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arXiv:0709.0817 · Physical Review Letters

Competition between Final-State and Pairing-Gap Effects in the Radio-Frequency Spectra of Ultracold Fermi Atoms

Andrea Perali, P. Pieri, Giancarlo Calvanese Strinati

Published Jan 7, 2008• 49 citations
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Abstract

The radio-frequency spectra of ultracold Fermi atoms are calculated by including final-state interactions affecting the excited level of the transition and compared with the experimental data. A competition is revealed between pairing-gap effects which tend to push the oscillator strength toward high frequencies away from threshold and final-state effects which tend instead to pull the oscillator strength toward threshold. As a result of this competition, the position of the peak of the spectra cannot be simply related to the value of the pairing gap, whose extraction thus requires support from theoretical calculations.

DOI
10.1103/physrevlett.100.010402

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The radio-frequency spectra of ultracold Fermi atoms are calculated by including final-state interactions affecting the excited level of the transition and compared with the experimental data. A competition is revealed between pairing-gap effects which tend to push the oscillator strength toward high frequencies away from threshold and final-state effects which tend instead to pull the oscillator strength toward threshold. As a result of this competition, the position of the peak of the spectra cannot be simply related to the value of the pairing gap, whose extraction thus requires support from theoretical calculations.
We present a simple and systematic characterization of the radio frequency (rf) spectra of homogeneous, paired atomic Fermi gases at general temperatures T in the presence of final-state interactions. The spectra, consisting of possible bound states and positive as well as negative detuning (nu) continua, satisfy exactly the zeroth- and first-moment sum rules at all T. We show how to best extract the pairing gap and how to detect the nu<0 continuum arising from thermally excited quasiparticles, not yet seen experimentally. We explain semiquantitatively recent rf experiments on "bound-bound" transitions, predicting effects of varying temperature.
We present a theoretical interpretation of radio frequency (RF) pairing gap experiments in trapped atomic Fermi gases, over the entire range of the BCS--Bose-Einstein condensation (BEC) crossover, for temperatures above and below Tc{T}_{c}Tc​. Our calculated RF excitation spectra, as well as the density profiles on which they are based, are in semiquantitative agreement with experiment. We provide a detailed analysis of the physical origin of the two different peak features seen in RF spectra, one associated with nearly free atoms at the edge of the trap, and the other with (quasi-)bound fermion pairs.
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The radio-frequency spectrum of the fermions in the unitary limit at finite temperatures is characterized by the sum-rule relations. We consider a simple picture where the atoms are removed by radio-frequency excitations from the strongly interacting states into a state of negligible interaction. We calculate the moments of the response function in the range of temperature 0.08ϵF<T<0.8ϵF0.08{ϵ}_{F}<T<0.8{ϵ}_{F}0.08ϵF​<T<0.8ϵF​ using auxiliary field Monte Carlo technique in which continuum auxiliary fields with a density-dependent shift are used. We estimate the effects of superfluid pairing from the clock shift. We find a qualitative agreement with the pairing gap--pseudogap transition behavior. We also find within the quasiparticle picture that in order for the gap to come into quantitative agreement with the previously known value at T=0T=0T=0, the effective mass has to be ${m}^{\ensuremath{\ast}}\ensuremath{\sim}1.43m$. Finally, we discuss implications for the adiabatic sweep of the resonant magnetic field.