In a hybrid quantum system composed of two quantum wells placed inside a cavity with a moving end mirror pumped by bichromatic coherent light, we address the formation of squeezed states of a mechanical resonator. The exciton mode and mechanical resonator interact indirectly via microcavity fields. Under the conditions of the generated coupling, we predict squeezing of the mechanical-mode beyond the resolved side-band regime with existing experimental parameters. Finally, we show that the robustness of this squeezing against thermal fluctuations is important for practical applications of such systems.
We are interested in the emission characteristics of an atom interacting with the polaritonic excitations of a semiconductor or insulator embedded in a one-mode cavity. Since polaritons inside of the cavity exhibit intrinsic squeezing, we discuss how the squeezed polariton ground state modifies the atomic emission and how an indirect evidence of polariton squeezing outside of he cavity may be obtained.
We consider a semiconductor quantum well in a microcavity driven by coherent light and coupled to a squeezed vacuum reservoir. By systematically solving the pertinent quantum Langevin equations in the strong coupling and low excitation regimes, we study the effect of exciton-photon detuning, external coherent light, and the squeezed vacuum reservoir on vacuum Rabi splitting and on quantum statistical properties of the light emitted by the quantum well. We show that the exciton-photon detuning leads to a shift in polariton resonance frequencies and a decrease in fluorescence intensity. We also …
We theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for sub-millimeter-sized cavities the particle motion, initially thermal and well above its ground state, b…
Generation of mechanical squeezing has attracted a lot of interest for its nonclassical properties, applications in quantum information, and high-sensitivity measurement. Here we propose a detuning-switched method that can rapidly generate strong and stationary mechanical squeezing. The pulsed driving can dynamically transpose the optomechanical coupling into a linear optical force and maintain an effective mechanical frequency, which can introduce strong mechanical squeezing in a short time. Moreover, we show the obtained strong mechanical squeezing can be frozen by increasing the pulse inter…
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…
To improve the performance of the traditional tripartite opto-mechanical system, we design a developed opto-mechanical tripartite system in which all subsystems such as an optical cavity, microresonator, and microcavity modes are coupled directly to each other. This system is analyzed quantum mechanically, and its dynamics of motion is studied by the Heisenberg-Langevin equations. Notably, the originality of this work contributes to embedding the spherical capacitor in the optical cavity where the plasmon-plasmon interaction between capacitor plates manipulates the internal electric field. The…
We analyze the entanglement between two matter modes in a hybrid quantum system consists of a microcavity, a quantum well, and a mechanical oscillator. Although the exciton mode in the quantum well and the mechanical oscillator are initially uncoupled, their interaction through the microcavity field results in an indirect exciton-mode--mechanical-mode coupling. We show that this coupling is a Fano-Agarwal-type coupling induced by the decay of the exciton and the mechanical modes caused by the leakage of photons through the microcavity to the environment. Using experimental parameters and for s…
We consider a small partially reflecting vibrating mirror coupled dispersively to a single optical mode of a high finesse cavity. We show this arrangement can be used to implement quantum squeezing of the mechanically oscillating mirror.
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 investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbit…
Being beneficial for the amplitude modulation of the pump laser, we propose a simple yet surprisingly effective mechanical squeezing scheme in a standard optomechanical system. By merely introducing a specific kind of periodic modulation into the single-tone driving field to cool down the mechanical Bogoliubov mode, the far beyond 3-dB strong mechanical squeezing can be engineered without requiring any additional techniques. Specifically, we find that the amount of squeezing is not simply dependent on the order of magnitude of the effective optomechanical coupling but strongly on the ratio of …
We report an efficient mechanism to generate a squeezed state of a mechanical mirror in an optomechanical system. We use especially tuned parametric amplifier (PA) inside the cavity and the parametric photon phonon processes to transfer quantum squeezing from photons to phonons with almost 100\% efficiency. We get 50\% squeezing of the mechanical mirror which is limited by the PA. We present analytical results for the mechanical squeezing thus enabling one to understand the dependence of squeezing on system parameters like gain of PA, cooperativity, temperature. As in cooling experiments the d…
Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3dB of squeezing in the steady state. We consider the effect of applying continuous weak measurement and feedback to this system. If the parametric drive is optimally detuned from resonance, correlations between the quadratures of motion allow unlimited steady-state squeezing. Compared to back-action evasion, we demonstrate that the measurement strength, temperature and eff…
We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atom…
Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we …
We study how strong mechanical squeezing (beyond 3 dB) can be achieved through reservoir engineering in an optomechanical system which is far from the resolved-sideband regime. In our proposed setup, the effect of unwanted counter-rotating terms is suppressed by quantum interference from two auxiliary cavities. In the weak coupling regime we develop an analytical treatment based on the effective master equation approach, which allows us to obtain explicitly the condition of maximum squeezing.
