导量子比特的混合光力系统中，利用CQNC抵消反作用噪声，结合提升OPA泵浦增益，在低激光功率下突破力传感的标准量子极限，提升弱力探测能力。
Force Sensing Beyond the Standard Quantum Limit in a Hybrid Optomechanical Platform
该研究通过混合光学机械平台利用量子点和光学参量放大器实现超越标准量子极限的力传感。
The measurement of weak continuous forces exerted on a mechanical oscillator is a fundamental problem in various physical experiments. It is fundamentally impeded by quantum back-action from the meter used to sense the displacement of the oscillator. In the context of interferometric displacement measurements, we here propose and demonstrate the working principle of a scheme for coherent back-action cancellation. By measuring the amplitude quadrature of the light reflected from a detuned optomechanical cavity inside which a stiff optical spring is generated, back-action can be cancelled in a n…
Enhanced weak force sensing through atom-based coherent noise cancellation in a hybrid cavity optomechanical system
本文提出在非线性混合光机械系统中利用相干量子噪声消除（CQNC）和调节OPA参数来消除后作用噪声并抑制低频散粒噪声，从而克服标准量子极限，显著增强弱力传感性能。
Enhanced weak force sensing based on atom-based coherent quantum noise cancellation in a hybrid cavity optomechanical system
该研究从理论上提出含超冷原子与OPA的混合腔光力系统CQNC弱力传感方案，可全频消除反作用噪声、降低低频噪声，小功率下也能超越SQL，为力传感与宏观量子控制提供新思路。
Quantum control techniques applied at macroscopic scales provide us with opportunities in fundamental physics and practical applications. Among them, measurement-based feedback allows efficient control of optomechanical systems and quantum-enhanced sensing. In this paper, we propose a near-resonant narrow-band force sensor with extremely low optically added noise in an optomechanical system subject to a feedback-controlled in-loop light. The membrane's intrinsic motion consisting of zero-point motion and thermal motion is affected by the added noise of measurement due to the backaction noise a…
In a canonical optomechanical system, mechanical vibrations are dynamically encoded on an optical probe field which reciprocally exerts a backaction force. Due to the weak single photon coupling strength achieved with macroscopic oscillators, most of existing experiments were conducted with large photon numbers to achieve sizeable effects, thereby causing a dilution of the original optomechanical non-linearity. Here, we investigate the optomechanical interaction of an ultrasensitive suspended nanowire inserted in a fiber-based microcavity mode. This implementation allows to enter far into the …
We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of back-action noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broad-band detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise cancels exa…
We theoretically investigate optical detection of a weak classical force acting on a free particle in a dissipative coupling optomechanical system with a degenerate parametric amplifier (PA). We show that the PA allows one to achieve the force sensitivity far better than the standard quantum limit (SQL) over a broad range of the detection frequencies. The improvement depends on the parametric gain and the driving power. Moreover, we discuss the effects of the mechanical damping and the thermal noise on the force sensitivity. We find that the robustness of the force sensitivity much better than…
Enhancing optomechanical force sensing utilizing synthetic magnetism
本文提出利用合成磁性调控声子跳跃，通过切换暗模式破缺状态，增强光机械力传感的探测带宽并抑制噪声，有望超越标准量子极限。
Using a flowchart representation of quantum optomechanical dynamics, we design coherent quantum-noise-cancellation schemes that can eliminate the back-action noise induced by radiation pressure at all frequencies and thus overcome the standard quantum limit of force sensing. The proposed schemes can be regarded as novel examples of coherent feedforward quantum control.
