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arXiv:1409.4454

Towards AC-induced optimum control of dynamical localization

F. Revuelta, Ricardo Chacón, F. Borondo

Published Sep 15, 2014• 0 citations
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Abstract

It is shown that optimum control of dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic forces having equidistant zeros depends on the \textit{impulse} transmitted by the external force over half-period rather than on the force amplitude. This result provides a useful principle for optimally controlling dynamical localization in general periodic systems, which is capable of experimental realization.

DOI
10.48550/arxiv.1409.4454

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It is shown that optimum control of dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic forces having equidistant zeros depends on the \textit{impulse} transmitted by the external force over half-period rather than on the force amplitude. This result provides a useful principle for optimally controlling dynamical localization in general periodic systems, which is capable of experimental realization.
It is shown that dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic modulations having equidistant zeros depends on the impulse transmitted by the external modulation over half-period rather than on the modulation amplitude. This result provides a useful principle for optimally controlling dynamical localization in general periodic systems, which is capable of experimental realization.
The scope of the present publication-based thesis on periodically forced optical lattices is twofold: In the first part, the reader is introduced to the main concepts required to formulate the central results of this thesis, and a review is given of landmark papers on coherently controlling ultracold atoms by subjecting them to periodic forces. The second part provides the author's own results of original research on the subject and consists of four publications and a preprint. It is shown how ultracold atoms in optical lattices can be used as strong-field simulators, dynamic localization in optical lattices are described in detail, and multiphoton-like processes are studied. A generalized acceleration theorem for spatiotemporal Bloch waves is developed and used to enable a controlled wave-packet manipulation in optical lattices.
We develop a time-optimal approach to force sensing using a Bose-Einstein condensate in a shaken optical lattice. Optimal control protocols are derived from a Fisher information framework and yield optimal dynamics that spontaneously organize in intereferometer-like structures, where multiple interferences combine to maximize sensitivity. We analyse how measurement precision scales with control time and how the finite momentum dispersion of the condensate changes the optimal dynamics, observing an abrupt change of conformation from single- to double-folded interference structures for robust controls. The protocols are implemented experimentally for cold atoms subjected to inertial and magnetic forces, demonstrating high sensitivity and robustness. Our approach establishes a general route to time-optimal quantum sensing beyond standard interferometric architectures, applcable across all quantum platforms.
In this work, we study finite-time effects in ultracold atomic systems by considering time-dependent modulations with variable waveforms and durations. These two characteristics can be controlled by adjusting only a single parameter. For arbitrarily short pulses, our model recovers the paradigmatic kicked rotor while maintaining the impulse transmitted per period and unit amplitude constant. Furthermore, we demonstrate that finite-time effects have a profound impact on dynamical localization, a result that cannot be captured by the δ-kicked-rotor model. Through a detailed analysis of the effects of different modulation amplitudes, periods, and waveforms, we identify the conditions for which dynamical localization is significantly enhanced. We show that the strength of dynamical localization increases sharply as the system approaches the δ-kicked-rotor limiting case. Moreover, we establish the existence of an optimal value of the period that maximizes dynamical localization for given values of the amplitude and shape parameter.
We report a direct observation of dynamical localization. This effect is a quantum suppression of diffusion in a system that is classically chaotic. Our experiment measures the momentum transferred from a modulated standing wave of a near-resonant laser to a sample of ultracold atoms and is a realization of a periodically driven rotor. The conceptual simplicity and experimental control over the time dependent Hamiltonian make this system an ideal testing ground for the predictions of quantum chaos.