Directed momentum current induced by the PT-symmetric driving

Abstract

We investigate the directed momentum current in the quantum kicked rotor model with $\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}$ 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.

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Cited by in corpus (6)

• Non-Hermitian Maryland Model
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Dynamics of wavepackets and entanglement in many-body kicked rotors under quantum resonance