In this article, we rigorously analyze the effects of the dispersion forces (Casimir and van der Waals forces) on a nano-optomechanical device based on a silicon waveguide and a silicon dioxide substrate, surrounded by air and driven by optical forces. The dispersion forces are calculated using a modified Lifshitz theory, in order to take into account the device thickness and material s dielectric permittivities, which are obtained from experimental optical data and validated by means of a rigorous 3D FDTD simulation. We also take into account the mechanical nonlinearity of the waveguide, whic…
Weak force sensing based on optical parametric amplification in a cavity optomechanical system coupled in series with two oscillators
本文提出在腔光力学系统中结合光学参量放大与两个串联耦合振子，通过简正模劈裂和腔场压缩的联合效应抑制量子噪声，从而提升弱力传感精度。
In this paper, we propose an experimentally viable scheme to enhance the sensitivity of force detection in a hybrid optomechanical setup assisted by squeezed vacuum injection, beyond the standard quantum limit (SQL). The scheme is based on a combination of the coherent quantum noise cancellation (CQNC) strategy with a variational homodyne detection of the cavity output spectrum in which the phase of the local oscillator is optimized. In CQNC, realizing a negative-mass oscillator in the system leads to exact cancellation of the backaction noise from the mechanics due to destructive quantum inte…
Precise measurements of the displacement of, and force acting on, a mechanical oscillator can be performed by coupling the oscillator to an optical cavity. Brownian thermal forces represent a fundamental limit to measurement sensitivity which impedes the ability to use precise force measurements as a tool of fundamental enquiry, particularly in the context of macroscopic quantum measurements and table-top gravitational experiments. A torsion pendulum with a low mechanical resonant frequency can be limited by very small thermal forces - from its suspensions - at frequencies above resonance. Her…
Mesoscopic mechanical oscillators can be prepared in quantum states and coherently manipulated using the optomechanical interaction. This has recently been used to prepare squeezed mechanical states. However, the scheme used in these experiments relies on slow, dissipative evolution that destroys the system's memory of its initial state. In this paper we propose a protocol based on a sequence of four pulsed optomechanical interactions. In addition to being coherent, our scheme executes in a time much shorter than a mechanical period. We analyse applications in impulsive force sensing and prese…
We provide a full quantum description of the optomechanical system formed by a Fabry-Perot cavity with a movable micro-mechanical mirror whose center-of-mass and internal elastic modes are coupled to the driven cavity mode by both radiation pressure and photothermal force. Adopting a quantum Langevin description, we investigate simultaneous cooling of the micromirror elastic and center-of-mass modes, and also the entanglement properties of the optomechanical multipartite system in its steady state.
Cavity optomechanical systems are approaching a strong-coupling regime where the coherent dynamics of nanomechanical resonators can be manipulated and controlled by optical fields at the single photon level. Here we propose an interferometric scheme able to detect optomechanical coherent interaction at the single-photon level which is experimentally feasible with state-of-the-art devices.
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 neglig…
In this work we theoretically investigate the stochastic resonance (SR) effect in an optomechanical membrane system subject to two weak signals (one optical field and one mechanical force). The quadratic optomechanical coupling allows us to find a region with tristability where the noise activated stochastic switching among three stable states occurs and SR phenomena are observed at the cooperation of input signals and noises. We show that the mechanical force and the optical field respectively serve as an additive signal and a multiplicative signal to the membrane position and they induce com…
Quantum experiments with nanomechanical oscillators are regarded as a testbed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macro-scale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes f…
Electrically coupled optomechanical cavities as a tool for quantum nondemolition measurement
本文提出两个电耦合光机械腔模型，发现库仑力耦合可产生交叉克尔相互作用，并论证其适合用于量子非破坏测量且实验上可行。
We consider a hybrid quantum many-body system formed by both a vibrational mode of a nanomembrane, which interacts optomechanically with light in a cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. After integrating over the light field, an effective Hamiltonian reveals a competition between the localizing potential force and the membrane displacement force. For increasing atom-membrane interaction we find a nonequilibrium quantum phase transition from a localized non-motional phase of the atom cloud to a phase of collective motion. Near the quantum critical po…
Quantum squeezing in mechanical systems is not only a key signature of macroscopic quantum effects, but can also be utilized to advance the metrology of weak forces. Here we show that strong mechanical squeezing in the steady state can be generated in an optomechanical system with mechanical nonlinearity and red-detuned monochromatic driving on the cavity mode. The squeezing is achieved as the joint effect of nonlinearity-induced parametric amplification and cavity cooling, and is robust against thermal fluctuations of the mechanical mode.
Constraining symmetron fields with a levitated optomechanical system
针对传统测量因屏蔽行为难以探测暗能量理论中的对称子场问题，提出利用纳米球-光学腔耦合的悬浮光力学系统，通过测量透射谱频移约束对称子参数，约束精度较现有方法提升1-3个数量级，为暗能量探测提供新途径。
We investigate quantum-squeezing-enhanced weak-force sensing via a nonlinear optomechanical resonator containing a movable mechanical mirror and an optical parametric amplifier (OPA). Herein, we determined that tuning the OPA parameters can considerably suppress quantum noise and substantially enhance force sensitivity, enabling the device to extensively surpass the standard quantum limit. This indicates that under realistic experimental conditions, we can achieve ultrahigh-precision quantum force sensing by harnessing nonlinear optomechanical devices.
Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force-sensing using a mirror-in-the-middle setup and use two coupled cavity modes originated from normal mode splitting for separating pump and probe fields. We find that this two-mode model can be reduced to an effective single-mode model, if we drive the pump mode strongly and detect the signal from the weak probe mode. The optimal force detection sensitivity at zero frequency (DC) is calculated and we show that one can beat the standard quantum limit …
Mechanical oscillators can be cooled by coupling them to an optical or microwave cavity. Going beyond the standard quantum noise approach we find an analytic expression for the steady-state phonon number in systems where the position of the mechanical oscillator modulates the cavity frequency as well as the cavity line width. We trace the origin for the quantum limit of cooling to fluctuations in the optical force both at and away from the mechanical frequency. Finally, we calculate the minimal phonon number for the different types of coupling. Our study elucidates how to beneficially combine …
We propose a generation of a low-noise state of optomechanical oscillator by a temperature dependent force. We analyze the situation in which a quantum optomechanical oscillator (denoted as the membrane) is driven by an external force (produced by the piston). Both systems are embedded in a common heat bath at certain temperature $T$. The driving force the piston exerts on the membrane is bath temperature dependent. Initially, for $T=T_0$, the piston is linearly coupled to the membrane. The bath temperature is then reversibly changed to $T\neq T_0$. The change of temperature shifts the membran…
We show that optomechanical systems in the quantum regime can be used to demonstrate EPR-type quantum entanglement between the optical field and the mechanical oscillator, via quantum-state steering. Namely, the conditional quantum state of the mechanical oscillator can be steered into different quantum states depending the choice made on which quadrature of the out-going field is to be measured via homodyne detection. More specifically, if quantum radiation pressure force dominates over thermal force, the oscillator's quantum state is steerable with a photodetection efficiency as low as 50%, …
Probing the boundary between classical and quantum mechanics has been one of the central themes in modern physics. Recently, experiments to precisely measure the force acting on milligram scale oscillators with optical cavities are attracting interest as promising tools to test quantum mechanics, decoherence mechanisms, and gravitational physics. In this paper, we review the present status of experiments using milligram scale optomechanical systems. We compare the feasibility of reaching the quantum regime with a pendulum, torsion pendulum, and optically levitated mirror. Considerations for de…
We describe and demonstrate a method to control a detuned movable-mirror Fabry-Perot cavity using radiation pressure in the presence of a strong optical spring. At frequencies below the optical spring resonance, self-locking of the cavity is achieved intrinsically by the optomechanical (OM) interaction between the cavity field and the movable end mirror. The OM interaction results in a high rigidity and reduced susceptibility of the mirror to external forces. However, due to a finite delay time in the cavity, this enhanced rigidity is accompanied by an anti-damping force, which destabilizes th…
Cascaded Optomechanical Sensing for Small Signals
本文提出一种基于级联光学机械谐振腔的相干传感方案，实现海森堡极限灵敏度，用于高精度力传感及重力场、暗物质等探测。
We study the optical cooling of the resonator mirror in a cavity-optomechanical system that contains an optical gain medium. We find that the optical damping rate is vanishingly small for an incoherently pumped laser above threshold. In the presence of an external coherent drive however, the optical damping rate can be enhanced substantially with respect to that of a passive cavity. We show that the strength of the incoherent pump provides a conduit to tune the damping rate and the minimum attainable phonon number with the same radiation pressure force, and the latter can be lowered from that …
We model optomechanical systems as linear optical amplifiers. This provides a unified treatment of diverse optomechanical phenomena. We emphasize, in particular, the relationship between ponderomotive squeezing and optomechanically induced transparency, two foci of current research. We characterize the amplifier response to quantum and deliberately applied fluctuations, both optical and mechanical. Further, we apply these results to establish quantum limits on external force sensing both on and off cavity resonance. We find that the maximum sensitivity attained on resonance constitutes an abso…
This paper investigates waveform estimation (tracking) of the time-varying force in a two-level optomechanical system with backaction noise by Kalman filtering. It is assumed that the backaction and measurement noises are Gaussian and white. By discretizing the continuous-time optomechanical system, the state of the resulting system can be estimated by the unbiased minimum variance Kalman filtering. Then an estimator of the time-varying force is obtained, provided that the external force is also in discrete time. Furthermore, the accuracy of the force estimation, described by the mean squared …
