Standard Optomechanical System Research Articles

Optomechanical squeezing with pulse modulation.

Quantum control technology provides an increasingly useful toolbox for quantum information tasks. In this Letter, by introducing a pulsed coupling to a standard optomechanical system, we show that stronger squeezing can be obtained with pulse modulation due to the reduction of the heating coefficient. Also, the general squeezed states, such as the squeezed vacuum, squeezed coherent, and squeezed cat states, can be obtained with their squeezing level exceeding 3 dB. Moreover, our scheme is robust to cavity decay, thermal temperature, and classical noise, which is friendly to experiments. The present work can extend the application of quantum engineering technology in optomechanical systems.

Simultaneous ground-state cooling of multiple degenerate mechanical modes through the cross-Kerr effect.

Simultaneous ground-state cooling of multiple degenerate mechanical modes is a difficult issue in optomechanical systems, owing to the existence of the dark mode effect. Here we propose a universal and scalable method to break the dark mode effect of two degenerate mechanical modes by introducing cross-Kerr (CK) nonlinearity. At most, four stable steady states can be achieved in our scheme in the presence of the CK effect, unlike the bistable behavior of the standard optomechanical system. Under a constant input laser power, the effective detuning and mechanical resonant frequency can be modulated by the CK nonlinearity, resulting in an optimal CK coupling strength for cooling. Similarly, there will be an optimal input laser power for cooling when the CK coupling strength stays fixed. Our scheme can be extended to break the dark mode effect of multiple degenerate mechanical modes by introducing more than one CK effect. To fulfill the requirement of the simultaneous ground-state cooling of N multiple degenerate mechanical modes, N - 1 CK effects with different strengths are needed. Our proposal provides new, to the best of our knowledge. insights into dark mode control and might pave the way to manipulating multiple quantum states in a macroscopic system.

High‐Efficiency Generation of Flat High‐Order Sidebands in a Gently Modulating Optomechanical System

AbstractThe high‐order sideband generation in a gently modulating optomechanical system, which consists of a standard optomechanical system driven by a mildly amplitude modulated field (MAMF) is investigated. It is found that the sideband generation can be effectively optimized by choosing an appropriate component number N of the MAMF, and this scheme can generate more and flatter high‐order sidebands with the same input power compared with the conventional model. The efficiency of the sideband generation is much superior to the traditional scheme. The challenge for high‐efficiently realizing a flat optical frequency comb based on optomechanical systems may be aided by this work.

Nonclassical photon statistics in two-tone continuously driven optomechanics

In cavity optomechanics, single photon detection of Raman scattered photons can be a useful tool for observing nonclassical features of both radiation and motion. While this tool has been employed in experiments with pulsed laser driving of a cavity mode, it has not been readily accessible to experiments with continuous and constant laser driving. To address this, we present a study of a standard optomechanical system where the cavity mode is continuously driven at two different frequencies, and where sideband photons are detected by single photon detectors after frequency filtering the output from the cavity mode around its resonance frequency. We first derive the normalized second order coherence associated with the detected photons, and show that it contains signatures of the quantum nature of the mechanical mode which would be absent with only single-tone driving. To identify model-independent nonclassical features, we derive two inequalities for the sideband photon statistics that should be valid in any classical model of the system. We show that these inequalities are violated in the proposed setup. This is provided that the average phonon occupation number of the mechanical mode is sufficiently small, which in principle can be achieved through sideband cooling intrinsic to the setup. Violation of the first inequality means that there is no well-defined probability distribution of the Glauber-Sudarshan type for the cavity mode. In contrast, a violation of the second inequality means that there is no joint probability distribution for the cavity mode at two times separated by a finite interval, which originates from the noncommutativity of the motional quadratures of the mechanical mode. The proposed setup thus employs a mechanical oscillator in order to generate a steady-state source of nonclassical radiation.

