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 Hamiltonian to the study of non-Gaussianity. We compute the non-Gaussian character of an optomechanical state as a function of the parameters in the Hamiltonian, and investigate the interplay between the non-Gaussianity, the strength of the nonlinear coupling and the strength of the single-mode mechanical squeezing term. We find that the strength and form of the nonlinear coupling strongly impacts the non-Gaussianity, and that its relationship with the squeezing term is highly complex. The third part concerns the use of nonlinear optomechanical systems as quantum sensors. We derive a general expression of the quantum Fisher information given the extended optomechanical Hamiltonian and demonstrate its applicability through three concrete examples: estimating the strength of a nonlinear light--matter coupling, the strength of a time-modulated mechanical displacement, and the strength of a single-mode mechanical squeezing parameter, all of which are modulated at resonance. In the last Chapter of the thesis, we consider the estimation of a constant gravitational acceleration with an optomechanical system. Our results suggest that optomechanical systems could, in principle, be used as powerful quantum sensors.
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intra-cavity squeezing, and optomechani…
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…
Entangled continuous variable (CV) Gaussian states with different wavelengths plays a central role in recent CV-based approaches to quantum network, quantum information processing and quantum metrology. Typically, experiments demonstrating CV entanglement exploit the optical parametric frequency down conversion. Due to the probabilistic nature of photon pair generation, the entanglement involving the post-selection of photonic qubits is limited to at most three colors. Here We theoretically present a scheme for the deterministic generation of entanglement among bright multicolor CV Gaussian st…
Optomechanically controlled response amplification for enhanced quantum sensing
Joint Laboratory of Optics of Palacký University and Institute of Physics ASCR, Faculty of Science, Palacký University（帕拉茨基大学与捷克科学院物理研究所联合光学实验室，帕拉茨基大学理学院）
Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Herewe investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows t…
Open-system dynamics play a key role in the experimental and theoretical study of cavity optomechanical systems. In many cases, the quantum Langevin equations have enabled excellent models for optical decoherence, yet a master-equation approach to the fully nonlinear optomechanical Hamiltonian has thus far proven more elusive. To address this outstanding question and broaden the mathematical tool set available, we derive a solution to the Lindblad master equation that models optical decoherence for a system evolving with the nonlinear optomechanical Hamiltonian. The method combines a Lie-algeb…
We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually through an optical fiber or a phonon tunneling. The cavities are filled with Kerr-type nonlinear medium. It is found that, no matter which the coupling and periodically modulation we choose, both of the quantum synchronization of nonlinear optomechanical system are more appealing than the linear optomechanical system. It is easier to observe greatly enhanced qua…
Optomechanical thermometry is a precise and reference-free method to measure absolute temperature. While pumping high optical power is needed to overcome noise and reduce the integration time, there is actually an upper limit to the useful optical power regardless of all other nonideal effects. Side-band inequivalence is a nonlinear effect obtained by higher-order operator algebra in quantum optomechanics and equivalent experiments, which causes asymmetric frequency shifts in side-bands and also an additional difference in their population. This chapter discusses previously unnoticed nonlinear…
This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical force sensing. When optical loss is present, these bounds are found to obey shot-noise scalings for arbitrary quantum states of light under certain realistic conditions, thus ruling out the possibility of asymptotic Heisenberg error scalings with respect to the average photon flux under those conditions. The proposed bounds are expected to be approachable using…
We propose a scheme to generate strong and robust mechanical squeezing in an optomechanical system in the highly unresolved sideband (HURSB) regime with the help of the Duffing nonlinearity and intracavity squeezed light. The system is formed by a standard optomechanical system with the Duffing nonlinearity (mechanical nonlinearity) and a second-order nonlinear medium (optical nonlinearity). In the resolved sideband regime, the second-order nonlinear medium may play a destructive role in the generation of mechanical squeezing. However, it can significantly increase the mechanical squeezing (la…
We investigate the resonant enhancement of nonlinear interactions in a three-mode cavity optomechanical system with two mechanical oscillators. By using the Keldysh Green's function technique we find that nonlinear effects on the cavity density of states can be greatly enhanced by the resonant scattering of two phononic polaritons, due to their small effective dissipation. In the large detuning limit and taking into account an upper bound on the achievable dressed coupling, the optimal point for probing the nonlinear effect is obtained, showing that such three-mode system can exhibit prominent…
Multiphonon state plays an important role in quantum information processing and quantum metrology. Here we propose a scheme to realize dynamical emission of phonon pairs based on the technique of stimulated Raman adiabatic passage in a single cavity optomechanical system, where the optical cavity is driven by two Gaussian pulse lasers. By exploring quantum trajectories of the state populations and the average phonon number, we find that the dynamical phonon-pair emission can be realized under the appropriate parameter conditions and is tunable by controlling the time interval between the conse…
