Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous

TL;DR

This paper introduces a novel quantum system where a harmonic oscillator is driven by spin measurement-induced kicks, exhibiting Floquet-like dynamics with crystalline and chaotic features without a classical counterpart.

Contribution

It presents an analytically solvable model of a Floquet-like quantum system driven by measurement, revealing complex phase-space structures and chaos without classical analogs.

Findings

Observed crystalline and quasicrystalline phase-space structures

Identified resonances and chaotic behavior in the system

Demonstrated analytical solvability of the dynamics

Abstract

We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancila is dynamically entangled with the oscillator position, while the background Hamiltonian remains static. The dynamics of this system is determined in closed analytical form, allowing for the evaluation of a properly defined Loschmidt echo, ensemble averages, and phase-space portraits. As in the case of standard Floquet systems we observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior, however, not originating from any classically chaotic system.