Mapping as a probe for heating suppression in periodically driven quantum many-body systems

TL;DR

This paper demonstrates that certain periodically driven quantum many-body systems can be completely free of heating by mapping them onto time-independent systems, revealing conditions for heating suppression and resonance phenomena.

Contribution

The authors construct an exact space-time mapping showing that some driven quantum systems are inherently free of heating, a novel insight into controlling energy absorption in Floquet systems.

Findings

Exact mapping to time-independent systems proves absence of heating.

Heating rate exhibits Fano resonances near critical driving frequencies.

Destructive interference explains zero-heating conditions.

Abstract

Experiments on periodically driven quantum systems have effectively realized quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessible in static condensed matter systems. Although the Floquet quasi-Hamiltonians are time-independent, however, these continuously driven systems can still suffer from heating due to a secular growth in the expectation value of the time-dependent physical Hamiltonian. Here we use an exact space-time mapping to construct a class of many-body systems with rapid periodic driving which we nonetheless prove to be completely free of heating, by mapping them exactly onto time-independent systems. The absence of heating despite the periodic driving occurs in these cases of harmonically trapped dilute Bose gas because the driving is a certain periodic but anharmonic modulation of the gas's two-body contact interaction, at a particular frequency. Although we prove that the absence of heating is exact within full quantum many-body theory, we then use mean-field theory to simulate 'Floquet heating spectroscopy' and compute the heating rate when the driving frequency is varied away from the critical value for zero heating. In both weakly and strongly non-linear regimes, the heating rate as a function of driving frequency appears to show a number of Fano resonances, suggesting that the exactly proven absence of heating at the critical frequency may be explained in terms of destructive interferences between excitation modes.