Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region

Abstract

We investigate the single-particle properties at T=0 of a trapped superfluid gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance leads to the BCS-BEC crossover, where the character of superfluidity continuously changes from the BCS-type to a BEC of composite bosons. In this paper, we extend our previous work for a uniform superfluid Fermi gas [Y. Ohashi and A. Griffin, Phys. Rev. A {\bf 67}, 063612 (2003)] to include the effect of a harmonic trap. We directly solve the Bogoliubov-de Gennes coupled equations, and find self-consistent values for the spatially-dependent local density $n(\mathbf{r})$ as well as the composite BCS order parameter $\tilde{\Delta }(\mathbf{r})$. Using these results, we calculate the single-particle density of states in the crossover region, and from this determine the true single-particle energy gap ($E_{\mathrm{g}}$) of the trapped Fermi superfluid at T=0. This is associated with the in-gap (or Andreev) states in the low density region at the edge of the trap. We calculate the laser-induced current $I(\omega )$, as measured in recent rf-spectroscopy experiments. We show how the high-energy part of $I(\omega )$ gives information about $\tilde{\Delta }(r=0)$ at the center of the trap. We emphasize that the narrow "unpaired atom" peak in the rf-data gives information about $E_g$ and the low-energy in-gap states of a Fermi superfluid. While our calculations are limited at T=0, we use them to discuss the recent Innsbruck data and the LDA calculations of Törmä and co-workers.

47 pages, 22 figures

References in corpus (6)

• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Weakly bound dimers of fermionic atoms
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance
• Pairing gaps in atomic gases at the BCS-BEC crossover

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