Bose-Einstein Condensate in Driven Parabolic Optical Lattice

Abstract

Over the last two decades, ultra-cold atoms in optical lattices, have become an important tool to simulate correlated many-body systems. These systems manifest a great deal of control via external modulating elds. In this thesis, we explain the dynamics of ultra-cold atoms in periodic potentials in the presence of the external forcing based on presently available experiments. The dynamics of ultra-cold atoms in parabolic optical lattices display two prominent dynamical modes, that are discerned as the Bloch and the Dipole oscillations. We discuss both these dynamical modes in detail as the eigenstates interlace between extended to localized states. In addition, we developed a general theoretical analysis of the physical system in the presence of periodic in time modulation. The e ective system shows all the characteristics of a static system and a gradual transition due to the presence of modulation. This strategy helps us to understand necessary dynamical interaction regimes. Moreover, we nd that for the exact resonance case the e ective mass becomes in nite as the group velocity approaches a maximum value, freezing the dispersion and narrowing the phase space dynamics. In addition, we have studied how the inter-band transition due to the external periodic force results in quantum dynamic localization. The dynamics of ultra-cold atoms in an amplitude-modulated optical lattice with harmonic con nement shows the existence of dynamical localization. This property is a signature of quantum supremacy over classical counterpart that manifests itself as the cold atoms exhibit quantum suppression of classical chaos in the dynamical system. The exponential localiza tion takes place both in momentum as well as in coordinate space within certain windows on modulation amplitude. We demonstrate that inter-band transitions, taking place due to the amplitude modulation in an optical lattice, play an important role in controlling the local ization of matter waves. Our obtained results can be generalized to other dynamical systems and are experimentally realizable as we consider the values of parameters from present-day available experiments