Coherent quantum noise cancellation (CQNC) can be used in optomechanical sensors to surpass the standard quantum limit (SQL). In this paper, we investigate an optomechanical force sensor that uses the CQNC strategy by cascading the optomechanical system with an all-optical effective negative mass oscillator. Specifically, we analyze matching conditions, losses and compare the two possible arrangements in which either the optomechanical or the negative mass system couples first to light. While both of these orderings yield a sub-SQL performance, we find that placing the effective negative mass …
Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their quantum states, as well as generation of optomechanical entanglement. The standard mechanism relies on the cavity photons directly modifying the state of the mechanical resonator. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. While many approaches exist, they typically share a simple ef…
We analyze the optomechanics of an atomic Bose-Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a uniform bias force such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice at the Bloch frequency. When the Bloch frequency is on the order of the cavity damping rate we find transport of the atoms either up or down the lattice. The transport dynamics can be interpreted as a manifestation of…
Quantum Noise Suppression Beyond the Standard Quantum Limit in a Hybrid Magnonic Optomechanical System
研究通过混合腔光机械平台设计降低量子测量噪声，利用磁子介导动力学提升灵敏度，实现辐射压力反作用完全抑制和OPA泵浦增益提升，突破标准量子极限。
Optomechanics, which explores the fundamental coupling between light and mechanical motion, has made important advances in both exploring and manipulating macroscopic mechanical oscillators down to the quantum level. However, dynamical effects related to the vectorial nature of the optomechanical interaction remain to be investigated. Here we study a nanowire with sub-wavelength dimensions strongly coupled to a tightly focused beam of light, enabling ultrasensitive readout of the nanoresonators dynamics. We experimentally determine the vectorial structure of the optomechanical interaction and …
We study the possibility of revealing a weak coherent force by using a pendular mirror as a probe, and coupling this to a radiation field, which acts as the meter, in a cavityless configuration. We determine the sensitivity of such a scheme and show that the use of an entangled meter state greatly improves the ultimate detection limit. We also compare this scheme with that involving an optical cavity.
Low threshold quantum correlations via synthetic magnetism in Brillouin optomechanical system
本文提出在布里渊光机械系统中利用相位调制的声子跳跃耦合诱导合成磁性，从而在低驱动阈值和低耦合强度下产生对热噪声鲁棒的量子关联，并观察到突然死亡与复苏现象，为量子通信、传感和计算提供新途径。
Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces. Here we give a theoretical study of a hybrid atom-optomechanical system in which the steady-state squeezing of the mechanical resonator can be generated via the mechanical nonlinearity and cavity cooling process. The validity of the scheme is assessed by simulating the steady-state variance of the mechanical displacement quadrature numerically. The scheme is robust against dissipation of the optical cavity, and the steady-state squeezing can be effecti…
We realise a simple and robust optomechanical system with a multitude of long-lived ($Q>10^7$) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate ($96~\mathrm{kHz}$) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures ($10\,\mathrm{K}$). Reaching this quantum regime entails, i.~a., quantum measurement backaction exceeding thermal forces, and thus detectable optomechanical quantum correlations. In particular, we observe ponderomotive squeez…
We derive the best possible bounds that can be placed on Yukawa- and chameleon-like modifications to the Newtonian gravitational potential with a cavity optomechanical quantum sensor. By modelling the effects on an oscillating source-sphere on the optomechanical system from first-principles, we derive the fundamental sensitivity with which these modifications can be detected in the absence of environmental noise. In particular, we take into account the large size of the optomechanical probe compared with the range of the fifth forces that we wish to probe and quantify the resulting screening e…
Exploring the fundamental quantum behaviour of optomechanical resonators is of great interest recently but requires the realization of the strong coupling regime. We study the optical photon-phonon coupling of the so-called membrane in the middle (MITM) optomechanical system. Using coupled-mode theory we find that the optomechanical coupling is proportional to the electric susceptibility of the membrane. By considering the doping atoms or spins into the membrane and driving these appropriately we induce a tunable ultra-large refractive index without absorption which enhances the optomechanical…
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