Unresolved Sideband Regime Research Articles

Simultaneous cooling of high-frequency difference resonators through voltage modulation and intracavity-squeezed light

We propose a scheme to achieve simultaneous cooling of the mechanical and radio-frequency resonators in a hybrid optoelectromechanical system. By introducing the voltage modulation switch and intracavity-squeezed light, the high-frequency difference resonators can be successfully cooled to their quantum ground states by eliminating cavity mode dissipation through precise phase and amplitude matching of the squeezed pump field and the cooling optical field. More significantly, ground-state cooling can be achieved even in the highly unresolved sideband regime, and the quantum backaction heating can be effectively suppressed, leading to a significant improvement in cooling performance. Our work provides an alternative approach for quantum coherent manipulation of multiple mechanical systems with different resonant frequencies.

Optical and mechanical squeezing with coherent feedback control beyond the resolved-sideband regime

The noise reduction in squeezed states makes them a powerful nonclassical resource in quantum technologies, especially in quantum sensing, and an essential step for the ongoing development of non-Gaussian states. In particular, optical and mechanical squeezing can both be generated when light interacts with a mechanical oscillator. Here we use a linear optical system as a controller and use coherent optical feedback to enhance squeezing in the unresolved-sideband regime of optomechanics. Feedback control is generally profitable for cooling, manipulating, and stabilizing the dynamics of mechanical oscillators; coherent feedback is then notable for its ability to steer a quantum system toward the highest squeezing without measurement, avoiding backaction. We thoroughly maximize optical and conditional mechanical squeezing feasible with state-of-the-art experimental setups and derive the optimal conditions under which quantum squeezing is generated in the system. Published by the American Physical Society 2024

Coherent feedback ground state cooling of the mechanical resonator in quadratic optomechanical system assisted by an atomic ensemble

We propose a scheme for cooling a mechanical resonator to its ground state in a quadratic optomechanical system, assisted by an atomic ensemble in the unresolved sideband regime. The system features an auxiliary cavity directly coupled to an optical cavity, with a portion of the optical cavity’s output field being fed back through an asymmetric beam splitter. Utilizing quantum Langevin and master equations, we derive the optical fluctuation spectrum, the cooling rate, and the mean phonon number of the mechanical resonator. Our results demonstrate that the feedback mechanism substantially enhances the cooling rate. Furthermore, under optimal cooling conditions, the mechanical resonator achieves ground state cooling even with weaker optomechanical coupling strengths and higher auxiliary cavity dissipation rates, thereby mitigating the experimental constraints associated with these parameters. Additionally, we provide the feasible ranges for optomechanical coupling strength and atomic decay rates. Our findings suggest promising avenues for quantum manipulation in nonlinear systems and its applications in macroscopic optical devices.

Intrinsic Kerr amplification for microwave electromechanics

Electromechanical transduction gain of 21 dB is realized in a micro-cantilever resonant force sensor operated in the unresolved-sideband regime. Strain-dependent kinetic inductance weakly couples cantilever motion to a superconducting nonlinear resonant circuit. A single pump generates motional sidebands and parametrically amplifies them via four-wave mixing. We study the gain and added noise, and we analyze potential benefits of this integrated amplification process in the context force sensitivity.

Dissipative and dispersive cavity optomechanics with a frequency-dependent mirror

An optomechanical microcavity can considerably enhance the interaction between light and mechanical motion by confining light to a subwavelength volume. However, this comes at the cost of an increased optical loss rate. Therefore, microcavity-based optomechanical systems are placed in the unresolved-sideband regime, preventing sideband-based ground-state cooling. A pathway to reduce optical loss in such systems is to engineer the cavity mirrors, i.e., the optical modes that interact with the mechanical resonator. In our work, we analyze such an optomechanical system, whereby one of the mirrors is strongly frequency dependent, i.e., a suspended Fano mirror. This optomechanical system consists of two optical modes that couple to the motion of the suspended Fano mirror. We formulate a quantum-coupled-mode description that includes both the standard dispersive optomechanical coupling as well as dissipative coupling. We solve the Langevin equations of the system dynamics in the linear regime showing that ground-state cooling from room temperature can be achieved even if the cavity is not in the resolved-sideband regime, but achieves effective sideband resolution through strong-optical-mode coupling. Importantly, we find that the cavity output spectrum needs to be properly analyzed with respect to the effective laser detuning to infer the phonon occupation of the mechanical resonator. Our work also predicts how to reach the regime of nonlinear quantum optomechanics in a Fano-based microcavity by engineering the properties of the Fano mirror. Published by the American Physical Society 2024

Simultaneous cooling of degenerate mechanical modes in unresolved sideband regime via optical and mechanical nonlinearities

