# Directed momentum current induced by the PT-symmetric driving

## TL;DR

This paper studies how PT-symmetric driving induces directed momentum currents in a quantum kicked rotor, revealing phase transitions, staircase growth, and quantized acceleration rates, supported by theoretical and numerical analysis.

## Contribution

It introduces a novel PT-symmetric potential in the quantum kicked rotor, analyzing the resulting phase transition and momentum current behavior, including quantized acceleration rates.

## Key findings

- Complex quasi-energy indicates PT symmetry breaking.
- Momentum current exhibits staircase growth near phase transition.
- Above the transition, the current increases linearly with quantized acceleration.

## Abstract

We investigate the directed momentum current in the quantum kicked rotor model with $\mathcal{PT}$ symmetric deriving potential. For the quantum non-resonance case, the values of quasi-energy become to be complex when the strength of imaginary part of the kicking potential exceeds \textbf{a} threshold value, which demonstrates the appearance of the spontaneous $\mathcal{PT}$ symmetry breaking. In the vicinity of the phase-transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasi-energy are significantly large. Above the phase-transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.