Phase transitions in a few low dimensional optical lattices: A quantum many body study

Abstract

Recent progresses in ultra-cold atoms [1], dipolar atoms [2], and polar molecules [3] have given opportunity to realize several quantum phases of strongly correlated systems. The tunibilty and controllability of optical lattice and availability of highly sophisticated measurement techniques gives realization of quantum phenomena which occurs from macroscopic scale to microscopic scales [4]. Ultracold atoms help to understand most fascinating and exotic phases, like super uidity and superconductivity, quite clearly. The perfect isolation from environment of ultracold atoms con ned in optical lattices, gives realization of excited state phases (like Super-Tonks-Girardeau gas) [5] and coherent dynamics on long timescales [6]. Optical lattices give also platform to study various dynamics and non-equilibrium phenomena, which generally is very di cult to realize in condensed matter systems [7{10]. Optical lattice with quasi-periodic structure, helps to investigate the disorder system and also realization of Anderson localizations [11]. The experimental realization of ultracold dipolar gases interacting with long range interactions [12], allow to study various types of conventional (s-wave) and unconventional (pwave) pairing phenomena. Research on dipolar system, has promise to nd to nd more exotic phases like, supersolid phases [13]. The recent advancement in optical lattice with arti cial gauge eld opened up the possibility of realization of various topological phases [14{19]. In fact, the recent developments leads to various application in the eld of quantum information [20,21], quantum computation [22, 23] and quantum optics.