Quantum control techniques applied at macroscopic scales provide us with opportunities in fundamental physics and practical applications. Among them, measurement-based feedback allows efficient control of optomechanical systems and quantum-enhanced sensing. In this paper, we propose a near-resonant narrow-band force sensor with extremely low optically added noise in a membrane in the middle optomechanical system subject to a feedback-controlled in-loop light. The membrane's intrinsic motion consisting of zero-point motion and thermal motion is affected by the added noise of measurement due to the backaction noise and imprecision noise. We show that, in the optimal low-noise regime, the system is analogous to an optomechanical system containing a near quantum-limited optical parametric amplifier coupled to an engineered reservoir interacting with the cavity. Therefore, the feedback loop enhances the mechanical response of the system to the input while keeping the optically added noise of measurement below the standard quantum limit. Moreover, the system based on feedback offers a much larger amplification bandwidth than the same system with no feedback. Without the need to hybridize it with other quantum systems or introduce nonlinearities, our force sensor may have broad applications ranging from biology and medicine to gravitational wave detection and tests of fundamental physics.
Quantum control techniques applied at macroscopic scales provide us with opportunities in fundamental physics and practical applications. Among them, measurement-based feedback allows efficient control of optomechanical systems and quantum-enhanced sensing. In this paper, we propose a near-resonant narrow-band force sensor with extremely low optically added noise in a membrane in the middle optomechanical system subject to a feedback-controlled in-loop light. The membrane's intrinsic motion consisting of zero-point motion and thermal motion is affected by the added noise of measurement due to the backaction noise and imprecision noise. We show that, in the optimal low-noise regime, the system is analogous to an optomechanical system containing a near quantum-limited optical parametric amplifier coupled to an engineered reservoir interacting with the cavity. Therefore, the feedback loop enhances the mechanical response of the system to the input while keeping the optically added noise of measurement below the standard quantum limit. Moreover, the system based on feedback offers a much larger amplification bandwidth than the same system with no feedback. Without the need to hybridize it with other quantum systems or introduce nonlinearities, our force sensor may have broad applications ranging from biology and medicine to gravitational wave detection and tests of fundamental physics.
Abstract A theoretical scheme is proposed to enhance the sensitivity of force sensors with quantum non-demolition measurement (QND) in an optomechanical setup assisted by four-tone optical driving and an optical parametric amplifier (OPA). With the help of special drive, the system can be simplified as the typical type of QND for force sensing, so that the backaction noise can be evaded to surpass the standard quantum limit. Besides, the added noise can be suppressed owing to the modified optical susceptibility resulting from the OPA. By introducing two oscillators coupling with two charged bodies respectively, the signal can be enhanced with the nonlinearity caused by Coulomb interaction, while the noise presents an exponential decrease. Moreover, considering the homodyne detection effect, the range of system parameters and frequency bands will be broadened. The present investigation may provide a route toward simultaneously evading backaction noise, reducing the mechanical thermal noise, and enhancing the external signal, which can be an alternative design for sensitive devices.
In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the s-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that, in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially which leads to the amplification of the weak input signal while the added noise of measurement (backaction noise) can be suppressed and lowered much below the standard quantum limit. Furthermore, because of its large mechanical gain, such a modulated hybrid system is a much better amplifier in comparison to the (modulated) bare optomechanical system which can generate a stronger output signal while keeping the sensitivity nearly the same as that of the (modulated) bare one. The other advantages of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities are its controllability as well as the extension of the amplification bandwidth.
The weak force sensing based on a coherent quantum noise cancellation (CQNC) scheme is presented in a hybrid cavity optomechanical system containing a trapped ensemble of ultracold atoms and an optical parametric amplifier (OPA). In the proposed system, the back-action noise can be completely eliminated at all frequencies and through the proper choice of the OPA parameters, and the noise spectral density can also be reduced at lower frequencies. This leads to a significant enhancement in the sensitivity of the cavity optomechanical weak force sensor, and the noise spectral density also surpasses the standard quantum limit (SQL) even for the small input power at the lower detection frequency. Furthermore, the experimental feasibility of this scheme is also briefly discussed. This study can be used for the realization of a force sensor based on hybrid cavity optomechanical systems and for the coherent quantum control in macroscopic systems.
The detection of weak forces plays a crucial role in various fields, from gravitational wave astronomy to biological sensing. A fundamental limitation in such measurements arises from quantum and thermal noise. Here, we present a theoretical scheme for force sensing that incorporates an optical parametric amplifier (OPA) in conjunction with a gain-assisted auxiliary cavity. We show that, in contrast to conventional lossy configurations, the presence of optical gain in the auxiliary cavity enables a substantial enhancement in sensitivity, allowing the system to exceed the standard quantum limit across a broad detection bandwidth. By carefully tuning the gain parameter, cavity-cavity coupling strength, OPA driving phase, and detuning conditions, the system achieves optimal noise suppression. Remarkably, this performance persists even under a twentyfold increase in environmental temperature, underscoring the robustness of the proposed scheme. Detailed noise analysis reveals that the contribution of the gain-assisted auxiliary cavity appears to be a negative value in the noise spectrum, effectively reducing the overall noise level of the system. This study is of significant importance to the design and fabrication of high-performance optomechanical sensors.
We investigate the reduction of measurement-added noise in force sensing by analyzing its power spectral density (PSD) within a hybrid optomechanical system. The setup is comprised of an optomechanical cavity equipped with a movable mirror which acts as the mechanical oscillator, a stationary semi-transparent mirror, a superconducting qubit, and an optical parametric amplifier (OPA). By utilizing the concept of coherent quantum noise cancellation (CQNC), we derive the conditions necessary for complete cancellation of back-action force, thereby enhancing force sensitivity. Furthermore, with the gradual increase in the OPA pump gains, we suppress the sensitivity beyond the standard quantum limit (SQL) at a lower value of laser power. The removal of back-action noise, along with the reduction of shot noise, improves force detection capabilities, thereby surpassing the standard quantum limit associated with weak force detection.
Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thereby enabling controlled stiffening or softening of the mechanical mode through adjusting quadratic optomechanical coupling, as well as effective modulation of the cavity decay rate via feedback control. More importantly, the synergistic interplay effect allows for a strategic reconfiguration of the system's stability regime, which in turn permits the presence of significantly enhanced effective optomechanical coupling strengths before entering the unstable regime. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.