Coherent Accelereation of Matter Waves

Abstract

The present work is based on atom optics Fermi accelerator that is realized via modulated gravitational cavity. We reported Fermi accelerator model and found Fermi acceleration both in an ensemble of classical particles and a quantum wave packet. Classically we found that diffusion of the ensemble is sharply reduced for modulation strengths within acceleration windows. Following each acceleration window, the momentum dispersion grows linearly with modulation strength. We interpret the sharply reduced value of dispersion as non dispersive, coherent acceleration of the atomic sample above atomic mirror. This coherent acceleration restricts the momentum space variance p, representing the absence of diffusive dynamics in the ensemble. Aspect ratios of the phase space give us a unique condition for the classification of accelerated, ballistic and chaotic dynamics in non linear systems in classical domain. Transition from accelerated mode to chaotic dynamics can be controlled by controlling the strength of modulation. In quantum domain in addition to modulation strength there is another limit which is controlled by quantum laws. Besides the Heisenberg uncertainty principle restricts the phase-space size of the initial atomic wave packet which results in coherent acceleration occurring on top of a diffusive background. Complete time-evolved wave packet is composed of a series of sharply-peaked Gaussian distributions is superposed to a broad background due to diffusive dynamics. We find that within the window of acceleration the atomic wave packet displays a linear growth in the square of the momentum variance and in the coordinate space variance. For modulation strengths within the acceleration window, growth in the square of the momentum variance displays oscillations of increasing periodicity whereas the variance in coordinate space follows with a phase difference of 1800. The out-of-phase oscillatory evolutions of p2 and z indicate a breathening of the wave packet and a signature of the coherence in accelerated dynamics.