Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2106.12750 · Physical Review Research

Tunneling Hamiltonian analysis of DC Josephson currents in a weakly-interacting Bose-Einstein condensate

Shun Uchino

Published Oct 21, 2021• 4 citations
arXivHTMLPDF

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 $\ensuremath{\pi}$ junction by using techniques of artificial gauge fields.

DOI
10.1103/physrevresearch.3.043058

Related papers

Josephson tunneling between weakly interacting Bose-Einstein condensates

F. Meier, W. Zwerger

Based on a tunneling Hamiltonian description, we calculate the Josephson, normal, and interference currents between two Bose-Einstein condensates described by the Bogoliubov theory. The dominant Josephson term is of first order in the tunneling with a critical current density proportional to the ground state pressure. In contrast to superconductors, the normal current remains finite at zero temperature. We discuss the dynamics of the relative phase in a semiclassical approximation derived from an exact functional integral approach, which includes the interaction effects at fixed total particle number. It is shown that the normal current leads to a damping of the Josephson oscillations and, at long times, eliminates the macroscopic quantum self-trapping predicted by Smerzi et al. Finally, we give estimates for an experimental realization of Josephson tunneling in cold atomic gases, which indicate that coherent transfer of atoms might be realized with a ${}^{23}\mathrm{Na}$ condensate.

arXiv:cond-mat/9904147•Physical Review A•Aug 17, 2001•88 citations

Coherent tunneling of atoms from Bose-condensed gases at finite temperatures

David L. Luxat, Allan Griffin

Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear-response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green's functions of isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-Einstein condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett, and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle ${u}^{2}$ and ${v}^{2}$ amplitudes.

arXiv:cond-mat/0111040•Physical Review A•Apr 10, 2002•21 citations

Josephson effects in an interaction-asymmetric junction across the BCS-BEC crossover

Anonymous, Hiroyuki Tajima

We theoretically study the Josephson effect in ultracold Fermi gases, where the two sides of the Josephson junction are independently tuned to different regions of the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover. Using the nonequilibrium Green's function approach combined with the tunnel Hamiltonian formalism and a mean-field approach, we evaluate the DC and AC Josephson currents throughout the entire crossover region. We calculate the DC Josephson current as a function of interaction strength by tuning both sides of the junction synchronously from the BCS to the BEC regimes, and give the asymptotic expression of the current in the deep BCS and BEC limits. We also study the AC Josephson junction through the interaction-asymmetric junction by fixing the interaction in one reservoir and tuning that of the other one. A peak of the tunneling current is found when one side is fixed in the BCS limit and the other side is tuned into the BEC regime, which corresponds to the interaction-biased Riedel peak. Our results indicate the competition between contributions of increasing pair spectral weight and decreasing chemical potential to Josephson tunneling throughout the BCS-BEC crossover, and demonstrate the realization of the Riedel peak in strong-coupling quantum gases.

arXiv:2603.25577•Physical review. B./Physical review. B•Jul 22, 2026•0 citations

Observation of nonlinear tunneling of a Bose-Einstein condensate in a single Josephson junction

M. Albiez

In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.

•Jan 1, 2005•9 citations

Josephson Effects in Dilute Bose-Einstein Condensates

S. Giovanazzi, Augusto Smerzi, Stefano Fantoni

We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.

arXiv:physics/0002041•Physical Review Letters•May 15, 2000•160 citations

Strongly correlated superfluid order parameters from dc Josephson supercurrents

W. J. Kwon, G. Del Pace, R. Panza +5 more

The direct-current (dc) Josephson effect provides a phase-sensitive tool for investigating superfluid order parameters. We report on the observation of dc Josephson supercurrents in strongly interacting fermionic superfluids across a tunneling barrier in the absence of any applied potential difference. For sufficiently strong barriers, we observed a sinusoidal current-phase relation, in agreement with Josephson's seminal prediction. We mapped out the zero-resistance state and its breakdown as a function of junction parameters, extracting the Josephson critical current behavior. By comparing our results with an analytic model, we determined the pair condensate fraction throughout the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover. Our work suggests that coherent Josephson transport may be used to pin down superfluid order parameters in diverse atomic systems, even in the presence of strong correlations.

arXiv:1908.09696•Science•Jul 2, 2020•79 citations
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 \ensuremathπ\ensuremath{\pi}\ensuremathπ junction by using techniques of artificial gauge fields.
Based on a tunneling Hamiltonian description, we calculate the Josephson, normal, and interference currents between two Bose-Einstein condensates described by the Bogoliubov theory. The dominant Josephson term is of first order in the tunneling with a critical current density proportional to the ground state pressure. In contrast to superconductors, the normal current remains finite at zero temperature. We discuss the dynamics of the relative phase in a semiclassical approximation derived from an exact functional integral approach, which includes the interaction effects at fixed total particle number. It is shown that the normal current leads to a damping of the Josephson oscillations and, at long times, eliminates the macroscopic quantum self-trapping predicted by Smerzi et al. Finally, we give estimates for an experimental realization of Josephson tunneling in cold atomic gases, which indicate that coherent transfer of atoms might be realized with a 23Na{}^{23}\mathrm{Na}23Na condensate.
Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear-response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green's functions of isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-Einstein condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett, and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle u2{u}^{2}u2 and v2{v}^{2}v2 amplitudes.
We theoretically study the Josephson effect in ultracold Fermi gases, where the two sides of the Josephson junction are independently tuned to different regions of the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover. Using the nonequilibrium Green's function approach combined with the tunnel Hamiltonian formalism and a mean-field approach, we evaluate the DC and AC Josephson currents throughout the entire crossover region. We calculate the DC Josephson current as a function of interaction strength by tuning both sides of the junction synchronously from the BCS to the BEC regimes, and give the asymptotic expression of the current in the deep BCS and BEC limits. We also study the AC Josephson junction through the interaction-asymmetric junction by fixing the interaction in one reservoir and tuning that of the other one. A peak of the tunneling current is found when one side is fixed in the BCS limit and the other side is tuned into the BEC regime, which corresponds to the interaction-biased Riedel peak. Our results indicate the competition between contributions of increasing pair spectral weight and decreasing chemical potential to Josephson tunneling throughout the BCS-BEC crossover, and demonstrate the realization of the Riedel peak in strong-coupling quantum gases.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.
We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.
The direct-current (dc) Josephson effect provides a phase-sensitive tool for investigating superfluid order parameters. We report on the observation of dc Josephson supercurrents in strongly interacting fermionic superfluids across a tunneling barrier in the absence of any applied potential difference. For sufficiently strong barriers, we observed a sinusoidal current-phase relation, in agreement with Josephson's seminal prediction. We mapped out the zero-resistance state and its breakdown as a function of junction parameters, extracting the Josephson critical current behavior. By comparing our results with an analytic model, we determined the pair condensate fraction throughout the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover. Our work suggests that coherent Josephson transport may be used to pin down superfluid order parameters in diverse atomic systems, even in the presence of strong correlations.