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arXiv:2410.22495 · The Journal of Chemical Physics

Noise-induced synchronization in coupled quantum oscillators

Eric R. Bittner, Bhavay Tyagi

Published Mar 12, 2025• 10 citations
arXivHTMLPDF

Abstract

We consider the quantum dynamics of a pair of coupled quantum oscillators coupled to a common correlated dissipative environment. The resulting equations of motion for both the operator moments and covariances can be integrated analytically using the Lyapunov equations. We find that for fully correlated and fully anti-correlated environments, the oscillators relax into a phase-synchronized state that persists for long-times when the two oscillators are nearly resonant and (essentially) forever if the two oscillators are in resonance. We identify an exceptional point that indicates the onset of broken symmetry between an unsynchronized and synchronized dynamical phase of the system as correlations within the environment are increased. We also show that the environmental noise correlation leads to quantum entanglement, and all the correlations between the two oscillators are purely quantum mechanical in origin. This work provides a robust mathematical foundation for understanding how long-lived exciton coherences can be linked to vibronic correlation effects.

DOI
10.1063/5.0246275

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We consider the quantum dynamics of a pair of coupled quantum oscillators coupled to a common correlated dissipative environment. The resulting equations of motion for both the operator moments and covariances can be integrated analytically using the Lyapunov equations. We find that for fully correlated and fully anti-correlated environments, the oscillators relax into a phase-synchronized state that persists for long-times when the two oscillators are nearly resonant and (essentially) forever if the two oscillators are in resonance. We identify an exceptional point that indicates the onset of broken symmetry between an unsynchronized and synchronized dynamical phase of the system as correlations within the environment are increased. We also show that the environmental noise correlation leads to quantum entanglement, and all the correlations between the two oscillators are purely quantum mechanical in origin. This work provides a robust mathematical foundation for understanding how long-lived exciton coherences can be linked to vibronic correlation effects.
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously synchronize when they are strongly coupled to a common bosonic quantum dissipative environment at zero temperature, in the absence of any driving mechanism. To do so, we compute the dynamics of the oscillators with an exact master equation obtained from a path integral formalism. Above some value of the system-environment coupling strength, we observe numerically a strongly reduced damping and a frequency locking in the dynamics of the oscillators. Beyond the synchronization mechanism, we also describe the rich phenomenology of the dynamics in the model and notably identify the additional emergence of a regime with long-lived oscillations.
We present a concise review and perspective on noise-induced synchronization and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signaling a collapse of the mode basis and the emergence of non-dissipative stabilized dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter, protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson-Kubo model, where the effective fluctuation strength scales as σ2(1±ξ)σ^2(1 \pm ξ)σ2(1±ξ), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio σ/γ σ/ γσ/γ. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens synchronized pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise-though classically stochastic-can organize quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronization in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.
We present a concise review and perspective on noise-induced synchronisation and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signalling a collapse of the mode basis and the emergence of non-dissipative stabilised dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter–protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson–Kubo model, where the effective fluctuation strength scales as σ2(1±ξ), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio σ/γ. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens' synchronised pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise–though classically stochastic–can organise quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronisation in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.