A Green’s function approach to the linear response of a driven dissipative optomechanical system

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 (QLEs) in the Heisenberg picture. The obtained results explain a wealth of phenomena, including the anti-resonance, normal mode splitting and the optomechanically induced transparency (OMIT). Furthermore, the reason why the Stokes or anti-Stokes sidebands are amplified or attenuated in the red or blue detuning regimes is clearly explained which is in exact coincidence, especially in the weak-coupling regime, with the Raman-scattering picture.

Ultraprecision quantum sensing and measurement based on nonlinear hybrid optomechanical systems containing ultracold atoms or atomic Bose–Einstein condensate

In this review, the authors study how a hybrid optomechanical system (OMS), in which a quantum micro- or nano-mechanical oscillator is coupled to the electromagnetic radiation pressure, consisting of an ensemble of ultracold atoms or an atomic Bose–Einstein condensate, can be used as an ultraprecision quantum sensor for measuring very weak signals. As is well-known in any precise quantum measurement, the competition between the shot noise and the backaction noise of measurement executes a limitation on the measurement precision which is the so-called standard quantum limit (SQL). In the case where the intensity of the signal is even lower than the SQL, one needs to perform an ultraprecision quantum sensing to beat the SQL. For this purpose, the authors review three important methods for surpassing the SQL in a hybrid OMS: (i) the backaction evading measurement of a quantum nondemolition variable of the system, (ii) the coherent quantum backaction noise cancelation, and (iii) the so-called parametric sensing, the simultaneous signal amplification, and added noise suppression below the SQL. Furthermore, the authors have shown in this article for the first time how the classical fluctuation of the driving laser phase, the so-called laser phase noise, affects the power spectrum of the output optical field in a standard OMS and induces an additional impression noise which makes the total system noise increase above the SQL. Also, for the first time in this review it has been shown that in the standard OMSs, it is impossible to amplify the signal while suppressing the noise below the SQL simultaneously.

Large and robust mechanical squeezing of optomechanical systems in a highly unresolved sideband regime via Duffing nonlinearity and intracavity squeezed light.

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 (larger than 3dB) in the HURSB regime when the parameters are chosen appropriately. Finally, we show the mechanical squeezing is robust against the thermal fluctuations of the mechanical resonator. The generation of large and robust mechanical squeezing in the HURSB regime is a combined effect of the mechanical and optical nonlinearities.

Enhanced photon blockade via driving a trapped Λ -type atom in a hybrid optomechanical system

A scheme is proposed to enhance the photon blockade effect in a hybrid optomechanical system with a $\mathrm{\ensuremath{\Lambda}}$-type atom driven by the microwave. Through analyzing the conventional and unconventional blockade mechanisms, we find that the enhanced photon blockade effect can be attributed to two aspects: (i) The nonresonant coupled $\mathrm{\ensuremath{\Lambda}}$-type atom reconstructs the anharmonic eigenenergy spectrum and (ii) the microwave driving field promotes the destructive quantum interference for two-photon excitation. By means of the joint enhancement effect, the perfect photon blockade, i.e., the second-order correlation function ${g}^{(2)}(0)\ensuremath{\simeq}0$, can be achieved without the strong single-photon optomechanical coupling as reported in the standard optomechanical system. All the analyses and derivations are further verified via simulating numerically the quantum master equation of the initial Hamiltonian, showing good agreement between analytical and numerical results. Moreover, the optimal parameter relation is given to optimize the photon blockade and maximize the occupancy probability of single-photon excitation at the same time. Our scheme provides a feasible method to engineer a high-quality and efficient single-photon source.

