Quantum Neimark-Sacker bifurcation

TL;DR

This paper explores a quantum analogue of the Neimark-Sacker bifurcation in an open quantum dimer system, revealing transitions in quantum state distributions and spectral properties akin to classical torus bifurcations.

Contribution

It introduces the concept of a quantum Neimark-Sacker bifurcation using a periodically modulated open quantum dimer model, connecting quantum dynamics with classical bifurcation phenomena.

Findings

Quantum system shows transition from unimodal to bagel-shaped distributions.

Spectral properties of Floquet map exhibit eigenvalues approaching the unit circle.

Dynamics on 'quantum torus' can be quantified by rotation number.

Abstract

Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated open quantum dimer model, we report and investigate a quantum Neimark-Sacker bifurcation. Its classical counterpart is the birth of a torus (an invariant curve in the Poincar\'{e} section) due to instability of a limit cycle (fixed point of the Poincar\'{e} map). The quantum system exhibits a transition from unimodal to bagel shaped stroboscopic distributions, as for Husimi representation, as for observables. The spectral properties of Floquet map experience changes reminiscent of the classical case, a pair of complex conjugated eigenvalues approaching a unit circle. Quantum Monte-Carlo wave function unraveling of the Lindblad master equation yields dynamics of single trajectories on "quantum torus" and allows for quantifying it by rotation number. The bifurcation is sensitive to the number of quantum particles that can also be regarded as a control parameter.