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arXiv:1305.5015 · Physical Review A

Radio-frequency spectrum of fermions near a narrow Feshbach resonance

Junjun Xu, Qiang Gu, Erich J. Mueller

Published Aug 7, 2013• 2 citations
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Abstract

We calculate the radio frequency (RF) spectrum of fermionic atoms near a narrow Feshbach resonance, explaining observations made in ultracold samples of ${}^{6}\mathrm{Li}$ [E. L. Hazlett et al., Phys. Rev. Lett. 108, 045304 (2012)]. We use a two channel resonance model to show that the RF spectrum contains two peaks. In the wide-resonance limit, nearly all spectral weight lies in one of these peaks, and typically the second peak is very broad. We find strong temperature dependence, which can be traced to the energy dependence of the two-particle scattering. In addition to microscopic calculations, we use sum rule arguments to find generic features of the spectrum which are model independent.

DOI
10.1103/physreva.88.023604

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We present a calculation of the spectral functions and the associated rf response of ultracold fermionic atoms near a Feshbach resonance. The single-particle spectra are peaked at energies that can be modeled by a modified BCS dispersion. However, even at very low temperatures their width is comparable to their energy except for a small region around the dispersion minimum. The structure of the excitation spectrum of the unitary gas at infinite scattering length agrees with recent momentum-resolved rf spectra near the critical temperature. A detailed comparison is made with momentum integrated, locally resolved rf spectra of the unitary gas at arbitrary temperatures and shows very good agreement between theory and experiment. The pair size defined from the width of these spectra is found to coincide with that obtained from the leading gradient corrections to the effective-field theory of the superfluid.
The last chapter focuses on radio-frequency spectroscopy of multi component fermion gases. Rf experiments of 6Li and 40K are first reviewed. We show that rf experiments essentially measure spin correlation functions, and internal symmetries of the interparticle interactions constrain the rf spectrum through sum rules. We self-consistently generate the spin correlation functions for 6Li within Hartree-Fock-BCS approximation. Our calculation reproduces the mean field shift observed in experiments for normal gases, and confirms that a second peak detected at higher frequencies in the rf spectrum at sufficiently low temperatures arises from paired fermions. We define a mean frequency shift by the sum rules, and show that it is proportional to the square of BCS pairing gap. The discrepancy between the mean shift and the peak frequency shift observed in experiment for the condensed phase lies in the broad width of the rf spectrum function.
We show that radio-frequency spectroscopy on weakly bound molecules is a powerful and sensitive tool to probe molecular energy structure as well as atomic scattering properties. An analytic expression of the excitation line shape is derived, which in general contains a bound-free component and a bound-bound component. In particular, we show that the bound-free process strongly depends on the sign of the scattering length in the outgoing channel and acquires a Fano-type profile near a Feshbach resonance. The derived line shapes provide an excellent fit to both numerical calculations and recent experimental measurements based on 6Li2^{6}\mathrm{Li}_{2}6Li2​.
We derive the atom-molecule theory for an atomic gas near a broad Feshbach resonance, where the energy dependence of the atom-molecule coupling becomes crucial for understanding experimental results. We show how our many-body theory incorporates the two-atom physics exactly. In particular, we calculate the magnetic moment of a two-component gas of 6Li^{6}\mathrm{Li}6Li atoms for a wide range of magnetic fields near the broad Feshbach resonance at about 834G834\phantom{\rule{0.3em}{0ex}}\mathrm{G}834G. We find excellent agreement with the experiment of Jochim et al. [Phys. Rev. Lett. 91, 240402 (2003)].
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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.