Enhanced optomechanically induced transparency and slow/fast light in a position-dependent mass optomechanics

We impart a theoretical method to enhance optomechanically induced transparency (OMIT) and slow/fast light in a standard optomechanical system composed of a fixed mirror and a moving end mirror. The system is driven by a strong pump field and probed by a weak probe field, respectively. We consider the mass of the mechanical resonator is position-dependent which generates a nonlinear effect in the system. In this paper, we show that the nonlinear parameter α of the position-dependent mass shifts the system from Stokes to the anti-Stokes regime, as a result, OMIT of the transmission field enhances. Further, we show the nonlinear parameter α changes the transparency window from symmetric to asymmetric window profile and looks like Fano resonances. Moreover, in the presence of α, we explain the behavior of mirror field coupling on the width of the transparency window as well. In particular, we present the enhancement of slow/fast light corresponds to the positive/negative dispersion of the phase associated with the transmission probe field.

Tunable optomechanically induced transparency by controlling the dark-mode effect

We study tunable optomechanically induced transparency by controlling the dark-mode effect induced by two mechanical modes coupled to a common cavity field. This is realized by introducing a phase-dependent phonon-exchange interaction, which is used to form a loop-coupled configuration. Combining this phase-dependent coupling with the optomechanical interactions, the dark-mode effect can be controlled by the quantum interference effect. In particular, the dark-mode effect in this two-mechanical-mode optomechanical system can lead to a double-amplified optomechanically induced transparency (OMIT) window and a higher efficiency of the second-order sideband in comparison with the standard optomechanical system. This is because the effective mechanical decay rate related to the linewidth of the OMIT window becomes a twofold increase in the weak-coupling limit. When the dark-mode effect is broken, controllable double transparency windows appear and the second-order sideband, as well as the light delay or advance, is significantly enhanced. For an N-mechanical-mode optomechanical system, we find that in the presence of the dark-mode effect, the amplification multiple of the linewidth of the OMIT window is nearly proportional to the number of mechanical modes, and that the OMIT with a single window becomes the one with N tunable windows by breaking the dark-mode effect. The study will be useful in optical information storage within a large-frequency bandwidth and multichannel optical communication based on optomechanical systems.

Cooling a Mechanical Oscillator in Opto-electro-mechanical System with Frequency Modulations

The opto-electro-mechanical system as a quantum interface between electronic information and optical information plays an important role in quantum information processing. Ground-state cooling of the macroscopic mechanical oscillator is a crucial requirement for this system in order to eliminate the effect of thermal fluctuations on transmission of information. Here, we propose a scheme of ground-state cooling for a mechanical oscillator which is coupled to an optical cavity through radiation pressure force and simultaneously coupled to a superconducting microwave cavity through an effective capacitance. Meanwhile, the periodical frequency modulations are applied to the optical mode, microwave cavity, and mechanical mode, respectively. The cooling efficiency is analyzed and cooling dynamics is simulated numerically by means of covariance matrix. The results show that the Stokes heating processes can be suppressed effectively by means of frequency modulations, and the mechanical oscillator can be cooled to near its ground-state with a higher efficiency than that of a standard optomechanical system due to the double cooling channel. Moreover, a complementary cooling effect is found between these two cooling channels, i.e., a high cooling efficiency can be achieved by cooperation between a good optical cavity and a bad microwave cavity, or vice versa. This cooperative cooling of the double channel breaks the limitation of resolved-sideband regime.

Strong mechanical squeezing in a standard optomechanical system by pump modulation

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 sideband strengths for it. To maximize the mechanical squeezing, we numerically and analytically optimize this ratio in the steady-state regime, respectively. The mechanical squeezing engineered in our scheme also has strong robustness and can survive at a high bath temperature. Compared with previous schemes based on the two-tone pump technique, our scheme involves fewer external control laser source and can be extended to other quantum systems to achieve strong squeezing effect.

