Abstract:
Ultracold atoms is one of the most rapidly expanding fields of modern science. Its ap-
plications are not restricted to just atomic and molecular physics, but also to condensed
matter physics, astrophysics, quantum information, and many more areas. This has be-
come possible because of the unprecedented advances on the experimental front, where
various physical quantities characterising a system can be exquisitely controlled to very
high precision. The focus of the thesis is on the existence of different quantum phases
and transitions between them in a system of ultracold bosonic atoms loaded in an optical
superlattice.
Using two different numerical techniques, the mean-field theory and the density matrix
renormalisation group (DMRG) method, this system has been analysed in details, re-
vealing novel quantum phases depending on the densities and the values of the system
parameters. This novel quantum phase, which has a periodic variation in the number oc-
cupancy in the sites, have been named as the superlattice induced Mott insulator (SLMI).
This phase arises in addition to the usual Mott insulator (MI) and superfluid (SF) phases.
Results from both the numerical methods are in qualitative agreement with each other.
The effects of the three-body interaction on these quantum phases and the critical points
of various quantum phase transitions are studied. At higher densities, it is found that the
insulating lobes get enlarged in the presence of the three-body interaction. Apart from
this, it is also seen that the SF phase shifts in the phase diagram when three-body inter-
action is included. A possible experimental scneario is proposed which can be employed
to measure the three-body interaction strengths.
Ultracold atoms in different lattice geometries are very interesting to explore since they
contain rich physics in it. Two such cases are studied in this thesis. First an optical
superlattice with nearest and next-nearest hopping is considered. Such a model can be
mapped exactly into a zig-zag ladder with different potential depths along the two chains.
Using finite-size DMRG method, a detailed analysis is performed for hard-core bosons
at half-filling, spanning a wide range of values of the next-nearest hopping amplitudes in
both positive and negative directions. In the positive region, it is found that the system
exhibits two phases, the SLMI phase and the SF phase, and there is a phase transition
to the latter as the magnitude of the next-nearest tunneling amplitude is increased. On
the negative side, in the absence of the superlattice potential, the system goes from the
SF phase to the bond-ordered (BO) phase because of the geometric frustration induced
in the system. The BO phase has a finite bond order parameter, which distinguishes it
from the other phases. However, for finite values of the superlattice potential, the system
enters the gapped SLMI phase, and hence the transition to the BO phase occurs at a
more negative value of the next-nearest hopping amplitude.
Secondly, a two-leg Bose ladder is considered with inter- and intra-chain hopping such
that it induces a net flux of π in each of the plaquette. For low values of interaction, the
system is in the gapless phase, with a finite loop current order in each plaquette. This
phase is called the chiral superfluid (CSF). At high values of the repulsive interaction,
the system resides in the gapped MI phase with no loop current order. However, there
lies an intermediate range of interaction values where the the system is gapped, but si-
multaneously supports staggered loop currents which spontaneously breaks time-reversal
symmetry. This unique phase is named as the chiral MI (CMI). The transition from CSF
to CMI falls to the Berezinskii-Kosterlitz-Thouless type whereas CMI to MI transition
belongs to the Ising class.
Having studied the time-independent properties of the optical superlattice, the dynamics
of ultracold atomic gases in optical superlattice is then pursued. The superlattice potential
is made a function of time (linear in nature), such that the system passes through two
critical points. Such a time evolution will generate defects. The scaling of these defects
formed with the rate of quenching is studied and the validity of Kibble-Zurek mechanism
is tested.