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.

11 pages, 7 figures

References in corpus (14)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Nonlinear PT-symmetric Optical Structures
• PT-Symmetric Phonon Laser
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• $\mathcal{P}\mathcal{T}$-Symmetry-Breaking Chaos in Optomechanics
• Steady-state Mechanical Squeezing in an Optomechanical System via Duffing Nonlinearity
• PT-Symmetric Wave Chaos
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Realizing PT-symmetric non-Hermiticity with ultra-cold atoms and Hermitian multi-well potentials
• From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
• $\mathcal{P}\mathcal{T}$-symmetric mode-locking
• Quantum Resonances and Ratchets in Free-Falling Frames
• Talbot self-imaging in $\mathcal{P}\mathcal{T}$-symmetric complex crystals

Cited by in corpus (6)

• Non-Hermitian Maryland Model
• Directed momentum current induced by the PT-symmetric driving
• 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
• Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
• Pseudoclassical dynamics of the kicked top
• A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model