Shortcut to synchronization in classical and quantum systems

TL;DR

This paper introduces a method for rapidly achieving synchronization in classical and quantum systems using tailored transient drives, addressing the challenge of speed in nonlinear quantum control.

Contribution

It develops an inverse engineering approach for fast synchronization in classical systems and adapts it for quantum systems considering finite-size effects.

Findings

Accelerated synchronization in classical Van der Pol oscillator.

Effective quantum control with density matrix close to synchronized state.

Raises questions about quantum speed limits in nonlinear systems.

Abstract

Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization regime more quickly. We exemplify an inverse engineering method to solve this issue on the classical Van der Pol oscillator. This approach cannot be directly transposed to the quantum case as the system is no longer point-like in phase space. We explain how to adapt our method by an iterative procedure to account for the finite-size quantum distribution in phase space. We show that the resulting driving yields a density matrix close to the synchronized one according to the trace distance. Our method provides an example of fast control of a nonlinear quantum system, and raises the question of the quantum speed limit concept in the presence of nonlinearities.