Simultaneous cooling of degenerate mechanical modes in unresolved sideband regime via optical and mechanical nonlinearities

Optomechanically induced transparency/absorption in a 3D microwave cavity architecture at ambient temperature

Leveraging advancements in cavity optomechanics, we explore Optomechanically Induced Transparency/Absorption (OMIT/OMIA) in the microwave domain at ambient temperature. Contrary to previous studies employing cryogenic temperatures, this work exploits a 3D microwave cavity architecture to observe these effects at ambient temperature, broadening the scope of possible applications. The work successfully enhances the optomechanical coupling strength, enabling observable and robust OMIT/OMIA effects, and demonstrating up to 25 dB in signal amplification and 20 dB in attenuation. Operating in the unresolved sideband regime enables tunability across a wider frequency range, enhancing the system’s applicability in signal processing and sensing. The findings herein highlight the potential of optomechanical systems, presenting a simplified, cost-effective, and more feasible approach for applications at ambient temperature.

Macroscopic quantum entanglement between an optomechanical cavity and a continuous field in presence of non-Markovian noise

Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises. Published by the American Physical Society 2024

Mechanical resonator cooling to the ground-state by coherent feedback in a double cavity setup including an atomic ensemble

This study concerns the cooling of a mechanical resonator to the ground-state in the unresolved sideband regime theoretically. To this aim, the optical modes of an optomechanical cavity are coupled with an atomic ensemble and an auxiliary cavity. Then, a coherent feedback loop is applied via a controllable beam splitter, which reflects a fraction of the output field to the input mirror of the optomechanical cavity. Considering the proposed feedback scheme, the optical response of the cavity is analyzed for weak optomechanical coupling to obtain the rate equations. Utilizing the electromagnetically-induced-transparency-like shape of the fluctuation spectrum of the optical force, optimal cooling conditions are calculated to place the peaks and dip of the spectrum at the desired frequencies to maximize the difference between cooling and heating rates. It is shown that the coherent feedback loop enhances the cooling effect while the heating rate is not affected. Moreover, by utilizing two coupled auxiliary systems, the effect of heating transitions is better suppressed compared to the case with one auxiliary system. As a result, not only lower limits for cooling but also larger values of net cooling rate are achieved. The results show that the proposed feedback cooling scheme significantly improves the cooling capability of the hybrid system, and the mechanical resonator can be cooled near the quantum limit. Furthermore, it is shown that the proposed method performs well in a wide range of system parameters.

Generation and enhancement of the sum sideband under double radiation pressure.

A theoretical scheme to enhance the sum sideband generation (SSG) via double radiation pressure is proposed. In this scheme, both sides of the double-cavity system are driven by red and blue detuned pump lasers and frequency components are generated at the sum sideband through optomechanical nonlinear interaction. The results show that the efficiency of SSG can be improved with orders of magnitude. We further investigate the properties of SSG in resolved and unresolved sideband regimes. The efficiencies of upper sum sideband generation (USSG) and lower sum sideband generation (LSSG) are the equivalent in the unresolved sideband regime when the threshold condition is satisfied. It is worth noting that with the increase of the ratio between the dissipation rate of the cavity field and the decay rate of the mechanical resonator (MR), the amplitude of the LSSG can be superior to that of the USSG. Our scheme may provide a potential application in realizing the measurement of high-precision weak forces and quantum-sensitive sensing.

Continuous Optical-to-Mechanical Quantum State Transfer in the Unresolved Sideband Regime.

Optical-to-mechanical quantum state transfer is an important capability for future quantum networks, quantum communication, and distributed quantum sensing. However, existing continuous state transfer protocols operate in the resolved sideband regime, necessitating a high-quality optical cavity and a high mechanical resonance frequency. Here, we propose a continuous protocol that operates in the unresolved sideband regime. The protocol is based on feedback cooling, can be implemented with current technology, and is able to transfer non-Gaussian quantum states with high fidelity. Our protocol significantly expands the kinds of optomechanical devices for which continuous optical-to-mechanical state transfer is possible, paving the way toward quantum technological applications and the preparation of macroscopic superpositions to test the fundamentals of quantum science.