Few-photon optomechanical effects are not only important physical evidences for understanding the radiation-pressure interaction between photons and mechanical oscillation, but also have wide potential applications in modern quantum technology. Here we study the few-photon optomechanical effects including photon blockade and generation of the Schrödinger cat states under the assistance of a cross-Kerr interaction, which is an inherent interaction accompanied the optomechanical coupling in a generalized optomechanical system. By exactly diagonalizing the generalized optomechanical Hamiltonian a…
It is well-known that some nonlinear phenomena such as strong photon blockade are hard to be observed in optomechanical system with current experimental technology. Here, we present a coherent feedback control strategy in which a linear cavity is coherently controlled by an optomechanical controller in a feedback manner. The coherent feedback loop transfers and enhances quantum nonlinearity from the controller to the controlled cavity, which makes it possible to observe strong nonlinear effects in either linear cavity or optomechanical cavity. More interestingly, we find that the strong photon…
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.
Using the Born-Oppenheimer approximation, we derive an effective Hamiltonian for an optomechanical system that leads to a nonlinear Kerr effect in the system's vacuum. The oscillating mirror at one edge of the optomechanical system induces a squeezing effect in the intensity spectrum of the cavity field. A near-resonant laser field is applied at the other edge to drive the cavity field, in order to enhance the Kerr effect. We also propose a quantum-nondemolition-measurement setup to monitor a system with two cavities separated by a common oscillating mirror, based on our effective Hamiltonian …
The interaction of a single-mode field with both a weak Kerr medium and a parametric nonlinearity in an intrinsically nonlinear optomechanical system is studied. The nonlinearities due to the optomechanical coupling and Kerr-down conversion lead to the bistability and tristability in the mean intracavity photon number. Also, our work demonstrates that the lower bound of the resolved sideband regime and the minimum attainable phonon number can be less than that of a bare cavity by controlling the parametric nonlinearity and the phase of the driving field. Moreover, we find that in the system un…
We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, …
We study theoretically nonlinear effects arising from the presence of a Kerr-down conversion nonlinear crystal inside an optomechanical cavity. For this system we investigate the influences of the two nonlinearities, i.e., the Kerr nonlinearity and the parametric gain, on the dynamics of the oscillating mirror, the intensity and the squeezing spectra of the transmitted field, and the steady-state mirror-field entanglement. We show that in comparison with a bare optomechanical cavity, the combination of the cavity energy shift due to the Kerr nonlinearity and increase in the intracavity photon …
We propose a scheme to significantly increase quadratic optomechanical couplings of optomechanical systems with the help of a nonlinear medium and two driving lasers. The nonlinear medium is driven by one laser and the optical cavity mode is driven by a strong laser. We derive an effective Hamiltonian using squeezing transformation and rotating wave approximation. The effective quadratic optomechanical coupling strength can be larger than the decay rate of the cavity mode by adjusting the two optical driving fields. The thermal noise of squeezed cavity mode can be suppressed totally with the h…
Cavity optomechanical system involving an optical parametric amplifier (OPA) can exhibit rich classical and quantum dynamical behaviors. By simply modulating the frequency of the laser pumping the OPA, we find two interesting parameter regimes, with one of them enabling to study quantum-classical correspondence in system dynamics, while there exist no classical counterparts of the quantum features for the other. For the former regime, as the parametric gain of OPA increases to a critical value, the classical dynamics of the optical or mechanical modes can experience a transition from the regul…
Quantum control of phonons has being become a focus of attention for developing quantum technologies. Here, we propose a proposal to realize phonon blockade in a quadratically coupled optomechanical system, where a strong nonlinear interaction between photons and phonons can be induced by an external field coherently driving the cavity, and the effective coupling strength is tunable by adjusting the amplitude of the driving field. This optically induced nonlinearity is different from standard methods for realization of phonon blockade, where the nonlinearity is achieved by coupling the mechani…
The coupling of laser light to a mechanical oscillator via radiation pressure leads to the emergence of quantum mechanical correlations between the amplitude and phase quadrature of the laser beam. These correlations form a generic non-classical resource which can be employed for quantum-enhanced force metrology, and give rise to ponderomotive squeezing in the limit of strong correlations. To date, this resource has only been observed in a handful of cryogenic cavity optomechanical experiments. Here, we demonstrate the ability to efficiently resolve optomechanical quantum correlations imprinte…
We examine whether metrological resolution beyond coherent states is a nonclassical effect. We show that this is true for linear detection schemes but false for nonlinear schemes, and propose a very simple experimental setup to test it. We find a nonclassicality criterion derived from quantum Fisher information.
