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arXiv:2309.03719

Quantum Nonlinear Effect in Dissipatively Coupled Optomechanical System

Wen-Quan Yang, Wei Niu, Yonghong Ma, Wen-Zhao Zhang

Published Sep 7, 2023• 0 citations
arXivHTMLPDF

Abstract

A full-quantum approach is used to study quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. The effective Hamiltonian shows that both dissipative and dispersive couplings possess imaginary- and real-Kerr nonlinearities. And unexpectedly, the nonlinearities caused by the dissipative coupling have non-Hermitian Hamiltonian-like properties. It can protect the quantum nature of the dispersive coupling beyond the traditional dissipation of the system. This protection mechanism allows the system to exhibit strong quantum nonlinear effects in the parameter region of the hyperbolic function $J^2 = Δ_c Δ_e$. Moreover, we can obtain strong anti-bunching effects whether in strong or weak coupling regimes with the help of the dispersive and dissipative couplings jointly. It may provide a new perspective to experimentally realize and study the strong quantum nonlinear effects.

DOI
10.48550/arxiv.2309.03719

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A full-quantum approach is used to study quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. The effective Hamiltonian shows that both dissipative and dispersive couplings possess imaginary- and real-Kerr nonlinearities. And unexpectedly, the nonlinearities caused by the dissipative coupling have non-Hermitian Hamiltonian-like properties. It can protect the quantum nature of the dispersive coupling beyond the traditional dissipation of the system. This protection mechanism allows the system to exhibit strong quantum nonlinear effects in the parameter region of the hyperbolic function J2=ΔcΔeJ^2 = Δ_c Δ_eJ2=Δc​Δe​. Moreover, we can obtain strong anti-bunching effects whether in strong or weak coupling regimes with the help of the dispersive and dissipative couplings jointly. It may provide a new perspective to experimentally realize and study the strong quantum nonlinear effects.
Macroscopic entanglement, as a critical quantum resource in quantum information science, has been extensively studied in coherent optomechanics over the past decades. However, entanglement in dissipative optomechanics, where the cavity linewidth depends on the position of the mechanical resonator, remains largely unexplored. In this work, we investigate quantum entanglement in a dissipative optomechanical system realized by a Michelson-Sagnac interferometer with a movable membrane. This configuration enables the switching between coherent and dissipative optomechanical couplings at will. With experimentally feasible parameters, we demonstrate that the steady-state mechanical displacement exhibits a nonlinear (linear) dependence on the driving power under coherent (dissipative) coupling. Furthermore, we show that the quantum entanglement generated via dissipative coupling is significantly stronger and more robust to noise than that generated via coherent coupling. When both coherent and dissipative couplings are simultaneously present, the entanglement is weakened due to quantum interference. Our results indicate that dissipative optomechanical coupling can be a promising route for engineering strong and noise-resilient quantum entanglement.
Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system. Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently, a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.
We investigate the quantum synchronization of two indirectly coupled mechanical oscillators with different frequencies in the Kerr resonator optomechanical system, where the two driving fields are modulated. Our findings indicate that Kerr nonlinearity facilitates quantum synchronization, while quadratic coupling tends to suppress it. When both nonlinearities are present, quadratic coupling enhances synchronization in the presence of weak Kerr nonlinearity, whereas strong Kerr nonlinearity causes it to suppress synchronization. These results imply the existence of an optimal parameter regime for maximizing quantum synchronization. Moreover, under the joint influence of Kerr nonlinearity and quadratic coupling, perfect synchronization can be achieved under specific parameters. Our results provide insight into the manipulation of quantum synchronization utilizing nonlinearities in cavity optomechanical systems.
The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure interaction between cavity and mechanical resonator is also inherently nonlinear but typically under strong drive of the cavity interaction can be linearized. However, if the optomechanical system is in the strong coupling regime nonlinear quantum effects become observable. These three cases provide the motivation for our studies. We start with backaction analysis of the classical regime of a dc SQUID (superconducting quantum interference device) with an embedded mechanical resonator. Then, we perform quantum analysis to understand how the asymmetry of two Josephson junctions influences the coupling strength of optomechanical interactions such as radiation pressure, cross-Kerr and single-photon beam splitter. Using variational method and self-consistent harmonic approximation we estimate the influence of the radiation pressure coupling and Kerr nonlinearity of the cavity on the effective frequency and dissipation of the cavity. The second part of this thesis focuses on the nonlinearity of the mechanical resonator coupled to the optical/microwave cavity. We study in details the nonlinear optomechanical response and draw the response map to summarize all results of the overcoupled and undercoupled cavity for the red and blue sidebands additionally to the weak and strong drive powers. In the end, w e confirm the developed theory by using it to numerically fit the experimental results.
Cavity optomechanics represents a flexible platform for the implementation of quantum technologies, useful in particular for the realization of quantum interfaces, quantum sensors and quantum information processing. However, the dispersive, radiation-pressure interaction between the mechanical and the electromagnetic modes is typically very weak, harnessing up to now the demonstration of interesting nonlinear dynamics and quantum control at the single photon level. It has already been shown both theoretically and experimentally that if the interaction is mediated by a Josephson circuit, one can have an effective dynamics corresponding to a huge enhancement of the single-photon optomechanical coupling. Here we analyze in detail this phenomenon in the general case when the cavity mode and the mechanical mode interact via an off-resonant qubit. Using a Schrieffer-Wolff approximation treatment, we determine the regime where this tripartite hybrid system behaves as an effective cavity optomechanical system in the strong coupling regime.
The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplification. Moreover, the amplified phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir, which ultimately leads to the realization of photon blockade in a weakly coupled OMS. The reached nonlinear quantum regime also allows us to engineer the nonclassical states (e.g., Schr\"odinger cat states) of the cavity field, which are robust against the phonon noise. This work offers an alternative approach to enhance the quantum nonlinearity of an OMS, which should expand the applications of cavity optomechanics in the quantum realm.