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Title: 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-Bose-Einstein condensate (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 67, 063612 (2003)] to include the effect of a harmonic trap. We do not use the local density approximation (LDA), but directly solve the Bogoliubov-de Gennes (BdG) coupled equations. While our explicit numerical solutions are for a weak (narrow) Feshbach resonance, we argue that the single-particle BdG excitation spectrum will exhibit the same features for a strong (broad) Feshbach resonance. Using these equations, we find self-consistent values for the spatially dependent local density n(r) as well as the composite BCS order parameter {delta}-tilde(r), the latter describing both the Cooper-pair and molecular condensate contributions. 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{sub g}) of the trapped Fermi superfluid. This is associated withmore » the in-gap (or Andreev) states in the low-density region at the edge of the trap. We calculate the laser-induced tunneling current I({omega}) into another hyperfine state, as measured in recent rf spectroscopy experiments. This rf spectrum gives a direct probe of the quasiparticle spectrum. We show how the high-energy part of I({omega}) gives information about {delta}-tilde(r=0) at the center of the trap (which is comparable to the Fermi energy {epsilon}{sub F} in the crossover region). We show that I({omega}) is very dependent on the spatial profile of the pair potential {delta}-tilde(r) that is used. We also emphasize that the narrow 'unpaired atom peak in the rf data gives information about E{sub g} and the low-energy (<<{epsilon}{sub F}) in-gap states of a Fermi superfluid. While our calculations are limited to T=0, we use them to discuss the recent data of Chin et al. and the LDA calculations of Toermae and co-workers. The LDA, while useful, can lead to an incorrect physical picture of the low-density surface region of the Fermi superfluid.« less

Authors:
 [1];  [2]
  1. Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305 (Japan)
  2. Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 (Canada)
Publication Date:
OSTI Identifier:
20718393
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 72; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.72.013601; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ABSORPTION SPECTRA; ABSORPTION SPECTROSCOPY; ATOMS; BOSE-EINSTEIN CONDENSATION; BOSONS; COOPER PAIRS; ENERGY GAP; EXCITATION; FERMI GAS; FERMI LEVEL; LASER RADIATION; NUMERICAL SOLUTION; ORDER PARAMETERS; PAIRING INTERACTIONS; POTENTIALS; RESONANCE; SUPERFLUIDITY; TRAPPING; TRAPS; TUNNEL EFFECT

Citation Formats

Ohashi, Y, Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, and Griffin, A. Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region. United States: N. p., 2005. Web. doi:10.1103/PhysRevA.72.013601.
Ohashi, Y, Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, & Griffin, A. Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region. United States. https://doi.org/10.1103/PhysRevA.72.013601
Ohashi, Y, Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, and Griffin, A. Fri . "Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region". United States. https://doi.org/10.1103/PhysRevA.72.013601.
@article{osti_20718393,
title = {Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region},
author = {Ohashi, Y and Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 and Griffin, A},
abstractNote = {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-Bose-Einstein condensate (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 67, 063612 (2003)] to include the effect of a harmonic trap. We do not use the local density approximation (LDA), but directly solve the Bogoliubov-de Gennes (BdG) coupled equations. While our explicit numerical solutions are for a weak (narrow) Feshbach resonance, we argue that the single-particle BdG excitation spectrum will exhibit the same features for a strong (broad) Feshbach resonance. Using these equations, we find self-consistent values for the spatially dependent local density n(r) as well as the composite BCS order parameter {delta}-tilde(r), the latter describing both the Cooper-pair and molecular condensate contributions. 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{sub g}) of the trapped Fermi superfluid. 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 tunneling current I({omega}) into another hyperfine state, as measured in recent rf spectroscopy experiments. This rf spectrum gives a direct probe of the quasiparticle spectrum. We show how the high-energy part of I({omega}) gives information about {delta}-tilde(r=0) at the center of the trap (which is comparable to the Fermi energy {epsilon}{sub F} in the crossover region). We show that I({omega}) is very dependent on the spatial profile of the pair potential {delta}-tilde(r) that is used. We also emphasize that the narrow 'unpaired atom peak in the rf data gives information about E{sub g} and the low-energy (<<{epsilon}{sub F}) in-gap states of a Fermi superfluid. While our calculations are limited to T=0, we use them to discuss the recent data of Chin et al. and the LDA calculations of Toermae and co-workers. The LDA, while useful, can lead to an incorrect physical picture of the low-density surface region of the Fermi superfluid.},
doi = {10.1103/PhysRevA.72.013601},
url = {https://www.osti.gov/biblio/20718393}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 72,
place = {United States},
year = {2005},
month = {7}
}