Optomechanical systems, due to its inherent nonlinear optomechanical coupling, owns rich nonlinear dynamics of different types of motion. The interesting question is that whether there exist some common quantum features to infer the nonlinear dynamical transitions from one type to another. In this paper, we have studied the quantum signatures of transitions from stable fixed points to limit cycles in an optomechanical phonon laser system. Our calculations show that the entanglement of stable fixed points in the long run does not change with time, however, it will oscillate periodically with ti…
We consider an optomechanical cavity made by two moving mirrors which contains a Kerr-down conversion nonlinear crystal. We show that the coherent oscillations of the two mechanical oscil- lators can lead to splitting in the electromagnetically induced transparency (EIT) resonance, and appearance of an absorption peak within the transparency window. In this configuration the coher- ent induced splitting of EIT is similar to driving a hyperfine transition in an atomic Lambda-type three-level system by a radio-frequency or microwave field. Also, we show that the presence of non- linearity provid…
We propose a novel scheme for realizing single-photon blockade in a weakly driven hybrid cavity optomechanical system consisting of a nonlinear photonic crystal. Sub-Poissonian statistics is realized even when the single-photon optomechanical coupling strength is smaller than the decay rate of the optical mode. The scheme relaxes the requirement of strong coupling for photon blockade in optomechanical systems. It is shown that photon blockade could be generated at the telecommunication wavelength.
We examine quantum detection via a Michelson interferometer embedded in a gas with Kerr nonlinearity. This nonlinear interferometer is illuminated by pulses of classical light. This strategy combines the robustness against practical imperfections of classical light with the improvement provided by nonlinear processes. Regarding ultimate quantum limits, we stress that, as a difference with linear schemes, the nonlinearity introduces pulse duration as a new variable into play along with the energy resources.
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new fi…
We consider how nonlinear interaction effects can manifest themselves and even be enhanced in a strongly driven optomechanical system. Using a Keldysh Green's function approach, we calculate modifications to the cavity density of states due to both linear and nonlinear optomechanical interactions, showing that strong modifications can arise even for a weak nonlinear interaction. We show how this quantity can be directly probed in an optomechanically-induced transparency type experiment. We also show how the enhanced interaction can lead to nonclassical behaviour, as evidenced by the behaviour …
With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a four-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between unperturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional two-mode optomech…
Optomechanical systems have been shown both theoretically and experimentally to exhibit an analogon to atomic electromagnetically induced transparency, with sharp transmission features that are controlled by a second laser beam. Here we investigate these effects in the regime where the fundamental nonlinear nature of the optomechanical interaction becomes important. We demonstrate that pulsed transistor-like switching of transmission still works even in this regime. We also show that optomechanically induced transparency at the second mechanical sideband could be a sensitive tool to see first …
Recently, the photon absorption attracts lots of interest and plays an important role in a variety of applications. Here, we propose a valuable scheme to investigate the perfect photon absorption in a hybrid atom-optomechanical system both under and beyond the low-excitation limit. The perfect photon absorption persists both in the linear atomic excitation regime and nonlinear atomic excitation regime, below the threshold of the optical bistability/multistability, respectively. We also show that the optical nonlinearity raised by the nonlinear optomechanical interaction and nonlinear atomic ex…
Quantum entanglement plays a key role in both understanding the fundamental aspects of quantum physics and realizing various quantum devices for practical applications. Here we propose how to achieve coherent switch of optomechanical entanglement in an optical whispering-gallery-mode resonator, by tuning the phase difference of the driving lasers. We find that the optomechanical entanglement and the associated two-mode quantum squeezing can be well tuned in a highly asymmetric way, providing an efficient way to protect and enhance quantum entanglement against optical backscattering, in compari…
We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantum interference device (SQUID) that terminates one of the resonators. This produces a nonlinear interaction on the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths t…
