CHINESE JOURNAL OF PHYSICS VOL. 39, NO. 4 AUGUST 2001 Atomic Evolution in a Driven Gravitational Cavity Farhan Saif Department of Electronics, Quaid-i-Azam University, Islamabad 45320, Pakistan (Received November 12, 2000) We propagate an atomic wavepacket in a gravitational cavity which is modulated by means of an external periodic driving force. We show that in classical evolution it displays classi- cal chaos, whereas in the quantum domain the wavepacket exhibits dynamical localization. Moreover, we also find dynamical revivals in the quantum evolution and prove that this is a generic characteristics of all driven systems. PACS. 03.65.Bz – Foundations, theory of measurement, miscellaneous theories. PACS. 05.45.+b – Theory and models of chaotic systems. PACS. 72.15.Rn – Quantum localization. I. Introduction The presence of periodically vibrating surfaces in a system poses interesting questions about its characteristics. In general such systems possess more than one degree of freedom and, therefore, exhibit chaotic evolution in both the classical and quantum domains [1, 2]. In this paper we consider optical surfaces which undergo periodic vibrations as a function of time and study the dynamics of atoms on them. Total internal reflection of laser light produces an evanescent wave field on the dielectric surface. Atoms moving towards this field experience an exponentially increasing force and are reflected back [3]. We provide a periodic modulation to the evanescent wave field by means of an acousto-optic modulator [4]. Atoms, bouncing under gravity on the modulated evanescent wave field, have a bounded motion. Therefore such a system is called a modulated gravitational cavity or Fermi accelerator [5] for the bouncing atoms. This system is of particular interest in the field of atom optics [6]. We show that, in the long time evolution which consists of many bounces of the atoms, they display dynamical localization. This localization of atoms is a prototype of the Anderson localization, as observed in solid state physics [7]. Moreover, the atoms exhibit the presence of dynamical revivals [8, 9]. We prove that this property is generic for all periodically modulated systems. Our paper is arranged as follows: In section II we explain the model of the experiment. In section III we discuss the characteristics of dynamical localization, whereas we discuss the presence of dynamical revivals in section IV and give an analytical expression for the revival time. In section V, we summarize the results. 311 c ° 2001 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA