We investigate the dynamics of multi-mode optical systems driven by two-photon processes and subject to non-local losses, incorporating quantum noise at the Gaussian level. Our findings show that the statistics from a single Gaussian quantum trajectory exhibit emergent thermal equilibrium governed by an Ising Hamiltonian encoded in the dissipative coupling between modes. The driving strength sets the system’s effective temperature relative to the oscillation threshold. Given the ultra-short time scales typical of all-optical devices, our study demonstrates that such multi-mode optical systems can operate as ultra-fast Boltzmann samplers, paving the way toward the realization of efficient hardware for combinatorial optimization, with promising applications in machine learning and beyond.
Month: December 2024
Non-Abelian Quantum Walk and Entanglement
https://arxiv.org/abs/2412.02429
Non-Abelian evolution is a landmark in modern theoretical physics. However, whether non-commutative dynamics significantly impact the control of entanglement and transport in quantum systems is an open question. Here, we propose to utilize non-Abelian Thouless pumping in one-dimensional discrete-time quantum walks in lattices with degenerate Bloch bands. We show how the interplay of non-commutativity and topology enables geometrically protected quantum coins and shift operators. Different classes of tunable protected quantum walks arise by composing different non-Abelian pumping cycles. Surprisingly, the walks break parity symmetry and generate a dynamic process described by a Weyl-like equation. The amount of entanglement can be varied by acting on the initial conditions. The asymptotic statistical distribution and features are determined by closed-form analytical expressions and confirmed numerically.
Mathstodon https://mathstodon.xyz/@nonlinearxwaves/113610374997139049