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Physical Review A

Transient phase-space localization

C. L. Stokely, F. B. Dunning, Carlos O Reinhold, Arjendu K. Pattanayak

Published Jan 16, 2002• 23 citations
Publisher

Abstract

We show that dynamics can, in general, be used to enhance the coherence of a Hamiltonian ensemble and we analyze the transient coherence using the coarse-grained entropy. We illustrate this concept using a Rydberg atom subject to an impulsive momentum transfer or ``kick.'' Classical simulations predict that the wave packet generated by the kick undergoes strong transient phase-space localization, which forms an excellent starting point for its further control and manipulation. Moreover, we show that such localized states can be ``trapped'' for extended periods using a train of subsequent kicks.

DOI
10.1103/physreva.65.021405

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We show that dynamics can, in general, be used to enhance the coherence of a Hamiltonian ensemble and we analyze the transient coherence using the coarse-grained entropy. We illustrate this concept using a Rydberg atom subject to an impulsive momentum transfer or kick.'' Classical simulations predict that the wave packet generated by the kick undergoes strong transient phase-space localization, which forms an excellent starting point for its further control and manipulation. Moreover, we show that such localized states can be trapped'' for extended periods using a train of subsequent kicks.
The field of coherent control has today been seeing significant progress, in a wide array of physical systems. One such system is the Rydberg atom. The long lifetime, strong dipole interactions, multiple degrees of freedom, and simple atomic structure make Rydberg atoms particularly appealing for experiments involving coherent control. The same properties have led to the exploration of Rydberg atoms as candidates for quantum information storage, processing and retrieval. Quantum information processing is a particular application of coherent control. Rather than being disparate subjects of study, coherent control of Rydberg atoms and processing of information stored as phase in different Rydberg levels are two sides of the same coin. In this dissertation, we experimentally characterize the effect of a half-cycle pulse on the phases of the states of a Rydberg wave packet and their mutual coherence. This has bearing both on our ability to control the states of the atom and on our ability to measure the information stored as quantum phase. We observe delay dependent phase shifts and losses of coherence. Despite a loss of information due to transfer of quantum amplitude to states outside the data register, we demonstrate partial retrieval of that information by the application of a second half cycle pulse. We also present an essential states model of the interaction, and we compare results from the model to experimental features observed. Although the particulars may vary, the concepts involved are quite general and may be applied to multilevel systems other than Rydberg atoms.
We demonstrate that strong transient phase-space localization can be achieved by the application of a single impulsive ``kick'' in the form of a short (600 ps) unidirectional electric-field pulse to a strongly polarized, quasi-one-dimensional Rydberg atom. The underlying classical dynamics is analyzed and it is shown that phase-space localization results from a focusing effect analogous to rainbow scattering. Moreover, it is shown that the essential features of the classical analysis remain valid in a quantum-mechanical treatment of the system in terms of its phase-space Husimi distribution. The degree of phase-space localization is characterized by the coarse-grained Renyi entropy. Transient phase-space localization is demonstrated experimentally using extreme redshifted m=0m=0m=0 potassium Stark states in the n=351n=351n=351 manifold and a short probe pulse. The experimental data are in good agreement with theoretical predictions. The localized state provides an excellent starting point for further control and manipulation of the electron wave packet.
Rydberg wave packets generated by a single half-cycle pulse (HCP) interacting with a stationary Rydberg state periodically localize within a narrow region in both momentum and coordinate space (i.e., phase space). This property is the key to shaping and manipulating wave packets. We investigate the dependence of this transient localization and focusing on the principal quantum number n and on the strength of the ultrashort HCP (``kick strength,'' $\ensuremath{\Delta}p).$ It is shown that the localization in momentum space of the wave packet, quantified by the momentum width, obeys a universal scaling rule which is controlled by an effective Planck constant ${\ensuremath{\Elzxh}}_{\mathrm{eff}}.$ Maximum focusing is reached in the classical limit $({\ensuremath{\Elzxh}}_{\mathrm{eff}}\ensuremath{\rightarrow}0).$
We study the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. This stroboscopic setting provides a controllable model of dephasing in driven quantum systems. Using a momentum-space formulation, we show that the evolution is governed by an accumulated phase whose structure determines the spreading of the wave packet. We find that the phase kicks strongly suppress ballistic transport and induce diffusion at long times. We derive an explicit analytical expression for the diffusion coefficient as a function of the correlation length, in excellent agreement with numerical simulations. Our results uncover a simple mechanism by which spatially correlated phase noise controls quantum transport, and provide a quantitatively testable prediction for diffusion in periodically driven lattice systems. Possible experimental realizations in cold-atom platforms are discussed.