Ground-state cooling of mechanical resonator in double optical cavity

<sec>The ground-state cooling of mechanical resonator is one of the fundamental problems in cavity quantum photomechanics. The so-called ground-state cooling is to make the number of steady-state phonons of the mechanical resonator less than one. In this paper, we first propose an electromagnetically-induced-transparency-like cooling mechanism in a double-cavity optomechanical system to cool a mechanical resonator. In the double-optical cavity optomechanical system, the right additional cavity, which is directly coupled to a standard optomechanical system, contains an ultra-cold two-level atomic ensemble. By selecting the optimal parameters to meet the cooling process of the mechanical resonator corresponding to the maximum value of the optical fluctuation spectrum and the heating process of the mechanical resonator corresponding to the minimum value of the optical fluctuation spectrum, the mechanical resonator can be cooled by monitoring the phonon number. We also exert the effects of the atomic additional cavity on the quantum Langevin equations and optical fluctuation spectrum. We find that the atomic double-cavity system may have a better ground-state cooling than the double-cavity in certain parameters.</sec><sec>To date, the researchers have proposed a number of theoretical cooling schemes in order to achieve the ground-state cooling of mechanical resonator. As far as we know, the sideband cooling for just a standard optomechanical system is a most famous scheme and the mechanical resonator is coupled to the optical field via radiation pressure force. By the quantum theory of mechanical resonator’s sideband cooling, the optical fluctuation spectrum determines the transition rate of both cooling and heating process of the mechanical resonator. That’s to say, the optical fluctuation spectrum at a mechanical resonator frequency <i>ω</i><sub>m</sub> is corresponding to the cooling transition, whereas the optical fluctuation spectrum at –<i>ω</i><sub>m</sub> is corresponding to the heating transition. They respectively correspond to anti-Stokes and Stokes effect in physics. Under resolvable sideband conditions, the optical field’s decay rate (the half-width of the single Lorentzian peak of optical fluctuation spectrum) is less than the frequency of the mechanical resonator. So, the ground-state cooling of the mechanical resonator can be obtained by making the maximum and minimum value of the optical fluctuation spectrum respectively correspond to the cooling anti-Stokes process and heating Stokes process.</sec><sec>In this paper, we mainly observe the electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system with an ensemble of two-level atoms. By adjusting the maximum and minimum value of the optical fluctuation spectrum at the position of <i>ω</i> = <i>ω</i><sub>m</sub> and <i>ω</i> = –<i>ω</i><sub>m</sub>, the mechanical resonator could be cooled down approximately to the ground state. Even when there exists an ensemble of two-level atoms in the right additional cavity, the mechanical resonator can be better cooled than just a cavity. These results may be conducive to the ground-state cooling of the mechanical resonator in the future experiment.</sec>

Mechanical squeezing beyond resolved sideband and weak-coupling limits with frequency modulation

It is usually difficult to generate mechanical squeezing in standard optomechanical systems when the decay rate of the cavity or the effective coupling strength of the system is too large. Here we investigate the mechanical squeezing beyond resolved sideband and weak-coupling limits in a standard optomechanical system by using frequency modulation acting on both the cavity field and the mechanical oscillator. It is shown that in the presence of frequency modulation, the beyond 3 dB strong mechanical squeezing can be achieved better than the standard optomechanical system without frequency modulation. Furthermore, the proposed scheme is feasible even in the unstable region of the standard optomechanical system, and a detailed numerical analysis is carried out from the physical essence to illuminate the reason for achieving better mechanical squeezing with frequency modulation. The scheme may open promising perspectives for studying the quantum effect in strong coupling regions without the limitations of system stability and the resolved sideband regime.

Theory of bifurcation amplifiers utilizing the nonlinear dynamical response of an optically damped mechanical oscillator

We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard optomechanical damping to the dynamical attractors known from the theory of optomechanical self-sustained oscillations. We also investigate the effect of thermal and quantum noise and estimate the noise-induced switching rate between the stable states of the system. We then consider applications of this system and primarily focus on how it can be used as bifurcation amplifiers for the detection of small mechanical or optical signals. Finally, we show that in a related but more complicated setup featuring resonant optomechanical interactions, the same effects can be realized with a relaxed requirement on the size of the mechanical oscillations.

