A quantum analog of Huygens’s clock; noise-induced spontaneous synchronization

Eric Bittner University of Houston

We investigate the quantum dynamics of coupled quantum oscillators interacting with a shared, correlated dissipative environment. The equations of motion for operator moments and covariances are analytically solvable using the Lyapunov equations. Our results reveal that the oscillators relax into a phase-synchronized state under fully correlated or fully anti-correlated environmental noise. This synchronization persists for extended durations when the oscillators are nearly resonant and can last indefinitely when they are in exact resonance. The underlying mechanism is tied to the symmetry of the Lindblad dissipator, which induces firm damping in some areas of the state space and underdamped in others. In the extreme cases of fully correlated or fully anti-correlated environments, specific regions of the state space become entirely decoupled from environmental influence. Additionally, we demonstrate that environmental noise correlations lead to quantum entanglement, with all correlations between the oscillators arising purely from quantum mechanical effects. This work establishes a robust mathematical framework for understanding the connection between long-lived exciton coherences and vibronic correlation effects.

[1] E. R. Bittner, H. Li, S. Shah, C. Silva-Acuna, and A. Piryatinski. Correlated noise enhancement of coherence and fidelity in coupled qubits. Philosophical Magazine, pages 1–17, 2024.

[2] E. R. Bittner and B. Tyagi. Noise-induced synchronization in coupled quantum oscillators. arXiv preprint arXiv:2410.22495, 2024.

[3] B. Tyagi, H. Li, E. R. Bittner, A. Piryatinski, and C. Silva-Acuna. Noise-induced quantum synchronization and entanglement in a quantum analogue of Huygens’ clock. The Journal of Physical Chemistry Letters, 15:10896–10902, 2024.