Localization, quantum resonances and ratchet acceleration in a periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric quantum rotator

Abstract

We consider wave transport phenomena in a $\mathcal{P}\mathcal{T}$-symmetric extension of the periodically-kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\mathcal{P}\mathcal{T}$ phase. In the delocalized (quantum resonance) regime, $\mathcal{P}\mathcal{T}$ symmetry is always in the broken phase and ratchet acceleration arises as a signature of unidirectional non-Hermitian transport. An optical implementation of the periodically-kicked $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian, based on transverse beam propagation in a passive optical resonator with combined phase and loss gratings, is suggested to visualize acceleration modes in fractional Talbot cavities.

arXiv comment11 pages, 7 figures

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• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Non-Hermitian Maryland Model
• Directed momentum current induced by the PT-symmetric driving
• Super-exponential diffusion in nonlinear 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
• PT-symmetric quantum graphs
• Effective protection of quantum coherence by non-Hermitian driving
• Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
• Pseudoclassical dynamics of the kicked top
• Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime
• Spin Josephson effects of spin-orbit-coupled Bose-Einstein condensates in a non-Hermitian double well
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors
• Non-monotonic diffusion rates in atom-optics Lévy kicked rotor
• Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box
• A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• A non-Hermitian PT-symmetric kicked top
• Dynamics of wavepackets and entanglement in many-body kicked rotors under quantum resonance