Abstract
Atomtronics experiments with ultracold atomic gases allow us to explore quantum transport phenomena of a weakly-interacting Bose-Einstein condensate (BEC). Here, we focus on two-terminal transport of such a BEC in the vicinity of zero temperature. By using the tunnel Hamiltonian and Bogoliubov theory, we obtain a DC Josephson current expression in the BEC and apply it to experimentally relevant situations such as quantum point contact and planar junction. Due to the absence of Andreev bound states but the presence of couplings associated with condensation elements, a current-phase relation in the BEC is found to be different from one in an s-wave superconductor. In addition, it turns out that the DC Josephson current in the BEC depends on the sign of tunneling elements, which allows to realize the so-called $\pi$ junction by using techniques of artificial gauge fields.
Highlights
Quantum transport between macroscopic reservoirs reveals colorful quantum phenomena
When macroscopic reservoirs are separated by a two-dimensional barrier, a variety of quantum tunneling phenomena that depends on quantum states of matter in reservoirs emerge [1]
For a self-contained description, Green’s function formulas used in quantum point contact and planar junction systems and DC Josephson current formula in an s-wave superconductor are respectively given in Appendices A and B
Summary
Quantum transport between macroscopic reservoirs reveals colorful quantum phenomena. When macroscopic reservoirs are separated by a two-dimensional barrier, a variety of quantum tunneling phenomena that depends on quantum states of matter in reservoirs emerge [1]. In order to reveal such quantum transport phenomena, typical condensed matter systems composed of semiconductors and superconductors have conventionally been examined. To this end, we apply the Bogoliubov theory that explains a BEC near zero temperature to the tunneling Hamiltonian, and adopt the Keldysh formalism to take into account higher-order tunneling processes in an efficient manner. For a self-contained description, Green’s function formulas used in quantum point contact and planar junction systems and DC Josephson current formula in an s-wave superconductor are respectively given in Appendices A and B
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