Novel Quantum Phases in Ultracold Atoms in Optical Superlattices Research Interest

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.