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arXiv:cond-mat/0507243 · Physical Review Letters

Beyond Linear Response Spectroscopy of Ultracold Fermi Gases

J. J. Kinnunen, Päivi Törmä

Published Feb 22, 2006• 7 citations
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Abstract

We study rf spectroscopy of ultracold Fermi gas by going beyond the linear response in the field-matter interaction. Higher order perturbation theory allows virtual processes and energy conservation beyond the single-particle level. We formulate an effective higher order theory, which agrees quantitatively with experiments on the pairing gap and is consistent with the absence of the mean-field shift in the spin-flip experiment.

DOI
10.1103/physrevlett.96.070402

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We consider rf spectroscopy of ultracold Fermi gases by exact simulations of the many-body state and the coherent dynamics in one dimension. Deviations from the linear response sum rule result are found to suppress the pairing contribution to the rf line shifts. We compare the coherent rotation and quasiparticle descriptions of rf spectroscopy which are analogous to NMR experiments in superfluid 3He^{3}\mathrm{He}3He and tunneling in solids, respectively. We suggest that rf spectroscopy in ultracold gases provides an interesting crossover between these descriptions that could be used for studying decoherence in quantum measurement, in the context of many-body quantum states.
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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 spin response functions measured in multicomponent fermion gases by means of rf transitions between hyperfine states are strongly constrained by the symmetry of the interatomic interactions. Such constraints are reflected in the spin fff-sum rule that the response functions must obey. In particular, only if the effective interactions are not fully invariant in SU(2)SU(2)SU(2) spin space, are the response functions sensitive to mean field and pairing effects. We demonstrate, via a self-consistent calculation of the spin-spin correlation function within the framework of Hartree-Fock-BCS theory, how one can derive a correlation function explicitly obeying the fff-sum rule. By contrast, simple one-loop approximations to the spin response functions do not satisfy the sum rule, except in special cases. As we show, the emergence of a second peak at higher frequency in the rf spectrum, as observed in a recent experiment in trapped 6Li^{6}\mathrm{Li}6Li, can be understood as the contribution from the paired fermions, with a shift of the peak from the normal particle response proportional to the square of the BCS pairing gap.