Ratchet current in a $\mathcal{PT}$-symmetric Floquet quantum system with symmetric sinusoidal driving

TL;DR

This paper demonstrates how symmetric sinusoidal driving in a $ ext{PT}$-symmetric Floquet quantum system can generate and control long-lasting ratchet currents, revealing new non-Hermitian mechanisms and resonance effects.

Contribution

It introduces the concept of non-Hermitian resonant currents driven by symmetric harmonic driving, highlighting the role of exceptional points and symmetry breaking in current generation.

Findings

Resonant currents are generated in the exact $ ext{PT}$ phase with symmetric driving.

The resonant current peaks when the imaginary and real parts of the potential are equal.

Directed currents increase linearly with the driving frequency due to symmetry breaking mechanisms.

Abstract

We consider the ratchet dynamics in a $\mathcal{PT}$-symmetric Floquet quantum system with symmetric temporal (harmonic) driving. In the exact $\mathcal{PT}$ phase, for a finite number of resonant frequencies, we show that the long-lasting resonant currents can be generated with the symmetric time-continuous driving, which would otherwise forbid the generation of directed currents in the Hermitian limit. Such a non-Hermitian resonant current can be enhanced by increasing the non-Hermitian level, and in particular, the resonant current peaks (reaches the largest negative value) under the condition that the imaginary part of the potential depth is equal to the real part, at which the stable asymptotic current occurs owing to exceptional points (EPs) mechanism. Moreover, the directed currents originating from the symmetry breaking are reported, which increase linearly with the driving frequency, the mechanism behind which is that the cutoff of the momentum eigenstates for the Floquet state with maximum imaginary quasienergy increases as the driving frequency is continuously increased. We also present a non-Hermitian three-level model that can account for the resonant currents and gives surprisingly good agreement with direct numerical results for weak driving, even in the $\mathcal{PT}$-broken regime for the first-order resonance. Our results provide a new means of realizing the non-Hermiticity-controlled ratchet current by means of a smooth continuous driving, previously used only to generate currents in Hermitian systems.