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arXiv:0810.1704 · Laser Physics

DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance

Luca Salasnich, F. Ancilotto, Nicola Manini, F. Toigo

Published Apr 1, 2009• 20 citations
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Abstract

We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the AAN side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.

DOI
10.1134/s1054660x09040173

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We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the AAN side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.
We show that the dc Josephson effect with ultracold fermionic gases in the Bose-Einstein-condensate (BEC) regime of composite molecules can be described by a nonlinear Schr\"odinger equation (NLSE). By comparing our results with Bogoliubov--de Gennes calculations [Phys. Rev. Lett. 99, 040401 (2007)] we find that our superfluid NLSE, which generalizes the Gross-Pitaevskii equation taking into account the correct equation of state, is reliable in the BEC regime of the BCS-BEC crossover up to the limit of very large (positive) scattering length. We also predict that the Josephson current displays relevant beyond-mean-field effects.
We introduce a quasianalytic nonlinear Schr\"odinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where kF∣a∣⪡1{k}_{F}|a|⪡1kF​∣a∣⪡1 with aaa the sss-wave scattering length and kF{k}_{F}kF​ the Fermi momentum, through the unitarity limit ${k}_{F}a\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ to the Bose-Einstein condensation (BEC) regime where kFa>0{k}_{F}a>0kF​a>0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.
We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one, finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase, calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is higher in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.
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.
On the basis of quantum hydrodynamical equations we derive a unitarity Schrödinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg–Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross–Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrödinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.
We show that the thermodynamic properties of an atomic Fermi gas near the unitarity limit for Feshbach scattering is not universal as long as the resonance is narrow on the scale of the Fermi energy. In view of ongoing quantum Monte Carlo simulations, we explore this behavior within a mean-field approach extended to a finite temperature by means of a model potential, which allows for a tuning of the scattering phase shift and its energy dependence. Our results may be relevant for constructing a complete theoretical description of the crossover from a Bose-Einstein condensation (BEC) of composite bosons to a Bardeen-Cooper-Schrieffer (BCS) of Cooper pairs.