The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two noninteracting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mechanical displacement and the cavity is driven at multiple frequencies. We show analytically that both schemes stabilize a Wigner-negative entangled state that combines the entanglement of a two-mode squeezed vacuum with a cubic nonlinearity, which we dub cubic-phase entangled (CPE) state. We then perform extensive numerical simulations to test the robustness of Wigner-negative entanglement attained by approximate CPE states stabilized in the presence of thermal decoherence. Published by the American Physical Society 2024
The generation of entangled states that display negative values of the Wigner function in the quantum phase space is a challenging task, particularly elusive for massive, and possibly macroscopic, systems such as mechanical resonators. In this work, we propose two schemes based on reservoir engineering for generating Wigner-negative entangled states unconditionally. We consider two noninteracting mechanical resonators that are radiation-pressure coupled to either one or two common cavity fields; the optomechanical coupling with the field(s) features both a linear and quadratic part in the mechanical displacement and the cavity is driven at multiple frequencies. We show analytically that both schemes stabilize a Wigner-negative entangled state that combines the entanglement of a two-mode squeezed vacuum with a cubic nonlinearity, which we dub cubic-phase entangled (CPE) state. We then perform extensive numerical simulations to test the robustness of Wigner-negative entanglement attained by approximate CPE states stabilized in the presence of thermal decoherence. Published by the American Physical Society 2024
The generation of non-Gaussian states of bosonic systems described by continuous quantum degrees of freedom is of interest in a variety of contexts, ranging from quantum foundations to computation and communication. A crucial feature of genuine non-Gaussian states is that they cannot be described in general with a non-negative Wignerquasi-probability distribution. In particular, this feature is equivalent to contextuality and it underpins all attempts at attaining quantum computational advantage in a universal setting. In this thesis, the generation of Wigner-negative states is addressed, pursuing two approaches. First, in an optomechanical-like setting, we develop schemes to generate Wigner-negative states of two massive mechanical systems, in turn correlated such that they also feature entanglement, another genuine quantum hallmark. These schemes are based on driven-dissipative systems where dissipation is properly engineered by taking advantage of linear-and-quadratic optomechanical interactions. We address the robustness of these schemes when uncontrollable noisy channels are included in the dynamics, proving that their resilience is comparable to Gaussian schemes that have already been implemented experimentally. Second, considering in particular circuit QED systems and trapped ions, we propose a method to engineer a set of Hamiltonian evolutions that are universal in terms of single-mode state preparation. This method is based on a driven quantum Rabi model, where the desired evolution is effectively imprinted on a continuous-variable degree of freedom by its interaction with a properly driven two-level system. We demonstrate the universality of such approach by simulating the generation of multi-squeezed and other states, including the celebrated cubic-phase state. We also consider the effect of noise in realistic settings, showing in particular that in systems involving superconducting qubits, the generation of tri-squeezed states --- a universal resource for continuous-variable quantum computation which we prove to display larger Wigner negativities with respect to Fock and cubic-phase states for the same energy --- is within experimental reach.
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.
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
Quantum entanglement is a crucial resource in quantum technologies, enabling advancements in quantum computing, quantum communication, and quantum precision measurement. Here, we propose a method to enhance optomechanical entanglement by introducing an optical Kerr nonlinear medium and a squeezed vacuum reservoir of the optomechanical cavity. By performing the displacement and squeezing transformations, the system can be reduced to a standard linearized optomechanical system with normalized driving detuning and linearized-coupling strength, in which the optical and mechanical modes are, respectively, coupled to an optical vacuum bath and a mechanical heat bath. We focus on the entanglement generation in the single stable regime of the system. By evaluating the steady-state logarithm negativity, we find that the optomechanical entanglement can be enhanced within a wide range of the Kerr constant. In addition, the Kerr nonlinearity can extend the stable region, enabling considerable entanglement generation in the blue-sideband parameter region. We also investigate the dependence of the entanglement generation on the average thermal phonon occupation of the mechanical bath and the optical driving amplitude. It is found that the presence of the Kerr nonlinearity allows the generation of optomechanical entanglement even when the thermal phonon occupation of the mechanical bath is as high as 3000. Our findings will provide valuable insights into enhancing fragile quantum resources in quantum systems.
Entanglement and squeezing are two useful resources in quantum technologies. Recent studies have increasingly focused on generating these nonclassical features in macroscopic objects. However, establishing entanglement and squeezing in the degrees of freedom of mechanical motion of macroscopic objects is generally hindered by thermal fluctuations of their environments. Here, we propose a scheme to generate steady-state squeezing and entanglement between two rotating mirrors of a Laguerre-Gaussian cavity by quantum squeezed-reservoir engineering. It is revealed that, by injecting a broadband squeezed light into the cavity, stable squeezing in the relative momentum and entanglement between the two rotating mirrors are created. Compared to the previous work where only the entanglement between the two rotating mirrors appears under the condition of different angular frequencies, our result highlights the stable entanglement of the two mirrors with identical frequency and the simultaneous presence of the entanglement and squeezing of the two mirrors. Our finding deepens our understanding of macroscopic quantum phenomena of Laguerre-Gaussian cavity optomechanical system.