Multicomponent Superfluidity and Josephson Dynamics in Ultracold Atomic Systems

Multicomponent superfluidity exhibits fruitful physics in contrast to single-component superfluids. In a binary superfluid with two different hyperfine states, the vorticity is modified from the single-component case and the circulation is no longer quantized, which affects thermodynamics and phase transitions. Josephson junctions prepared by trapping superfluids in a double-well potential are a platform to investigate the dynamics of multicomponent superfluids. Several experiments of Bose Josephson junctions or superconducting Josephson circuits enable us to clarify the quantum effects on the relaxation dynamics. In this Thesis, we analyzed quantum effects on multicomponent superfluidity from the viewpoints of phase transitions in a binary Bose superfluid and the dynamics in Josephson junctions. In Chap. 1, we start with an introduction to superfluidity and ultracold atomic physics. We present comprehensive ideas on why we focus on ultracold atoms and their advantages. Then, we conclude the introduction by presenting the motivation and outline of this Thesis. In Chap. 2, we present the fundamental overview of quantum fluids including the occurrence of Bose-Einstein condensation, superfluid hydrodynamics, quantized vortices, and Berezinskii-Kosterlitz-Thouless transitions, which are the basis of the discussions in the following chapters. In Chap. 3, we provide analyses of sound velocities in a single-component collisional Bose superfluid in $D$-dimension. Including the beyond-mean-field correction, we discuss the quasicrossing behavior of the first and second sound velocities in collisional Bose superfluids. In Chap. 4, we discuss Berezinskii-Kosterlitz-Thouless transitions in a Rabi-coupled binary Bose superfluid in two dimensions. Starting from the miscibility condition and vortex excitations, which are distinct from a single-component superfluid, we discuss the Berezinskii-Kosterlitz-Thouless transition in the binary Bose superfluid. Since it is a phase transition originating from vortex excitations, the different vortex excitations peculiar to multicomponent superfluids play a crucial role. We give the comprehensive behaviors of the superfluid density, superfluid transition temperature, and sound modes. In particular, the sound modes show significantly different behavior from the single-component case analyzed in Chap. 3, and we propose experimental verification of our result based on the sound velocities. In Chap. 5, we discuss quantum effects on the dynamics in multicomponent superfluids focusing on Josephson junctions. We reveal that a Bose Josephson junction can be mapped to a Caldeira-Leggett-type model and it exhibits damped Langevin dynamics. Such a damped Langevin dynamics can be also observed in a superconducting Josephson circuit. However, due to the different types of coupling between the Josephson mode and bath modes, the correlation functions exhibit different relaxation dynamics. We clarify the effects of quantum fluctuations on the correlation functions. Finally, we conclude Chap. 5 by showing the quantum correction also to the Josephson frequency. In Chap. 6, we summarize this Thesis.