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Synchronization of chaotic optomechanical system with plasmonic cavity for secured quantum communication

Mulubirhan Dangish, Abebe Belay, Alemayehu Getahun Kumela, Umer Sherefedin, Ruth Birhanu

Published Jan 1, 2025• 1 citation

Abstract

Cavity optomechanical systems generate, manipulate, and detect quantum states of light by exploiting the intricate interplay between light confined to optical cavities and mechanical vibrations. However, these systems can be subjected to thermal noise due to the inherent thermal vibrations of the mechanical components, introducing fluctuations that can obscure the delicate quantum states and dynamics of the system. Therefore, in this study, we present a theoretical analysis of the synchronization dynamics in chaotic optomechanical systems comprising two cavity modes: one strongly influenced by a localized surface plasmon field and another exhibiting minimal influence. We investigated the energy transfer efficiency of silicon divacancies, gallium arsenide, and indium phosphide by analyzing their absorption and extinction cross sections. The results indicate that gallium arsenide surpasses both silicon divacancies and indium phosphide in performance. Employing the Hamiltonian notation, we calculated the effect of optical force and damping rates on the optomechanical system over time. In addition, using Lyapunov chaotic attractors, we demonstrated that the localized surface plasmons significantly boost the strength of the electromagnetic field within the strongly influenced cavity mode and effectively synchronize the two modes through a coherent phase relationship with minimal error. Further, we exploited the initial chaotic behavior for quantum key generation, showcasing the system’s potential for efficient and secure quantum communication within a time frame of 0.7 μs. Our findings pave the way for enhanced coherence and reliability in secure quantum communication systems, thus contributing to the advancement of this rapidly evolving field.

DOI: 10.1063/5.0241558

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Cavity optomechanical systems generate, manipulate, and detect quantum states of light by exploiting the intricate interplay between light confined to optical cavities and mechanical vibrations. However, these systems can be subjected to thermal noise due to the inherent thermal vibrations of the mechanical components, introducing fluctuations that can obscure the delicate quantum states and dynamics of the system. Therefore, in this study, we present a theoretical analysis of the synchronization dynamics in chaotic optomechanical systems comprising two cavity modes: one strongly influenced by a localized surface plasmon field and another exhibiting minimal influence. We investigated the energy transfer efficiency of silicon divacancies, gallium arsenide, and indium phosphide by analyzing their absorption and extinction cross sections. The results indicate that gallium arsenide surpasses both silicon divacancies and indium phosphide in performance. Employing the Hamiltonian notation, we calculated the effect of optical force and damping rates on the optomechanical system over time. In addition, using Lyapunov chaotic attractors, we demonstrated that the localized surface plasmons significantly boost the strength of the electromagnetic field within the strongly influenced cavity mode and effectively synchronize the two modes through a coherent phase relationship with minimal error. Further, we exploited the initial chaotic behavior for quantum key generation, showcasing the system’s potential for efficient and secure quantum communication within a time frame of 0.7 μs. Our findings pave the way for enhanced coherence and reliability in secure quantum communication systems, thus contributing to the advancement of this rapidly evolving field.

Chaos is central to secure communication and physical random-number generation. Conventional cavity-optomechanical implementations, however, usually rely on weak single-photon optomechanical coupling and low-frequency mechanical modes, so access to deterministic chaotic dynamics often requires large driving power and careful suppression of thermal noise. Here we theoretically study a hybrid molecular optomechanical system formed by coupling a plasmonic nanocavity to a whispering-gallery-mode (WGM) microcavity. The plasmonic nanocavity provides terahertz-scale single-photon optomechanical coupling to a molecular vibration, while the WGM resonator offers a low-loss photonic channel that mitigates the short plasmon lifetime. By integrating the semiclassical equations of motion and evaluating the largest Lyapunov exponent, we map the nonlinear dynamical regimes in the parameter spaces of WGM detuning, plasmon--WGM coupling, and plasmon--vibration optomechanical coupling. We show that increasing the plasmon--vibration coupling drives the system from self-sustained oscillations to chaos through a period-doubling cascade. At moderate coupling strengths, isolated chaos windows can be opened or closed by tuning the WGM detuning and the inter-cavity coupling. These results identify molecular optomechanics as a controllable room-temperature platform for on-chip chaotic light generation and random-signal applications.

