We exploit local quantum estimation theory to investigate the measurement of linear and quadratic coupling strengths in a driven-dissipative optomechanical system. For experimentally realistic values of the model parameters, we find that the linear coupling strength is considerably easier to estimate than the quadratic one. Our analysis also reveals that the majority of information about these parameters is encoded in the reduced state of the mechanical element, and that the best estimation strategy for both coupling parameters is well approximated by a direct measurement of the mechanical position quadrature. Interestingly, we also show that temperature does not always have a detrimental effect on the estimation precision, and that the effects of temperature are more pronounced in the case of the quadratic coupling parameter.
The cooling performance of an optomechanical system comprising both dispersive and dissipative coupling is studied. We present a scheme to cool a mechanical resonator to its ground state in finite time by employing a chirped pulse. When the cavity damping strength increases, the phonon occupation of the resonator will decrease. Moreover, the cooling behaviors of this dispersively and dissipatively coupled system with different incident pulses, different system coupling strengths are explored. Our scheme is feasible to cool the resonator in a wide parameter region.
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 analyze a cavity optomechanical setup, in which position of an oscillator modulates optical loss. We show that in such setup quantum limited position measurements can be performed if the external cavity coupling rate matches the optical loss rate, a condition known as "critical coupling". Additionally, under this condition the setup exhibits a number of potential benefits for practical operation including the complete absence of dynamical backaction, and hence optomechanical instability, and rejection of classical laser noise and thermal fluctuations of cavity frequency from the measurement…
We propose and analyze nonlinear optomechanical protocols that can be implemented by adding a single atom to an optomechanical cavity. In particular, we show how to engineer the environment in order to dissipatively prepare the mechanical oscillator in a superposition of Fock states with fidelity close to one. Furthermore, we discuss how a single atom in a cavity with several mechanical oscillators can be exploited to realize nonlinear many-body physics by stroboscopically driving the mechanical oscillators. We show how to prepare non-classical many-body states by either applying coherent prot…
In this paper, we first try to shed light on the ambiguities that exist in the literature in the generalization of the standard linear response theory (LRT) which has been basically formulated for closed systems to the theory of open quantum systems in the Heisenberg picture. Then, we investigate the linear response of a driven-dissipative optomechanical system (OMS) to a weak time-dependent perturbation using the so-called generalized LRT. It is shown how the Green's function equations of motion of a standard OMS as an open quantum system can be obtained from the quantum Langevin equations (Q…
We theoretically study an optomechanical system, which consists of a two-sided cavity and a mechanical membrane that is placed outside of it. The membrane is positioned close to one of its mirrors, and the cavity is coupled to the external light field through the other mirror. Our study is focused on the regime where the dispersive optomechanical coupling in the system vanishes. Such a regime is found to be possible if the membrane is less reflecting than the adjacent mirror, yielding a potentially very strong dissipative optomechanical coupling. Specifically, if the absolute values of amplitu…
The recent demonstration of cooling of a macroscopic silicon nitride membrane based on dissipative coupling makes dissipatively coupled optomechanical systems as promising candidates for squeezing. We theoretically show that such a system in a cavity on resonance can yield good squeezing which is comparable to that produced by dispersive coupling. We also report the squeezing resulting from the combined effects of dispersive and dissipative couplings and thus the device can be operated in one regime or the other. We derive the maximal frequency and quadrature angles to observe squeezing for gi…
We investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with the perturbative oscillator-qubit coupling. It is shown that such a hybrid system is very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the approaches of master equation and covariance matrix, we discuss the respective squeezing effects in detail and find that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is …
We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser-driven in the resolved blue-sideband regime. To keep our results tractable, we have switched to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows s…
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement …
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.
Cooling of mesoscopic mechanical resonators represents a primary concern in cavity optomechanics. Here in the strong optomechanical coupling regime, we propose to dynamically control the cavity dissipation, which is able to significantly accelerate the cooling process while strongly suppressing the heating noise. Furthermore, the dynamic control is capable of overcoming quantum backaction and reducing the cooling limit by several orders of magnitude. The dynamic dissipation control provides new insights for tailoring the optomechanical interaction and offers the prospect of exploring macroscop…
We study a dissipative, mechanically coupled optomechanical system that accommodates gain and loss. The gain (loss) is engineered by driven a purely dispersive optomechanical cavity with a blue-detuned (red-detuned) electromagnetic field. By taking into account the dissipative coupling, the Exceptional Point (EP), which is the $\mathcal{PT}-$symmetry phase transition, occurs at low threshold driving strength compared to the purely dispersive system. In the linear regime, the $\mathcal{PT}-$symmetry is unbroken and the dissipative coupling induces strong coupling between the mechanical resonato…
We investigate the squeezing for a movable mirror in the dissipative optomechanics in which the oscillating mirror modulates both the resonance frequency and the linewidth of the cavity mode. Via feeding a much weaker broadband squeezed vacuum light accompanying the coherent driving laser field into the cavity, the master equation for the cavity-mirror system is derived by following the general reservoir theory based on the density operator in which the reservoir variables are adiabatically eliminated by using the reduced density operator for the system in the interaction picture. When the mir…
We study theoretically the squeezing spectrum and second-order correlation function of the output light for an optomechanical system in which a mechanical oscillator modulates the cavity linewidth (dissipative coupling). We find strong squeezing coinciding with the normal-mode frequencies of the linearized system. In contrast to dispersive coupling, squeezing is possible in the resolved-sideband limit simultaneously with sideband cooling. The second-order correlation function shows damped oscillations, whose properties are given by the mechanical-like, the optical-like normal mode, or both, an…
The interaction between dielectric particles and a laser-driven optical cavity gives rise to both conservative and dissipative dynamics, which can be used to levitate, trap and cool nanoparticles. We analytically and numerically study a two-mode setup in which the optical potentials along the cavity axis cancel, so that the resulting dynamics is almost purely dissipative. For appropriate detunings of the laser-drives, this dissipative optomechanical dynamics can be used to sort particles according to their size, to rectify their velocities and to enhance transverse cooling.
