Spin-orbit-coupled ultracold bosons in continuum and optical lattices

Abstract

The spin-orbit coupling (SOC) is a central theme explored in several research endeavors due to its fascinating effects, including quantum spin-Hall states and topological insulators. It also has immense potential for use in various quantum devices and information processing. Among the spin-orbit-coupled (SO-coupled) physical systems, ultracold quantum gases with synthetic SOC are of special interest due to their pristine and tunable nature. In this thesis, we have studied the Rashba SO-coupled spinor condensates in the continuum as well as optical lattices. Our study explores the emergence of self-trapped supersolid-like crystalline structures in a quasi-two-dimensional (q2D) SO-coupled spin-2 condensate. Different strengths of SOC and interatomic interactions result in a variety of nontrivial density patterns. For small SOC strengths, γ ≈ |c0| ≈ 0.5 where γ and c0 are (dimensionless) SOC and spin independent interaction strengths, the ground state is an axisymmetric multiring soliton for polar, cyclic and weakly ferromagnetic interactions, whereas for stronger ferromagnetic interac tions, a circularly asymmetric soliton emerges as the ground state. Depending on the values of interaction parameters, a stripe phase may emerge as the ground state with an increase in SOC strength. A triangular-lattice soliton can emerge in all magnetic phases, for γ ≈ 2|c0| ≈ 1 in addition to the aforementioned solitons. Further increases in SOC strength result in a square lattice and a superstripe soliton as quasidegenerate states. We have also demonstrated the spontaneous generation of spatially periodic supersolid-like superlattice and stripe solitons in q2D Rashba SO-coupled spin-1 and spin-2 nonmagnetic BECs, which are generally thought to be associated with spinor interactions. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian. In addition to this, we have studied quantum phase transitions of a two-dimensional two component Bose-Hubbard model in the presence of a Rashba SOC, both with and without thermal fluctuations. Our analysis reveals that the interplay of single-particle hopping, the strength of the SOC, and the interspin interaction leads to superfluid phases with distinct properties. We have found that when the interspin interaction is weaker than the intraspin interaction, the SOC induces two finite-momentum superfluid phases. One of these is a phase twisted superfluid that exists at low hopping strengths and reduces the domain of insulating phases. At higher hopping strengths, there is a transition from the phase-twisted to a finite momentum stripe superfluid. On the other hand, when the interspin interaction is stronger than the intraspin interaction, the system exhibits a phase-twisted to a ferromagnetic phase transition. However, at finite temperatures, the thermal fluctuations destroy the phase-twisted superfluidity and lead to a wide region of normal-fluid states. On the dynamics front, we have studied the quench dynamics in a two-component bosonic mixture within an optical lattice, finding qualitative differences from one-component Bose gas. We have examined quench dynamics across both first- and second-order Mott insulator (MI) to superfluid (SF) phase transitions, observing critical slowing down of dynamics near the transition point in semblance with the Kibble-Zurek mechanism. In the case of second-order MI-SF tran sitions with homogeneous lattice-site distributions in the MI phase, our numerical simulations yield dynamical critical exponents close to mean-field predictions.