The preparation of mechanical quadrature-squeezed states holds significant importance in cavity optomechanics because the squeezed states have extensive applications in understanding fundamental quantum mechanics and exploiting modern quantum technology. Here, we propose a reliable scheme for generating mechanical quadrature squeezing in a typical cavity optomechanical system via seeking optimal cavity-field driving pulses using the gradient-descent algorithm. We realize strong quadrature squeezing in a mechanical resonator that exceeds the 3-dB steady-state limit, even with a thermal phonon occupancy of 100. Furthermore, the mechanical squeezing can be ultrarapidly created within one mechanical oscillation period. We also obtain the optimal pulsed drivings associated with the created mechanical squeezings and analyze the mechanism for mechanical squeezing generation. This paper will promote the application of optimal quantum control in quantum optics and quantum information science.
The preparation of mechanical quadrature-squeezed states holds significant importance in cavity optomechanics because the squeezed states have extensive applications in understanding fundamental quantum mechanics and exploiting modern quantum technology. Here, we propose a reliable scheme for generating mechanical quadrature squeezing in a typical cavity optomechanical system via seeking optimal cavity-field driving pulses using the gradient-descent algorithm. We realize strong quadrature squeezing in a mechanical resonator that exceeds the 3-dB steady-state limit, even with a thermal phonon occupancy of 100. Furthermore, the mechanical squeezing can be ultrarapidly created within one mechanical oscillation period. We also obtain the optimal pulsed drivings associated with the created mechanical squeezings and analyze the mechanism for mechanical squeezing generation. This paper will promote the application of optimal quantum control in quantum optics and quantum information science.
Quantum squeezing is an important resource in modern quantum technologies, such as quantum precision measurement and continuous-variable quantum information processing. The generation of squeezed states of mechanical modes is a significant task in cavity optomechanics. Motivated by recent interest in multimode optomechanics, it becomes an interesting topic to create quadrature squeezing in multiple mechanical resonators. However, in the multiple-degenerate-mechanical-mode optomechanical systems, the dark-mode effect strongly suppresses the quantum effects in mechanical modes. Here we study the generation of mechanical squeezing in a two-mechanical-mode optomechanical system by breaking the dark-mode effect with the synthetic-gauge-field method. We find that, when the mechanical modes work at a finite temperature, the mechanical squeezing is weak or even disappears due to the dark-mode effect, while the strong mechanical squeezing can be generated once the dark-mode effect is broken. In particular, the thermal-phonon-occupation tolerance of the mechanical squeezing is approximately three orders of magnitude larger than that without breaking the dark-mode effect. We also generalize this method to break the dark modes and to create the mechanical squeezing in multiple-mechanical-mode optomechanical systems. Our results describe a general physical mechanism and pave the way towards the generation of noise-resistant quantum resources.
In this paper, we propose an optomechanical scheme for generating mechanical squeezing over the 3 dB limit, with the mechanical mirror being driven by a strong and linear harmonic force. In contrast to parametric mechanical driving, the linearly driven force shakes the mechanical mirror periodically oscillating at twice the mechanical eigenfrequency with large amplitude, where the mechanical mirror can be dissipatively stabilized by the engineered cavity reservoir to a dynamical squeezed steady state with a maximum degree of squeezing over 8 dB. The mechanical squeezing of more than 3 dB can be achieved even for a mechanical thermal temperature larger than 100 mK. The scheme can be implemented in a cascaded optomechanical setup, with potential applications in engineering continuous variable entanglement and quantum sensing.
We discuss how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes. The scheme does not rely on any explicit measurement or feedback, nor does it simply involve a modulation of an optical spring constant. Instead, it uses a dissipative mechanism with the driven cavity acting as an engineered reservoir. It can equivalently be viewed as a coherent feedback process, obtained by minimally perturbing the quantum nondemolition measurement of a single mechanical quadrature. This shows that in general the concepts of coherent feedback schemes and reservoir engineering are closely related. We analyze how to optimize the scheme, how the squeezing scales with system parameters, and how it may be directly detected from the cavity output. Our scheme is extremely general, and could also be implemented with, e.g., superconducting circuits.
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.
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.
We propose an efficient scheme to generate quadrature squeezing of a higher-order sideband spectrum in an optomechanical system. This is achieved by exploiting a well-established optomechanical circumstance, where a second-order nonlinearity is embedded into the optomechanical cavity driven by a strong control field and a weak probe pulse. Using experimentally achievable parameters, we demonstrate that the second-order nonlinearity intensity and the frequency detuning of a control field allow us to modify the amplitude of higher-order sidebands and improve the amount of squeezing of a higher-order sideband spectrum. Furthermore, in the presence of a strong second-order nonlinearity, an optimizing quadrature squeezing of a higher-order sideband spectrum can be achieved, which provides a practical opportunity to design the squeezed frequency combs and other precision measurements.