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arXiv:0712.1007 · Physical Review Letters

Final-State Effects in the Radio Frequency Spectrum of Strongly Interacting Fermions

Sourish Basu, Erich J. Mueller

Published Aug 8, 2008• 34 citations
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Abstract

We model the impact of final-state interactions on the radio frequency spectrum of a strongly interacting two-component superfluid Fermi gas. In addition to a broad asymmetric peak coming from the breakup of Cooper pairs, we find that, for appropriate parameters, one can observe a sharp symmetric "bound-bound" spectral line coming from the conversion of Cooper pairs in one channel to pairs or molecules in another.

DOI
10.1103/physrevlett.101.060405

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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.
This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.
The nature of the normal state of an ultracold Fermi gas in the BCS-BEC crossover regime is an intriguing and controversial topic. While the many-body ground state remains a condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules as a function of the interaction strength. How this occurs is still largely unknown. We explore this question with measurements of the distribution of single-particle energies and momenta in a nearly homogeneous gas above T(c). The data fit well to a function that includes a narrow, positively dispersing peak that corresponds to quasiparticles and an "incoherent background" that can accommodate broad, asymmetric line shapes. We find that the quasiparticle's spectral weight vanishes abruptly as the strength of interactions is modified, which signals the breakdown of a Fermi liquid description. Such a sharp feature is surprising in a crossover.
We show that bimodal radio frequency spectra universally arise at intermediate temperatures in models of strongly interacting trapped Fermi gases. The bimodality is independent of superfluidity or pseudogap physics, depending only on the functional form of the equation of state---which is constrained by dimensional analysis at low temperatures and the virial expansion at high temperatures. In addition to these model independent results, we present a simple calculation of the radio frequency line shape of a highly polarized Fermi gas which uses energetic considerations to include final state interactions. While this model only qualitatively captures the line shapes observed in the experiments, it provides a conceptually clean and powerful technique for estimating the energy scales and how they vary with experimental parameters.
We calculate the radio frequency (RF) spectrum of fermionic atoms near a narrow Feshbach resonance, explaining observations made in ultracold samples of 6Li{}^{6}\mathrm{Li}6Li [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.