We report the experimental observation of two-mode squeezing in the oscillation quadratures of a thermal micro-oscillator. This effect is obtained by parametric modulation of the optical spring in a cavity opto-mechanical system. In addition to stationary variance measurements, we describe the dynamic behavior in the regime of pulsed parametric excitation, showing enhanced squeezing effect surpassing the stationary 3dB limit. While the present experiment is in the classical regime, our technique can be exploited to produce entangled, macroscopic quantum opto-mechanical modes.
We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an opto-mechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively providing a squeezed heat-bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane/mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions…
We study the physical properties of double-cavity optomechanical system in which the mechanical resonator interacts with one of the coupled cavities and another cavity is used as an auxiliary cavity. The model can be expected to achieve the strong optomechanical coupling strength and overcome the optomechanical cavity decay, simultaneously. Through the coherent auxiliary cavity interferences, the steady-state squeezing of mechanical resonator can be generated in highly unresolved sideband regime. The validity of the scheme is assessed by numerical simulation and theoretical analysis of the ste…
Witnessing quantumness in mesoscopic objects is an important milestone for both quantum technologies and foundational reasons. Cavity optomechanics offers the ideal system to achieve this by combing high precision optical measurements with mechanical oscillators. However, mechanical quantumness can only be established if the behaviour is incompatible with any classical description of an oscillator. After explicitly considering classical and hybrid quantum-classical descriptions of an optomechanical system, we rule out squeezing of the optical field as such a witness by showing it is also predi…
We present a hybrid optomechanical scheme to achieve dynamical squeezing of position quadrature of a mesoscopic mechanical oscillator, that can be externally controlled by classical fields. A membrane-in-the-middle set up is employed, in which an atom in $Λ$ configuration is considered to be trapped on either side of the membrane inside the cavity. We show that a considerable amount of squeezing (beyond the 3 dB limit) can be achieved that is not affected by the decay of the cavity and the spontaneous emission of the atom. Squeezing depends upon the initial preparation of atomic states. Furthe…
Squeezing of quantum fluctuation plays an important role in fundamental quantum physics and has marked influence on ultrasensitive detection. We propose a scheme to generate and enhance the squeezing of mechanical mode by exposing the optomechanical system to a non-Markovian environment. It is shown that the effective parametric resonance term of mechanical mode can be induced due to the interaction with cavity and non-Markovian reservoir, thus resulting in quadrature squeezing of the mechanical resonator. And jointing the two kinds of interactions can enhance the squeezing effect. Comparing w…
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…
A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such as system without invoking the standard rotating wave approximations and the adiabatic approximation. Using this formalism we deduce both the conditional and unconditional state of a mechanical oscillator using the optimal control and feedback that leads to mechanical cooling and mechanical squeezing. We find large discrepancies between the exact solutions and the approximate solutions stressing the import…
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…
In this paper, we investigate theoretically the quantum state transfer in a laser driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources …
We theoretically demonstrate the enhanced and dephasing immune squeezing in the resonance fluorescence of a single quantum dot (QD) confined to a pillar-microcavity and driven by a continuous wave laser. We employ a formalism based on Polaron master equation theory for incorporating the influence of exciton-phonon coupling quite accurately in the dot-cavity system. We show a significant enhancement of squeezing due to cavity coupling of the QD as compared to that of an ideal single two-level system in free space. Particularly, we show a four-fold enhancement in squeezing as compared to that of…
We report on a hitherto unexplored application of squeezed light: for quantum-enhancement of mechanical transduction sensitivity in microcavity optomechanics. Using a toroidal silica microcavity, we experimentally demonstrate measurement of the transduced phase modulation signal with a sensitivity $-0.72(\pm 0.01)$\,dB below the shot noise level. This is achieved for resonant probing in the highly under-coupled regime, by preparing the probe in a weak coherent state with phase squeezed vacuum states at sideband frequencies.