Optomechanical damping basis

We present a closed-form analytical solution to the eigenvalue problem of the Liouville operator generating the dissipative dynamics of the standard optomechanical system. The corresponding Lindblad master equation describes the dynamics of a single-mode field inside an optical cavity coupled by radiation pressure to its moving mirror. The optical field and the mirror are in contact with separate environments, which are assumed at zero and finite temperature, respectively. The optomechanical damping basis refers to the exact set of eigenvectors of the generator that, together with the exact eigenvalues, are explicitly derived. Both the weak- and the strong-coupling regime, which includes combined decay mechanisms, are solved in this work.

Effects of the Casimir force on the properties of a hybrid optomechanical system**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574092, 61775062, 61378012, 91121023, and 60978009), the National Basic Research Program of China (Grant No. 2013CB921804), and the Innovation Project of Graduate School of South China Normal University (Grant No. 2017LKXM090).

We investigate the effects of the Casimir force on the output properties of a hybrid optomechanical system. In this system, a nanosphere is fixed on the movable-mirror side of the standard optomechanical system, and the nanosphere interacts with the movable-mirror via the Casimir force, which depends on the mirror–sphere separation. In the presence of the probe and control fields, we analyze the transmission coefficient and the group delay of the field-component with the frequency of the probe field. We also study the transmission intensity of the field-component with the frequency of a newly generated four-wave mixing (FWM) field. By manipulating the Casimir force, we find that a tunable slow light can be realized for the field-component with the frequency of the probe field, and the intensity spectrum of the FWM field can be enhanced and shifted effectively.

Optical-response properties in hybrid optomechanical systems with quadratic coupling

We theoretically investigate the optical-response properties of the four-mode quadratically coupled optomechanical system (OMS), in which two standard OMSs with quadratic coupling are coupled to each other via a common waveguide. In the presence of a strong control field applied to one cavity and a weak probe field applied to the other, we show that by suitably tuning the system parameters, there appears the normal mode splitting, optomechanically induced absorption, and double or triple electromagnetically induced transparency phenomena in the probe absorption spectrum. In particular, the explicit physical explanations for those fantastic phenomena are detailed discussed. Moreover, we also show that our proposal can be exploited to implement the optical switch as well as the slow and fast light effects.

Response of a mechanical oscillator in an optomechanical cavity driven by a finite-bandwidth squeezed vacuum excitation

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 three-peaked and a four-peaked structure, respectively, for the squeezing injection from DPO and NDPO. Besides, some anomalous characteristics of the spectra such as squeezing-induced pimple, hole burning, and dispersive profile are found to be highly sensitive to the squeezing parameters and the temperature of the mirror. We also evaluate the mean-square fluctuations in position and momentum quadratures of the movable mirror and analyze the influence of the squeezing parameters of the input field on the mechanical squeezing. It will be shown that the parameters of driven squeezed vacuum affects the squeezing. We find the optimal mechanical squeezing is achievable via finite bandwidth squeezed vacuum injection which is affected by the intensity of squeezed vacuum. We also show that the phase of incident squeezed vacuum determines whether position or momentum squeezing occurs. Our proposed scheme not only provides a feasible experimental method to detect and characterize squeezed light by optomechanical systems, but also suggests a way for controllable transfer of squeezing from an optical field to a mechanical oscillator.

Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system

We propose to cool a mechanical resonator close to its ground state via an electromagnetically-induced-transparency- (EIT-) like cooling mechanism in a double-cavity optomechanical system, where an additional cavity couples to the original one in the standard optomechanical system. By choosing optimal parameters such that the cooling process of the mechanical resonator corresponds to the maximum value of the optical fluctuation spectrum and the heating process to the minimum one, the mechanical resonator can be cooled with the final mean phonon number less than that at the absence of the additional cavity. And we show the mechanical resonator may be cooled close to its ground state via such an EIT-like cooling mechanism even when the original resolved sideband condition is not fulfilled at the absence of the additional cavity.