Mechanical Photoluminescence Excitation Spectra of a Strongly Driven Spin-Mechanical System

We report experimental studies of a driven spin-mechanical system, in which a nitrogen-vacancy ($\mathrm{N}\text{\ensuremath{-}}$V) center couples to out-of-plane vibrations of a diamond cantilever through the excited-state deformation potential. Photoluminescence excitation studies show that in the unresolved sideband regime and under strong resonant mechanical driving, the excitation spectra of a $\mathrm{N}\text{\ensuremath{-}}$V optical transition feature two spectrally sharp peaks, corresponding to the two turning points of the oscillating cantilever. In the limit that the strain-induced frequency separation between the two peaks far exceeds the $\mathrm{N}\text{\ensuremath{-}}$V zero-phonon linewidth, the spectral position of the individual peak becomes sensitive to minute detuning between the mechanical resonance and the external driving force. For a fixed optical excitation frequency near the $\mathrm{N}\text{\ensuremath{-}}$V transition, $\mathrm{N}\text{\ensuremath{-}}$V fluorescence as a function of mechanical detuning features resonances with a linewidth that can be orders of magnitude smaller than the intrinsic linewidth of the mechanical mode. This enhanced sensitivity to mechanical detuning can potentially provide an effective mechanism for mechanical sensing, for example, mass sensing via measurements of induced changes in the mechanical oscillator frequency.

Nonlinear optomechanical resonance entering a self-organized energy transfer pattern

The energy transfer between different subsystems or different vibration modes is always one of the most interested problems in the study of the resonance phenomena in coupled nonlinear dynamical systems. With an optomechanical system operating in the regime of unresolved sideband, where its mechanical frequency is lower than the cavity field damping rate, we illustrate the existence of a special nonlinear resonance phenomenon. This type of previously unknown resonance manifests an organized pattern of the coupled cavity field and mechanical oscillation, so that the cavity field precisely pushes the mechanical oscillator within an appropriate small time window in each mechanical oscillation period and the mechanical energy will increase by a jump of almost fixed amount after each oscillation cycle. The scenario is realized at a resonance point where the frequency difference of two driving fields matches the mechanical frequency of the system, and this condition of drive-frequency match is found to trigger a mechanism to lock the two subsystems of an unresolved-sideband optomechanical system into a highly ordered energy transfer as the above mentioned. Due to a significantly enhanced nonlinearity in the vicinity of the resonance point, optical frequency combs can be generated under pump powers of thousand times lower, as compared to the use of a single-tone driving field for the purpose. An unresolved sideband system under the drives without satisfying the resonance condition also demonstrates other interesting dynamical behaviors. Most of all, by providing a realistic picture for the nonlinear optomechanical dynamics in unresolved sideband regime, our study points to a direction to observe novel dynamical phenomena and realize other applications with the systems of less technical restrictions.

Optical Coherent Feedback Control of a Mechanical Oscillator

Feedback is a powerful and ubiquitous technique both in classical and quantum system control. Its standard implementation relies on measuring the state of a system, processing the classical signal, and feeding it back to the system. In quantum physics, however, measurements not only read out the state of the system but also modify it irreversibly. Coherent feedback is a different kind of feedback that coherently processes and feeds back quantum signals without actually measuring the system. Here, we report on the experimental realization and the theoretical analysis of an optical coherent feedback platform to control the motional state of a nanomechanical membrane in an optical cavity. The coherent feedback loop consists of a light field interacting twice with the same mechanical mode through different cavity modes, without {performing any} measurement. Tuning the optical phase and delay of the feedback loop allows us to control the motional state of the mechanical oscillator, its resonance frequency and also its damping rate, which we use to cool the membrane close to the quantum ground state. Our theoretical analysis provides the optimal cooling conditions, showing that this new technique enables ground-state cooling. Experimentally, we show that we can cool the membrane to a state with $\bar{n}_m = 4.89 \pm 0.14 $ phonons (${480}\,{\mu \mathrm{K}}$) in a ${20}\,\mathrm{K}$ environment. This lies below the theoretical limit of cavity dynamical backaction cooling in the unresolved sideband regime and is achieved with only 1$\%$ of the optical power required for cavity cooling. Our feedback scheme is very versatile, offering new opportunities for quantum control in a variety of optomechanical systems.

Optomechanically induced gain using a trapped interacting Bose-Einstein condensate

We investigate the realization of the phenomenon of optomechanically induced gain in a hybrid optomechanical system consisting of an interacting Bose-Einstein condensate trapped inside the optical lattice of a cavity which is generated by an external coupling laser tuned to the red sideband of the cavity. It is shown that the system behaves as an optical transistor while the cavity is exposed to a weak input optical signal which can be amplified considerably in the cavity output if the system is in the unresolved sideband regime. Interestingly, the system has the capability to switch from the resolved to unresolved sideband regime by controlling the s-wave scattering frequency of atomic collisions. We show that the system gain can be enhanced considerably by controlling the s-wave scattering frequency as well as the coupling laser intensity while the system remains in the stable regime. Based on our obtained results, the input signal can be amplified more than 100 million percent in the system output which is much larger than those already reported in the previously proposed similar schemes.