Abstract In this paper, we study quantum synchronization in a hybrid optomechanical system that includes photon hopping and atomic ensembles. The covariance matrix method is used to examine synchronization between cavity–cavity, cavity–atom, and cavity–mechanical subsystems. Our results demonstrate that strong photon hopping improves synchronization by enabling efficient transfer of energy and phase between the coupled modes. Furthermore, we reveal that synchronization exhibits a non-monotonic dependence on both the atomic coupling strength and system detuning, initially increasing up to a critical threshold before gradually declining. In contrast, decoherence effects especially atomic decay rate reduce synchronization by destroying phase coherence. While cavity-mechanical synchronization is heavily suppressed by an increasing thermal phonon number, cavity-cavity and cavity-atomic synchronization remain uniquely robust against thermal noise. Ultimately governed by the competition between coherent coupling and environmental dissipation, these results provide valuable insights into controlling quantum synchronization for future applications in quantum information processing, precision metrology, and scalable hybrid quantum networks.

In this work, we investigate the dynamics of quantum synchronization in a four-mode optomechanical system, focusing on the influence of the Coulomb interaction between two mechanical resonators. We analyze the effect of the Coulomb coupling on three distinct synchronization regimes, i.e., complete quantum synchronization,

φ

-synchronization, and quantum phase synchronization. Our results show that while the Coulomb interaction plays a pivotal role in significantly enhancing quantum phase synchronization by facilitating energy exchange and phase coherence, it has little impact on complete and

φ

-synchronization. This indicates that amplitude and frequency locking are primarily determined by the optical driving, whereas phase alignment depends critically on inter-resonator coupling. We also demonstrate that the oscillations of the two optical cavities, which are indirectly coupled via the mechanical resonators, can become aligned over time, resulting in classical synchronization. These findings provide a robust mechanism for controlling collective quantum dynamics and offer a foundation for applications in quantum communication, precision sensing, and the development of synchronized quantum networks.

In the field of optomechanics, one typically studies the interaction of a single mechanical resonator and a single optical cavity mode. In this thesis, we investigate collective quantum effects in optomechanical systems with two or more optical and mechanical modes. First, we study the generation and destruction of entanglement between two mechanical resonators effected by optical cavity fields. We also describe how the optomechanical interaction can be employed to mediate strong coherent coupling and entanglement between a micromechanical membrane and a single atom. Secondly, we show that a configuration with two optical and a single mechanical mode can lead to enhanced nonlinear interactions, which can be exploited for quantum non-demolition measurements of the phonon and photon numbers. Finally, we explore the quantum many-body dynamics of optomechanical arrays. In particular, we research into the transition from a disordered state due to quantum noise to a state with phasecoherent mechanical oscillations. As an intermediate step towards this study, we also investigate the nonlinear classical dynamics of single- and multi-mode optomechanical setups and compare theoretical predictions to experimental data.

The nonlinear dynamics of a mechanical resonator in an optomechanical system with linear, quadratic and cubic photon-vibration interactions (with respect to mechanical displacements) in a modulated driving field under conditions of adiabatic elimination of the optical field is studied. Based on the constructed bifurcation diagrams of the mechanical coordinate and the largest Lyapunov exponent as a function of the modulation amplitude, as well as power spectra, phase portraits and Poincare sections, regions of regular and chaotic dynamics of the optomechanical system are identified. It is also shown that for a certain modulation amplitude in the presence of all three types of interactions, chaotic dynamics of the mechanical resonator (oscillator) is realized, which is replaced by quasi-periodic oscillations in the absence of cubic interaction, and the system returns to chaotic behavior if only linear interaction remains. This non-monotonic dependence of chaotic dynamics on the order of nonlinearity originates from the interplay between parametric driving and effective potential reshaping and manifests that nonlinearity does not always enhance chaos. For an optomechanical system in a membrane-in-the-middle configuration, where only quadratic photon-vibration interaction is present, it is demonstrated that at small modulation amplitudes the mechanical oscillator exhibits quasi-periodic motion in each of the wells of a symmetric two-minimum potential, whereas large modulation amplitudes lead to chaotic motion, involving interwell transitions.

In this work, we study the quantum synchronization and quantum $\ensuremath{\phi}$ synchronization of two mechanical oscillators in a coupled optomechanical system. The oscillators are coupled to an optical cavity filled with a Kerr nonlinear medium and subjected to periodic modulation of the cavity detunings and driving amplitudes by a common driving field. Our results show that the quantum synchronization and quantum $\ensuremath{\phi}$ synchronization in nonlinear systems exhibit more favorable behaviors than in linear systems. In addition, we have investigated the performances of two synchronization measurements to various parameters by analyzing the sensitivity of $\ensuremath{\phi}$. Accordingly, perfect synchronization can be achieved under specific parameters by periodically modulating the cavity and driving field. Our findings could offer insights into other quantum effects and pave the way for studying quantum correlations.