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arXiv:0711.2141 · Physical Review A

Macroscopic periodic tunneling of Fermi atoms in the BCS-BEC crossover

Luca Salasnich, Nicola Manini, Flavio Toigo

Published Apr 8, 2008• 54 citations
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Abstract

We study the macroscopic quantum tunneling of two weakly linked superfluids made of interacting fermionic atoms. We derive atomic Josephson junction equations and find that zero-mode and $\ensuremath{\pi}$-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of $^{40}\text{K}$ atoms, we calculate these oscillation frequencies in the crossover from the Bardeen-Cooper-Schrieffer state of weakly bound Cooper pairs to the Bose-Einstein condensate of strongly bound molecular dimers.

DOI
10.1103/physreva.77.043609

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We study the macroscopic quantum tunneling of two weakly linked superfluids made of interacting fermionic atoms. We derive atomic Josephson junction equations and find that zero-mode and \ensuremathπ\ensuremath{\pi}\ensuremathπ-mode frequencies of coherent atomic oscillations depend on the tunneling coefficient and the sound velocity of the superfluid. By considering a superfluid of 40K^{40}\text{K}40K atoms, we calculate these oscillation frequencies in the crossover from the Bardeen-Cooper-Schrieffer state of weakly bound Cooper pairs to the Bose-Einstein condensate of strongly bound molecular dimers.
We investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen—Cooper—Schrieffer (BCS) superfluid to Bose—Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.
In this work, we study the nonlinear Josephson dynamics of Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in a double-well potential. Under a two-mode approximation, we derive a full two-mode (fTM) model including all interaction energy terms. By solving the fTM model numerically, we study the zero-phase and [Formula: see text]-phase modes of Josephson oscillations in the BCS–BEC crossover. We find that in the strongly interacting regime the cross interaction terms not appearing in the two-mode model cannot be easily ignored. The cross interactions can alter the behaviors of Josephson dynamics substantially, and interestingly the alterations for the zero-phase and [Formula: see text]-phase modes are just opposite.
The Josephson effect is a macroscopic quantum phenomenon that reveals the broken symmetry associated with any superfluid state. Here we report on the observation of the Josephson effect between two fermionic superfluids coupled through a thin tunneling barrier. We show that the relative population and phase are canonically conjugate dynamical variables throughout the crossover from the molecular Bose-Einstein condensate (BEC) to the Bardeen-Cooper-Schrieffer (BCS) superfluid regime. For larger initial excitations from equilibrium, the dynamics of the superfluids become dissipative, which we ascribe to the propagation of vortices through the superfluid bulk. Our results highlight the robust nature of resonant superfluids.
We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly bound Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal long-range order for fermions we calculate analytically and numerically the pair binding energy, the energy gap, and the condensate fraction of Cooper pairs as a function of interaction strength and filling factor of atoms in the lattice at zero temperature.
Abstract In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.
We study the tunnelling dynamics of superfluid Fermi gases trapped in multi-well system along the BEC-BCS crossover. Within the hydrodynamical model and by using the multi-mode approximation, the self-trapping dynamics of superfluid Fermi gases in multi-well system are obtained numerically. We find that the self-trapping to diffusion transition strongly depends on the well number. When the well number is less than three, the self-trapped state takes place easier on the BEC side than that on the BCS side. However, when the well number is larger than three, the self-trapped state takes place easier on the BCS side instead of the BEC side. Furthermore, by considering a superfluid of 40 K atoms, we obtain the zero-mode and π-mode Josephson frequencies of coherent atomic oscillations in double-well system. It is noteworthy that the Josephson mode, especially, the existence of π-mode frequency strongly depends on the atoms number on the BCS side.