Many-body physics of interacting bosons in optical lattice

Abstract

This thesis addresses the many-body physics of ultra-cold bosons loaded in optical lattices. Ultracold atoms in an external trap has received most attention from both experimental and theoretical research as it is considered as the ideal testbed to study the rich many-body physics. The existing mean-field Gross-Pitaevskii method is inadequate to probe the highly correlated and strongly interacting atoms in optical lattice. To solve the many-body Schrödinger equation, we use multi configurational time-dependent Harte method for bosons (MCTDHB) which is an ab-initio many-body calculation. This thesis can be divided into three different parts. A quick overview of optical lattices is provided in the first section. In addition, the formulation of the MCTDHB method is explained in detail. The next section of the thesis comprises time-independent many-body calculations of bosons in an optical lattice. Bosons exhibit distinct phases in an optical lattice. Because of quantum fluctuations, quantum phase transitions can occur even at absolute zero. We have characterized those phases utilizing Shannon information entropy and Glauber normalized correlation measures. The time-dependent many-body theory is the subject of the last part of the thesis. MCTDHB is an efficient theoretical tool to study the dynamical evolution of the interacting bosons in the optical lattice. Here we utilize MCTDHB to study the quench dynamics and to address whether thermalization and statistical relaxation is ubiquitous in nature. To study the time dynamics, we have quenched the system by manipulating the interaction strength or the lattice depth and studied different dynamical measures. Bosons tunnelling in a double well potential are also discussed in this thesis. Self-trapping is seen at a moderate interaction regime, whereas Josephson oscillation is observed at non-interacting limit. Furthermore, in the strong-interaction regime, we found a unique phase of tunneling dynamics which was not observed in the mean-field scenario. Additionally, we have addressed the path from the SF phase to the MI phase by directly monitoring the change in order, disorder, and complexity of the system. We demonstrated that complexity is a more comprehensive measure that may be used as a ‘figure of merit’ to accurately estimate the time-scale during time dynamics.