We present a theoretical study of optomechanical systems in which the mechanical resonator modulates both the resonant frequency (dispersive coupling) and the decay rates (dissipative coupling) of the optical cavity. We extend the generic dispersive framework to a more general case in which the dissipative coupling is split between its external and intrinsic contribution. We report a complete analysis of the influence of each kind of optical losses (intrinsic and external) on the three coupling mechanisms and highlight the interest of each external decay rate regime. The basic tools to experim…
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 …
Dissipative and dispersive optomechanical couplings are experimentally observed in a photonic crystal split-beam nanocavity optimized for detecting nanoscale sources of torque. Dissipative coupling of up to approximately $500$ MHz/nm and dispersive coupling of $2$ GHz/nm enable measurements of sub-pg torsional and cantilever-like mechanical resonances with a thermally-limited torque detection sensitivity of 1.2$\times 10^{-20} \text{N} \, \text{m}/\sqrt{\text{Hz}}$ in ambient conditions and 1.3$\times 10^{-21} \text{N} \, \text{m}/\sqrt{\text{Hz}}$ in low vacuum. Interference between optomecha…
We theoretically investigate two quantum modes interacting via local couplings to a dissipative field. Our model considers two mechanical modes with distinct frequencies coupled optomechanically to the same cavity mode. The dissipative cavity field mediates the interaction between the mechanical modes but also leads to decoherence of the mechanical oscillators. Depending on the ratio between effective interaction strength and dissipation rate, which can be chosen via the pump detuning, the interaction assumes a quantum mechanical or classical character. For any cavity decay, there is a regime …
We study the optomechanical coupling of a single-layer graphene with a high-Q Fabry-Perot microcavity in the membrane-in-the-middle configuration. In ordinary dissipative coupling systems, mechanical oscillators modulate the loss associated with the input coupling of the cavity mode; while in our system, the graphene oscillator couples dissipatively with the cavity mode through modulating its absorption loss. By analyzing the effects of the interband transition of a graphene suspended near the node of the cavity field, we obtain strong and tunable dissipative coupling without excessively reduc…
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 pos…
In this paper we study cavity optomechanical systems in which the position of a mechanical oscillator modulates both the resonance frequency (dispersive coupling) and the linewidth (dissipative coupling) of a cavity mode. Using a quantum noise approach we calculate the optical damping and the optically-induced frequency shift. We find that dissipatively coupled systems feature two parameter regions providing amplification and two parameter regions providing cooling. To investigate the strong-coupling regime, we solve the linearized equations of motion exactly and calculate the mechanical and o…
Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular …
Combination of dissipative and dispersive coupling in the cavity optomechanical systems
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）；Quantum Technology Centre, M.V. Lomonosov Moscow State University（莫斯科国立大学量子技术中心）
Optomechanical system with tunable dissipative and dispersive couplings
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University（山西大学光电研究所量子光学与量子光学器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Model-level synthetic-flux control of hyperchaos order and matched-resource sensing in dissipative optomechanics
University of Yaoundé I（雅温得第一大学）；University of Ngaoundéré（恩加安德雷大学）；National Advanced School of Mines and Petroleum Industries, University of Maroua（马里乌阿大学国家高等矿业和石油工业学院）
The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nano-mechanical devices either in a transient or a probabilistic fashion have been put forward. Here we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion…
Motivated by the increasing interest in the properties of multimode optomechanical devices, here we study a system in which a driven mode of a large-area optical cavity is despersively coupled to a deformable mechanical element. Two different models naturally appear in such scenario, for which we predict the formation of periodic patterns, localized structures (cavity solitons), and domain walls, among other complex nonlinear phenomena. Further, we propose a realistic design based on intracavity membranes where our models can be studied experimentally. Apart from its relevance to the field of …
We calculate the optomechanical coupling strength for a multi-membrane in a cavity system. The optimal configuration for an array of $N$ membranes placed near the center of a cavity is identified. This results in a coupling strength much greater than previously proposed multi-membrane configurations. We find that the coupling strength scales exponentially with the number of membranes until saturating due to complete localization of the field within the array. Furthermore we explore two sources of loss, those due to light absorption within the membrane(s) and leakage through the cavity's end-mi…
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…
Optomechanical devices have been cooled to ground-state and genuine quantum features, as well as long-predicted nonlinear phenomena, have been observed. When packing close enough more than one optomechanical unit in the same substrate the question arises as to whether collective or independent dissipation channels are the correct description of the system. Here we explore the effects arising when introducing dissipative couplings between mechanical degrees of freedom. We investigate synchronization, entanglement and cooling, finding that collective dissipation can drive synchronization even in…
