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Brazilian Journal of Physics

Particle Current in Double-Path Josephson Junction under Rashba Interaction Connected to Bose-Einstein Condensate Reservoirs

Satoshi Kawaguchi

Published Dec 24, 2024• 1 citation
Publisher

Abstract

Abstract We investigate the properties of a double-path Josephson junction connected to Bose-Einstein condensate reservoirs. By comparing the current in the proposed setup with that in a similar system connected to superconductors, we elucidate the key differences between the two systems. The systems are influenced by the Aharonov-Bohm effect, Rashba spin-orbit interaction, and phase difference of order parameters between left and right leads. Utilizing the Keldysh formalism, it turns out that, in the system connected to Bose-Einstein condensate reservoirs, the Josephson current includes higher frequency components of the phase difference between left and right reservoirs. Additionally, the dependence of critical current on energy level does not show the complete symmetric resonance but the Fano-type resonance with single or double peaks. These differences result from the bosonic statistics of reservoirs.

DOI
10.1007/s13538-024-01641-5

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Abstract We investigate the properties of a double-path Josephson junction connected to Bose-Einstein condensate reservoirs. By comparing the current in the proposed setup with that in a similar system connected to superconductors, we elucidate the key differences between the two systems. The systems are influenced by the Aharonov-Bohm effect, Rashba spin-orbit interaction, and phase difference of order parameters between left and right leads. Utilizing the Keldysh formalism, it turns out that, in the system connected to Bose-Einstein condensate reservoirs, the Josephson current includes higher frequency components of the phase difference between left and right reservoirs. Additionally, the dependence of critical current on energy level does not show the complete symmetric resonance but the Fano-type resonance with single or double peaks. These differences result from the bosonic statistics of reservoirs.
We investigate the coherent dynamics of a noninteracting Bose-Einstein condensate in a system consisting of two bosonic reservoirs coupled via a spatially localized mode. We describe this system by a two-terminal Fano-Anderson model and investigate analytically the time evolution of observables such as the Josephson current. In doing so, we find that the Josephson current sensitively depends on the on-site energy of the localized mode. This facilitates using this setup as a transistor for a Bose-Einstein condensate. We identify two regimes. In one regime, the system exhibits well-behaved long-time dynamics with a slowly oscillating and undamped Josephson current. In a second regime, the Josephson current is a superposition of an extremely weakly damped slow oscillation and an undamped fast oscillation. Our results are confirmed by finite-size simulations.
We theoretically study the Fano resonance in Josephson current. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). To treat the Coulomb interaction inside the QD, we employ the Hubbard-I approximation, in which the correlation {δ n ↑ δ n ↓ ) can be taken into account beyond the Hartree-Fock approximation. It is found that the dependence of the Josephson critical current on the QD energy level has an asymmetric resonance, which is similar to the Fano resonance in normal metal systems. Moreover, we find that the sign of the critical current can change around the resonance, and such behavior is not seen without the Coulomb interaction. These results indicate that the cooperation of the Fano effect and the Coulomb interaction induces the 0-π transition.
We theoretically investigate the Fano effect in dc Josephson current at the absolute zero of temperature. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). Here the Kondo temperature is assumed to be much smaller than the superconducting gap, and the Coulomb interaction inside the QD is treated by the Hartree-Fock approximation. It is shown that the Josephson critical current exhibits an asymmetric resonance against the QD energy level. This behavior is caused by the interference between the two tunneling processes between the superconductors: the direct tunneling across the insulating barrier and the resonant one through the QD. Moreover, we find that the Josephson critical current changes its sign around the resonance when the Coulomb interaction is sufficiently strong. Our results suggest that $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition is induced by the cooperation of the Fano effect and the Coulomb interaction inside the QD.
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\ensuremath{\pi} (\ensuremath{\pi}$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^{3}\mathrm{He}\ensuremath{-}B$ and the internal Josephson effect in ${}^{3}\mathrm{He}\ensuremath{-}A$ are also discussed.
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 sss-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 $\ensuremath{\pi}$ junction by using techniques of artificial gauge fields.
Two aspects of the transport of the repulsive Bose-Einstein condensate (BEC) in a double-well trap are inspected: impact of the interatomic interaction and analogy to the Josephson effect. The analysis employs a numerical solution of 3D time-dependent Gross-Pitaevskii equation for a total order parameter covering all the trap. The population transfer is driven by a time-dependent shift of a barrier separating the left and right wells. Sharp and soft profiles of the barrier velocity are tested. Evolution of the relevant characteristics, involving phase differences and currents, is inspected. It is shown that the repulsive interaction substantially supports the transfer making it possible i) in a wide velocity interval and ii) three orders of magnitude faster than in the ideal BEC. The transport can be approximately treated as the d.c. Josephson effect. A dual origin of the critical barrier velocity (break of adiabatic following and d.c.-a.c. transition) is discussed. Following the calculations, robustness of the transport (d.c.) crucially depends on the interaction and barrier velocity profile. Only soft profiles which minimize undesirable dipole oscillations are acceptable.