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arXiv:1610.06007 · Physical Review A

Localization, quantum resonances, and ratchet acceleration in a periodically kicked PT -symmetric quantum rotator

Stefano Longhi

Published Jan 19, 2017• 36 citations
arXivHTMLPDF

Abstract

We consider wave transport phenomena in a $\mathcal{PT}$-symmetric extension of the periodically kicked quantum rotator model and reveal that dynamical localization assists the unbroken $\mathcal{PT}$ phase. In the delocalized (quantum resonance) regime, $\mathcal{PT}$ 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 $\mathcal{PT}$-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.

DOI
10.1103/physreva.95.012125

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We consider wave transport phenomena in a PT\mathcal{PT}PT-symmetric extension of the periodically kicked quantum rotator model and reveal that dynamical localization assists the unbroken PT\mathcal{PT}PT phase. In the delocalized (quantum resonance) regime, PT\mathcal{PT}PT 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 PT\mathcal{PT}PT-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.
We consider the ratchet dynamics in a PT\mathcal{PT}PT-symmetric Floquet quantum system with symmetric temporal (harmonic) driving. In the exact PT\mathcal{PT}PT-symmetry 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 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 broken-PT\mathcal{PT}PT-symmetry regime for the first-order resonance. Our results provide a 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.
We report the observation of high order resonances of the quantum δδδ-kicked accelerator using a BEC kicked by a standing wave of light. The signature of these resonances is the existence of quantum accelerator modes. For the first time quantum accelerator modes were seen near 1/4 and 1/3 of the Talbot time. Using a BEC enabled us to study the detailed structure of the modes and resonances which are related to the fractional Talbot effect. We present a general theory for this system and apply it to predict the behavior of the accelerator modes.
PT{\mathscr{PT}}PT -symmetry from Lindblad dynamics in a linearized optomechanical system
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The periodically kicked Rydberg atom displays quantum localization, features of which depend on the orientation and strength of the unidirectional kicks. They include scarring of the wave function, localization by cantori, and exponential localization in the regime of strong perturbation resembling dynamical localization. Using the semiclassical Herman-Kluk propagator we investigate the degree to which semiclassical dynamics can mimic quantum localization. While the semiclassical approximation has difficulties to reproduce the scarred wave functions, the exponential tail which is a typical signature of the dynamical localization is well represented in the case of strong classical diffusion. Also the localization by broken tori is observed in the semiclassical recurrence probability for short times but the deviation from the corresponding quantum dynamics becomes more pronounced for the long-time evolution.
In this thesis we investigate quantum resonant effects in the atom-optical ὁ-kicked accelerator. Using Floquet analysis, we theoretically study the time evolution of quantum systems which have a classical counterpart that exhibits chaotic dynamics. We introduce quantum resonance and quantum antiresonance features of the quantum ὁ -kicked rotor by setting the pulse period to an integer multiple of the half-Talbot time. The model is generalised to the atom-optical ὁ -kicked accelerator by considering thermal alkali atoms subject to a periodically pulsed standing wave potential formed from counter-propagating laser beams. The dynamics of the momentum distribution is analysed by evaluating the momentum moments and momentum cumulants. We derive analytic solutions for these observables for the ultracold and thermal limiting cases, and observe fractional quantum resonant phenomena. Simulations have been developed to examine the time evolution for individual momentum eigenstates, which we use to construct a non-interacting finite temperature gas, based upon a Monte Carlo method. We investigate the temperature dependence of the ὁ-kicked rotor, neglecting gravitational effects, and show that the atomic dynamics is highly sensitive to the initial momentum width of the gas. A generalisation of the model to quantify the transition between the ultracold and thermal temperature regimes of the atom-optical ὁ -kicked accelerator is examined using linear regression analysis. High order quantum resonance features are found to be sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. We assess the dependence of the ὁ -kicked accelerator upon gravitational acceleration, quantifying the width of the high order quantum resonance features, which we use to assess the prospect for precision measurement using a finite temperature gas.