Journal of Russian Laser Research, Volume 30, Number 2, 2009 CONTROLLED ACCELERATION OF A MODULATED QUANTUM BOUNCER Javed Akram, * Khalid Naseer, and Farhan Saif Department of Electronics Quaid-i-Azam University 45320 Islamabad, Pakistan * Corresponding author, e-mail: jvdakramqau @ gmail.com e-mail: Farhan.Saif @ fulbrightmail.org Abstract Cold atoms bouncing on a modulated atomic mirror exhibit dynamic localization and acceleration subject to modulated strength. We explain the characteristics of acceleration using accelerated map- ping and define control parameters. We show that the effective Planck’s constant plays a vital role in limiting overall linear growth of accelerated atoms with time. For large values of the effective Planck’s constant, the atomic quantum accelerated is seized if the localization window overlaps the accelerated window. Keywords: Fermi accelerator, quantum bouncer, accelerating mapping, dynamical localization, quan- tum mapping and unbounded acceleration, dynamical delocalization. 1. Introduction A classical system subjected to time-periodic modulation, in general, becomes globally chaotic at increasing modulation strengths and absorbs energy from the external field in a diffusive way. However, in the corresponding quantum domain the diffusive dynamics may be suppressed by quantum interference effects. It is a manifestation of the dynamical localization phenomenon in the system, which is an analog of the Anderson localization of solid state physics. The phenomenon has been discussed in model systems in quantum chaos, such as kicked rotator [1], modulated quantum bouncer [2], atoms in modulated standing wave fields [3], ion in a Paul trap [4,5], and molecular systems in the presence of electric and magnetic fields [6]. Dynamical localization is a very general phenomenon in periodically driven systems [7, 8]. The delocalization in such quantum systems is a purely quantum effect since the long-time unbounded propagation is not related to the corresponding classical diffusion [9, 10]. The Fermi accelerator or modulated quantum bouncer is a system well-investigated in studying the classical Hamiltonian chaos and its manifestations in quantum-mechanical systems [11]. Its dynamics is described by the standard map, which explains that the size of the stochasticity in the phase space of the map increases with the driving strength, and when the latter is sufficiently strong, the global diffusion takes place. However, for a particular set of initial data in the phase space and conditions on modulation strength [12], the onset of accelerator modes takes place [13, 14]. In recent experiments [15,16], atoms move in a direction parallel to the gravitational acceleration in a quantum bouncer. A fraction of the atoms may accelerate in the presence of a driving field, at a rate Manuscript submitted by the authors in English first on February 18, 2009 and in final form on March 19, 2009. 1071-2836/09/3002-0157 c  2009 Springer Science+Business Media, Inc. 157