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Mathematical Problems in Engineering

Acceleration of Material Waves in Fermi Accelerator

Javed Akram, Khalid Naseer, Inam ur Rehman, Farhan Saif

Published Jan 1, 2009• 6 citations
Publisher

Abstract

Cold Atoms bouncing on modulated atomic mirror exhibits acceleration and dynamical localization subject to modulated strength. We explain characteristics of acceleration and define control parameters in terms of effective Planck′s constant. We show that the effective Planck′s constant plays a vital role in limiting classical‐like overall linear growth of the variance of accelerated atoms with time. For large values of the effective Planck′s constant the atomic quantum acceleration is seized as localization window overlaps the accelerated window.

DOI
10.1155/2009/246438

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Cold Atoms bouncing on modulated atomic mirror exhibits acceleration and dynamical localization subject to modulated strength. We explain characteristics of acceleration and define control parameters in terms of effective Planck′s constant. We show that the effective Planck′s constant plays a vital role in limiting classical‐like overall linear growth of the variance of accelerated atoms with time. For large values of the effective Planck′s constant the atomic quantum acceleration is seized as localization window overlaps the accelerated window.
Cosmic rays are deemed to be generated by a process known as "Fermi acceleration" in which charged particles scatter against magnetic fluctuations in astrophysical plasmas. The process itself is, however, universal, has both classical and quantum formulations, and is at the basis of dynamical systems with interesting mathematical properties, such as the celebrated Fermi-Ulam model. Despite its effectiveness in accelerating particles, Fermi acceleration has so far eluded unambiguous verifications in laboratory settings. Here, we realize a fully controllable Fermi accelerator by colliding ultracold atoms against engineered movable potential barriers. We demonstrate that our Fermi accelerator, which is only 100 μm in size, can produce ultracold atomic jets with velocities above 0.5 m/s. Adding dissipation, we also experimentally test Bell's general argument for the ensuing energy spectra, which is at the basis of any model of cosmic ray acceleration. On the one hand, our Letter effectively opens the window to the use of cold atoms to study phenomena relevant for high energy astrophysics. On the other, the performance of our Fermi accelerator is competitive with those of best-in-class accelerating methods used in quantum technology and quantum colliders, but with substantially simpler implementation no fundamental physics limit.
Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose–Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck’s constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 ° out of phase with the initial state.