We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time…
The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) syst…
Quantum networks enable a broad range of practical and fundamental applications spanning distributed quantum computing to sensing and metrology. A cornerstone of such networks is an interface between telecom photons and quantum memories. Here we demonstrate a novel approach based on cavity optomechanics that utilizes the susceptibility of spin qubits to strain. We use it to control electron spins of nitrogen-vacancy centers in diamond with photons in the 1550 nm telecommunications wavelength band. This method does not involve qubit optical transitions and is insensitive to spectral diffusion. …
We investigate a hybrid electro-optomechanical system that allows us to obtain controllable strong Kerr nonlinearities in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are predicted in the weak-coupling regime, which is feasible for most curre…
Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven…
Regular and chaotic dynamics of nonlinear optomechanical systems controlled by modulated light
Scientific-Practical Material Research Centre, Belarus National Academy of Sciences（白俄罗斯科学院科学实用材料研究中心）；Institute of Molecular Physics, Polish Academy of Sciences（波兰科学院分子物理研究所）
We investigate the effects of atomic collisions as well as optomechanical mirror-field coupling on the optical bistability in a hybrid system consisting of a Bose-Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mi…
Nonlinear optomechanical coupling is the basis for many potential future experiments in quantum optomechanics (e.g., quantum non-demolition measurements, preparation of non-classical states), which to date have been difficult to realize due to small non-linearity in typical optomechanical devices. Here we introduce an optomechanical system combining strong nonlinear optomechanical coupling, low mass and large optical mode spacing. This nanoscale "paddle nanocavity" supports mechanical resonances with hundreds of fg mass which couple nonlinearly to optical modes with a quadratic optomechanical …
We propose a scheme for enhancing the optomechanical coupling between microwave and mechanical resonators by up to seven orders of magnitude to the ultrastrong coupling limit in a circuit optomechanical setting. The tripartite system considered here consists of a Josephson junction Cooper-pair box that mediates the coupling between the microwave cavity and the mechanical resonator. The optomechanical coupling can be modified by tuning the gate charge and the magnetic flux bias of the Cooper-pair box which in turn affect the Josephson capacitance of the Cooper-pair box. We additionally show tha…
Intracavity squeezing is a promising technique that may improve the sensitivity of gravitational wave detectors and cool optomechanical oscillators to the ground state. However, the photothermal effect may modify the occurrence of optomechanical coupling due to the presence of a nonlinear optical crystal in an optical cavity. We propose a novel method to predict the influence of the photothermal effect by measuring the susceptibility of the optomechanical oscillator and identifying the net optical spring constant and photothermal absorption rate. Using this method, we succeeded in precisely es…
We consider a cavity optomechanical cooling configuration consisting of a mechanical resonator (denoted as resonator b) and an electromagnetic resonator (denoted as resonator a), which are coupled in such a way that the effective resonance frequency of resonator a depends linearly on the displacement of resonator b. We study whether back-reaction effects in such a configuration can be efficiently employed for suppression of decoherence. To that end, we consider the case where the mechanical resonator is prepared in a superposition of two coherent states and evaluate the rate of decoherence. We…
A significant challenge in the development of chip-scale cavity-optomechanical devices as testbeds for quantum experiments and classical metrology lies in the coupling of light from nanoscale optical mode volumes to conventional optical components such as lenses and fibers. In this work we demonstrate a high-efficiency, single-sided fiber-optic coupling platform for optomechanical cavities. By utilizing an adiabatic waveguide taper to transform a single optical mode between a photonic crystal zipper cavity and a permanently mounted fiber, we achieve a collection efficiency for intracavity phot…
We consider a nanomechanical analogue of a nonlinear interferometer, consisting of two parallel, flexural nanomechanical resonators, each with an intrinsic Duffing nonlinearity and with a switchable beamsplitter-like coupling between them. We calculate the precision with which the strength of the nonlinearity can be estimated and show that it scales as $1/n^{3/2}$, where $n$ is the mean phonon number of the initial state. This result holds even in the presence of dissipation, but assumes the ability to make measurements of the quadrature components of the nanoresonators.
