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.
