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arXiv:2307.12383 · Physical Review Applied

Resonance-dominant optomechanical entanglement in open quantum systems

Cheng Shang, Hongchao Li

Published Apr 25, 2024• 23 citations
arXivHTMLPDF

Abstract

Motivated by entanglement protection, our work utilizes a resonance effect to enhance optomechanical entanglement in the coherent-state representation. We propose a filtering model to filter out the significant detuning components between a thermal-mechanical mode and its surrounding heat baths in the weak-coupling limit. We reveal that protecting continuous-variable entanglement involves the elimination of degrees of freedom associated with significant detuning components, thereby resisting decoherence. We construct a nonlinear Langevin equation of the filtering model and numerically show that the filtering model doubles the robustness of the stationary maximum optomechanical entanglement to the thermal fluctuation noise and mechanical damping. Furthermore, we generalize these results to an optical cavity array with one oscillating end mirror to investigate the long-distance optimal optomechanical-entanglement transfer. Our study breaks new ground for applying the resonance effect to protect quantum systems from decoherence and advancing the possibilities of large-scale quantum information processing and quantum network construction.

DOI
10.1103/physrevapplied.21.044048

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We propose a scheme to generate robust stationary continuous-variable entanglement in optomechanical systems, based on geometrical nonlinearity that occurs for large mechanical displacements. Such nonlinearity is often used to correct the dynamics of the systems in the strong-coupling regime. It appears that geometrical nonlinearity enhances the entanglement and shifts its maximum towards high detuning values. Using the experimental parameters, we find that such a scheme generates a very robust entanglement against thermal decoherence even at room temperature. Our results show that geometrical nonlinearity affects entanglement as the optomechanical quantum interface.
Quantum entanglement not only plays an important role in the study of the fundamentals of quantum theory, but also is considered as a crucial resource in quantum information science. The generation of macroscopic entanglement involving multiple optical and mechanical modes is a desired task in cavity optomechanics. However, the dark-mode effect is a critical obstacle against the generation of quantum entanglement in multimode optomechanical systems consisting of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity mode. Here we propose an auxiliary-cavity-mode method to enhance optomechanical entanglement in a multimode optomechanical system by breaking the dark-mode effect. We find that the introduction of the auxiliary cavity mode not only assists the entanglement creation between the cavity mode and the mechanical modes, but also improves the immunity of the optomechanical entanglement to the thermal excitations by about three orders of magnitude. We also study the optomechanical entanglement in the network-coupled optomechanical system consisting of two mechanical modes and two cavity modes. By analyzing the correspondence between the optomechanical entanglement and the dark-mode effect, we find that optomechanical entanglement can be largely enhanced once the dark mode is broken. In addition, we study the mechanical entanglement and find that it is negligibly small. We also present some discussions on the experimental implementation with a microwave optomechanical setup, on the relationship between the dark-mode-breaking mechanism and the center-of-mass and relative coordinates, and on the explanation of the important role of the dark-mode breaking in the enhancement of optomechanical entanglement. Our results pave the way towards the preparation of entangled optomechanical networks and noise-resistant quantum resources.
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A pulsed scheme for generating robust optical entanglement via the coupling of two optical modes to a mechanical oscillator is proposed. This scheme is inspired by the S\o{}rensen-M\o{}lmer approach for entangling trapped ions in a thermal environment and is based on the use of optical driving pulses that are slightly detuned from the respective sideband resonance. We show that for certain pulse durations, the optomechanical interaction can return the mechanical oscillator to its initial state, disentangling the mechanical and optical systems. The corresponding optical entanglement generation is robust against thermal mechanical noise in the weak as well as the strong-coupling regimes. Significant optical entanglement can be generated in the weak-coupling regime, even in the presence of a large thermal phonon occupation.
Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field---even when the environmental temperature is high and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes that are ordered by the entanglement strength to better understand the entanglement structure, analogously to the energy spectrum of an atomic system. In particular, we derive the optical mode that is maximally entangled with the mechanical oscillator, which will be useful for future quantum computing and encoding information into mechanical degrees of freedom.
Multipartite entanglement is a key resource for quantum information processing and quantum communication. We show that the robust entanglement among four filtered output optical modes can be achieved when there is a nonlinear crystal inside an optomechanical cavity. The optical parametric amplifier (OPA) gives rise to single-mode squeezing of the cavity modes; therefore, the entanglement among four output optical modes can be enhanced remarkably. Furthermore, the degree of quadripartite entanglement is influenced by the nonlinear gain of OPA and bandwidth of the filters. Large entanglement can be obtained by optimizing the filter functions, which is important for utilizing entangled light beams more efficiently in real experiments. This kind of multipartite entanglement will be useful and valuable in the area of quantum communication networks.