We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cramér--Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely result in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times in the order of one time pe…
This thesis focuses on the mathematical description and application of nonlinear cavity optomechanical systems. The first part is concerned with solving the dynamics of the standard nonlinear optomechanical Hamiltonian with an additional time-dependent mechanical displacement and single-mode squeezing term. The solution is based on identifying a Lie algebra that generates the time-evolution of the system, which reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. The second part applies the solutions of the extended optomechanical Hamilt…
Micro- and nanoscale optical or microwave cavities are used in a wide range of classical applications and quantum science experiments, ranging from precision measurements, laser technologies to quantum control of mechanical motion. The dissipative photon loss via absorption, present to some extent in any optical cavity, is known to introduce thermo-optical effects and thereby impose fundamental limits on precision measurements. Here, we theoretically and experimentally reveal that such dissipative photon absorption can result in quantum feedback via in-loop field detection of the absorbed opti…
We consider an optical and mechanical mode interacting through both linear and quadratic dispersive couplings in a general cavity-optomechanical set-up. The parity and strength of an intrinsic quadratic optomechanical coupling (QOC) provides an opportunity to control the optomechanical (OM) interaction. We quantify this interaction by studying normal-mode splitting (NMS) as a function of the QOC's strength. The proposed scheme exhibits NMS features equivalent to a hybrid-OM system containing either an optical parametric amplifier (OPA) or a Kerr medium. Such a system in reality could offer an …
We introduce a passively-aligned, flexure-tuned cavity optomechanical system in which a membrane is positioned microns from one end mirror of a Fabry-Perot optical cavity. By displacing the membrane through gentle flexure of its silicon supporting frame (i.e., to ~80 m radius of curvature (ROC)), we gain access to the full range of available optomechanical couplings, finding also that the optical spectrum exhibits none of the abrupt discontinuities normally found in "membrane-in-the-middle" (MIM) systems. More aggressive flexure (3 m ROC) enables >15 microns membrane travel, milliradian tilt t…
Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators. In many applications, linearised form of the interaction is used, which allows for the system dynamics to be fully described using a Lyapunov equation for the covariance matrix of the Wigner function. This approach, however, is problematic in situations where the Hamiltonian becomes time dependent as is the case for systems driven at multiple frequencies simultaneously. This scenario is highly relevant as …
We propose a scheme to suppress the laser phase noise without increasing the optomechanical single-photon coupling strength. In the scheme, the parametric amplification terms, created by Kerr and Duffing nonlinearities, can restrain laser phase noise and strengthen the effective optomechanical coupling, respectively. Interestingly, decreasing laser phase noise leads to increasing thermal noise, which is inhibited by bringing in a broadband-squeezed vacuum environment. To reflect the superiority of the scheme, we simulate quantum memory and stationary optomechanical entanglement as examples, an…
We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semi-transparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in t…
We consider how a single photon can probe the quantum nature of a moving mirror in the context of quantum optomechanics. In particular, we demonstrate how the single-photon spectrum reveals resonances that depend on how many phonons are created as well as on the strength of the mirror-photon interaction. A dressed-state picture is used to explain positions and relative strengths of those resonances. The time-dependent spectrum shows how the resonances are built up over time by the photon interacting with the moving mirror.
We present a quantum theory for a fully coupled hybrid optomechanical system where all mutual couplings between a two-level atom, a confined photon mode and a mechanical oscillator mode are considered. In such a configuration, new quantum interference effects and correlations arise due to the interplay and competition between the different physical interactions. We present an analytical diagonalization of the related fully coupled Hamiltonian, showing the nature and energy spectra of the tripartite dressed excitations. We determine the driven-dissipative dynamics of such hybrid systems and stu…
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 …
The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: from sideband cooling and backaction-evading measurements to pondermotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case, Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiqitious in optomechanical systems. Specifically,…
We study the driven-dissipative dynamics of photons interacting with an array of micromechanical membranes in an optical cavity. Periodic membrane driving and phonon creation result in an effective photon-number conserving non-unitary dynamics, which features a steady state with long-range photonic coherence. If the leakage of photons out of the cavity is counteracted by incoherent driving of the photonic modes, we show that the system undergoes a dynamical phase transition to the state with long-range coherence. A minimal system, composed of two micromechanical membranes in a cavity, is studi…
