Acceleration Modes in Fermi Accelerator

We explain Fermi acceleration of particles bouncing in a gravitational field and experiencing a force due to a modulated evanescent laser field. The acceleration strongly depends upon the initial conditions in the phase space and certain modulation amplitude. We study the accelerated modes by the Poincaré surface of sections and Lyapunov exponents. Furthermore, we identify the initial areas of the phase space that support accelerated dynamics and write a mapping for accelerated dynamics. We show that a distinction between accelerated and chaotic evolutions can be made with the help of the aspect ratio. The Lyapunov exponent shows that the accelerated mode supports ordered evolution.