Executive Summary : | The proposed project shall theoretically examine the quantum phases and out-of-equilibrium dynamics of ultracold atoms with long-range interactions in the disordered 2D optical lattices. This shall fill an important research gap in the field of ultracold atoms in optical lattices. The optical lattices filled with ultracold atoms are considered as an ideal platform to simulate the physics of condensed matter systems and study the physics of quantum many-body systems. This is on account of their tunability in terms of interaction strength, particle density, lattice geometry, system dimensions, strength of external fields, nature of disorder, etc. Disorder is present in almost all the condensed matter systems. Hence, introducing disorder is essential for ultracold atoms in optical lattices to emulate condensed matter systems. In addition, introduction of long-range interaction is also required to represent the effects of the long-range electron-electron interactions in the condensed matter systems. There are very few works on ultracold atoms in optical lattices which have considered both disorder and long-range interactions. The project shall address this research gap by identifying the quantum phases supported by the system. The Bose-Hubbard Model modified to include disorder and dipolar interaction shall be used to model the system. To solve the model the single-site and cluster mean-field theory, and exact diagonalization shall be used to obtain the ground state of the system. This shall form the first phase of the proposed project. The ultracold atoms in optical lattices have potential applications in the emerging field of quantum technologies. This involves control and manipulation of the system between different quantum states. For such maneuvers of the system a detailed understanding of the out-of-equilibrium evolution is required. This shall be undertaken during the second half of the proposed project by evolving the system with changes in the system parameters. The dynamical evolution shall be done by solving the time-dependent Schrödinger equation. Previous works have studied out-of-equilibrium dynamics in ultracold atoms. However, these works have not examined the combined effect of disorder and long-range interactions in optical lattices. The results from the proposed project shall provide an understanding on this important topic. |