Quantum Emulation with Classical Waves: New Frontiers in Open-System Dynamics

We present a platform for quantum emulation using fully classical wave dynamics, with particular emphasis on open-system evolution and decoherence. The central observation is that weakly nonlinear, narrowband surface-gravity wave envelopes propagating in a controlled background flow obey a paraxial evolution law that is mathematically equivalent to the time-dependent Schrödinger equation, with the roles of time and propagation distance interchanged. Exploiting this correspondence, we realize a Lindblad-type evolution by mapping the non-unitary dynamics of a density matrix onto an ensemble of unitary evolutions generated by two effective Hamiltonians. Experimentally, these evolutions are implemented by reversing the direction of a homogeneous flow, which produces opposite linear potentials, while momentum-displaced evolutions are achieved through controlled carrier-frequency offsets (“kicks”) applied to the initial wave packet.

We demonstrate the approach using the Wigner continuous-measurement model of decoherence for a free particle, initialized in a Schrödinger-cat superposition of two Gaussian wave packets. From measured surface-elevation time traces, we reconstruct the complex wave envelope using a Hilbert-transform technique and construct the corresponding analog density matrix. This allows us to directly observe the progressive suppression of off-diagonal coherence and to quantify decoherence through the decay of state purity over successive effective time steps, in quantitative agreement with numerical simulations.

Finally, we outline near-term extensions toward quantum simulation and quantum-information emulation using optical classical waves, including spatial-mode and polarization analogs, as well as pulsed-laser systems that naturally support discrete-time, rapid Hamiltonian reconfigurability, and scalable ensemble averaging. Together, these directions point toward a practical and flexible route for emulating broad classes of non-Hermitian, imaginary-time, and dissipative quantum dynamics using controllable classical wave platforms.