Enhancement of mechanical entanglement and asymmetric steering with coherent feedback

We propose a scheme to enhance entanglement and asymmetric steering between two mechanical oscillators in an optomechanical system with coherent feedback control. In the system, an optical cavity interacts with two mechanical oscillators and an auxiliary cavity whose output field is fed back into the input port of the optical cavity via a feedback loop. Due to the coherence between the auxiliary cavity and feedback, we derive the effective decay rate and a nonzero frequency shift of the optical cavity. Consequently, the induced beam-splitter-type and parametric-type interactions between the two mechanical oscillators are modulated, which leads to the enhancement of entanglement and the generation of asymmetric steering even if the two mechanical oscillators possess identical decoherence properties. And the direction of asymmetric steering can be controlled by tuning the jumping phase between two cavities and optimizing the ratio of drive asymmetry. In contrast to the method of adding losses or noises to one subsystem at the cost of reducing steerability, this scheme provides an active way to achieve enhanced asymmetric steering. Furthermore, the steady-state and dynamical entanglement and asymmetric steering can be generated in the unresolved-sideband regime, which is friendly for experimental implementation.

Cooling of mechanical resonator in a hybrid intracavity squeezing optomechanical system.

A hybrid intracavity squeezing optomechanical cooling system, in which an auxiliary cavity couples to an optomechanical cavity with a nonlinear medium inside it, is proposed to realize the ground state cooling of the mechanical resonator in the highly unresolved sideband regime. We demonstrate that the quantum backaction heating can be suppressed perfectly by the intracavity squeezing, and the cooling process can be further promoted by adjusting the tunnel coupling between the coupled cavities. The scheme has good performance in resisting the environmental thermal noise and better tolerance for the auxiliary cavity quality factor and provides the possibility for the quantum manipulation of the mechanical resonator with large mass and low frequency.

Cavity optomechanics in a fiber cavity: the role of stimulated Brillouin scattering

We study the role of stimulated Brillouin scattering in a fiber cavity by numerical simulations and a simple theoretical model and find good agreement between experiment, simulation and theory. We also investigate an optomechanical system based on a fiber cavity in the presence of the nonlinear Brillouin scattering. Using simulation and theory, we show that this hybrid optomechanical system increases optomechanical damping for low mechanical resonance frequencies in the unresolved sideband regime. Furthermore, optimal damping occurs for blue detuning in stark contrast to standard optomechanics. We investigate whether this hybrid optomechanical system is capable of cooling a mechanical oscillator to the quantum ground state.

Magnon squeezing enhanced ground-state cooling in cavity magnomechanics

Cavity magnomechanics has recently become a new platform for studying macroscopic quantum phenomena. The magnetostriction induced vibration mode of a large-size ferromagnet or ferrimagnet reaching its ground state represents a genuine macroscopic quantum state. Here we study the ground-state cooling of the mechanical vibration mode in a cavity magnomechanical system, and focus on the role of magnon squeezing in improving the cooling efficiency. The magnon squeezing is obtained by exploiting the magnon self-Kerr nonlinearity. We find that the magnon squeezing can significantly and even completely suppress the magnomechanical Stokes scattering. It thus becomes particularly useful in realizing ground-state cooling in the unresolved-sideband regime, where the conventional sideband cooling protocols become inefficient. We also find that the coupling to the microwave cavity plays only an adverse effect in mechanical cooling. This makes essentially the two-mode magnomechanical system (without involving the microwave cavity) a preferred system for cooling the mechanical motion, in which the magnon mode is established by a uniform bias magnetic field and a microwave drive field.

Cavity-assisted coherent feedback cooling of a mechanical resonator to the ground-state in the unresolved sideband regime

This paper presents a cavity-assisted coherent feedback scheme to cool a mechanical resonator to the ground-state in a weak optomechanical coupling setup. Based on the theory of sideband cooling, resolved sideband regime is a mandatory condition for the ground-state cooling (GSC) in optomechanical systems. Assisted cooling and feedback cooling methods have been proposed and shown to be beneficial for cooling in unresolved sideband cases. In this paper, a cooling method is proposed by combining both approaches. In the proposed method, a coherent feedback loop is added to a cavity-assisted optomechanical system to enhance the cooling performance. The proposed feedback aims to reach the mechanical ground-state in the unresolved sideband regime (USR). Rate equations of the mechanical resonator are derived, and then, by applying Fermi’s golden rule and analyzing the fluctuation spectrum of the optical force, optimal conditions for cooling are obtained. Results show that applying coherent feedback, improves the cooling performance of the system significantly and it is possible to achieve GSC in USR. Moreover, it is shown that the proposed method is capable of cooling the mechanical resonator to much lower energy levels than it is achievable in cavity assisted method.