In this paper, we theoretically investigate the displacement and momentum fluctuations spectra of the movable mirror in a standard optomechanical system driven by a finite bandwidth squeezed vacuum light accompanying a coherent laser field. Two cases in which the squeezed vacuum is generated by degenerated and non-degenerate parametric oscillators (DPO and NDPO) are considered. We find that for the case of finite bandwidth squeezed vacuum injection, the two spectra exhibit unique features, which strongly differ from those of broadband squeezing excitation. In particular, the spectra exhibit a …
We investigate the dynamics of an optomechanical system where a cavity with a movable mirror involves a degenerate optical parametric amplifier and is driven by a periodically modulated laser field. Our results show that the cooperation between the parametric driving and periodically modulated cavity driving results in a two-fold squeezing on the movable cavity mirror that acts as a mechanical oscillator. This allows the fluctuation of the mechanical oscillator in one quadrature (momentum or position) to be reduced to a level that cannot be reached by solely applying either of these two drivin…
We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction evading measurement to directly quantify the squeezing, we observe $4.7\pm0.9$ dB of squeezing below the zero-point level, surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of …
We analyze the amplitude and phase noise of limit-cycle oscillations in a mechanical resonator coupled parametrically to an optical cavity driven above its resonant frequency. At a given temperature the limit-cycle oscillations have lower amplitude noise than states of the same average amplitude excited by a pure harmonic drive; for sufficiently low thermal noise a sub-Poissonian resonator state can be produced. We also calculate the linewidth narrowing that occurs in the limit-cycle states, and show that while the minimum is set by direct phase diffusion, diffusion due to the optical spring e…
Processing quantum information on continuous variables requires a highly nonlinear element in order to attain universality. Noise reduction in processing such quantum information involves the use of a nonlinear phase state as a non-Gaussian ancilla. A necessary condition for a nonlinear phase state to implement a nonlinear phase gate is that noise in a selected nonlinear quadrature should decrease below the level of classical states. A reduction of the variance in this nonlinear quadrature below the ground state of the ancilla, a type of nonlinear squeezing, is the resource embedded in these n…
Effects of Quadratic Optomechanical Coupling on Bipartite Entanglements, Mechanical Ground-State Cooling and Squeezing in an Electro-Optomechanical System
We study an optomechanical system consisting of an optical cavity and movable mirror coupled through dispersive linear optomechanical coupling (LOC) and quadratic optomechanical coupling(QOC). We work in the resolved side band limit with a high quality factor mechanical oscillator in a strong coupling regime. We show that the presence of QOC in the conventional optomechanical system (with LOC alone) modifies the mechanical oscillator's frequency and reduces the back-action effects on mechanical oscillator. As a result of this the fluctuations in mechanical oscillator can be suppressed below st…
Backaction-evading (BAE) measurements of a mechanical resonator, by continuously monitoring a single quadrature of motion, can achieve precision below the zero-point uncertainty. When this happens, the measurement leaves the resonator in a quantum squeezed state. The squeezed state so generated is however conditional on the measurement outcomes, while for most applications it is desirable to have a deterministic, i.e., unconditional, squeezed state with the desired properties. In this work we apply feedback control to achieve deterministic manipulation of mechanical squeezing in an optomechani…
Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of $5.9~\text{dB}$ for $20$ spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for $20$ spins with a fidelity of $\sim 0.62$ at cryogenic temperature. The numerical simulations show th…
We consider a hybrid optomechanical system which is composed of the atomic ensemble and a standard optomechanical cavity driven by the periodically modulated external laser field. We investigate the asymptotic behaviors of Heisenberg operator first moments and clearly show the approaching process between the exact numerical results and analytical solutions. Based on the specific modulation forms of external driving and effective optomechanical coupling, we discuss in detail the atom-mirror entanglement enhancement, respectively. Compared with the constant driving regime, the entanglement can b…
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…
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.
Entanglement between optical mode and microwave mode is a critical issue in illumination systems. Traditionally, optomechanical systems are applied to couple the optical mode to microcavity modes. However, due to some restrictions of this system such as sensitivity to the thermal noise at room temperature, a novel optoelectronic system is designed in this study to fix the recent system problems. Unlike recent optomechanical systems, the optical modes are directly coupled to the microwave cavity through the optoelectronic elements with no need mechanical system. The main objective of this work …
In a recent work, Abdel-Aty and Obada [2002 J. Phys. B 35 807-813] analyzed the quantum inversion of cold atoms in a microcavity, the motion of the atoms being described quantum mechanically. Two-level atoms were assumed to interact with a single mode of the cavity, and the off-resonance case was considered (namely the atomic transition frequency is detuned from the single mode cavity frequency). We demonstrate in this paper that this case is incorrectly treated by these authors and we question therefore their conclusions.
