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arXiv:1101.2836 · Physical Review A

Probing the homogeneous spectral function of a strongly interacting superfluid atomic Fermi gas in a trap using phase separation and momentum-resolved radio-frequency spectroscopy

Qijin Chen

Published Jul 29, 2011• 1 citation
arXivHTMLPDF

Abstract

It is of central importance to probe the local spectral function $A(\mathbf{k},\ensuremath{\omega})$ of a strongly interacting Fermi gas in a trap. Momentum-resolved rf spectroscopy has been demonstrated to be able to probe the trap-averaged $A(\mathbf{k},\ensuremath{\omega})$. However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum-resolved rf spectra of the minority fermions of a phase-separated, population-imbalanced Fermi gas at low temperature, one can effectively extract $A(\mathbf{k},\ensuremath{\omega})$ of a homogeneous superfluid Fermi gas (at the trap center). In support, we present calculated spectral functions and spectral intensity maps for various cases from BCS through Bose-Einstein condensation regimes using different theories.

DOI
10.1103/physreva.84.013624

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It is of central importance to probe the local spectral function A(k,\ensuremathω)A(\mathbf{k},\ensuremath{\omega})A(k,\ensuremathω) of a strongly interacting Fermi gas in a trap. Momentum-resolved rf spectroscopy has been demonstrated to be able to probe the trap-averaged A(k,\ensuremathω)A(\mathbf{k},\ensuremath{\omega})A(k,\ensuremathω). However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum-resolved rf spectra of the minority fermions of a phase-separated, population-imbalanced Fermi gas at low temperature, one can effectively extract A(k,\ensuremathω)A(\mathbf{k},\ensuremath{\omega})A(k,\ensuremathω) of a homogeneous superfluid Fermi gas (at the trap center). In support, we present calculated spectral functions and spectral intensity maps for various cases from BCS through Bose-Einstein condensation regimes using different theories.
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.
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We address recent momentum-resolved radio frequency (rf) spectroscopy experiments, showing how they yield more stringent tests than other comparisons with theory, associated with the ultracold Fermi gases. We demonstrate that, by providing a clear dispersion signature of pairing, they remove the ambiguity plaguing the interpretation of previous rf experiments. Our calculated spectral intensities are in semiquantitative agreement with the data. Even in the presence of a trap, the spectra are predicted to exhibit two BCS-like branches.
In this paper we present an overview of radio frequency (RF) spectroscopy in the atomic Fermi superfluids. An ultimate goal is to suggest new directions in the cold gas research agenda from the condensed matter perspective.Our focus is on the experimental and theoretical literature of cold gases and photoemission spectroscopy of the cuprates particularly as it pertains to areas of overlap. This paper contains a systematic overview of the theory of RF spectroscopy, both momentum integrated and momentum resolved. We discuss the effects of traps, population imbalance, final state interactions over the entire range of temperatures and compare theory and experiment. We show that this broad range of phenomena can be accomodated within the BCS-Leggett description of BCS-BEC crossover and that this scheme also captures some of the central observations in photoemission experiments in the cuprates. In this last context, we note that the key themes which have emerged in cuprate photoemission studies involve characterization of the fermionic self energy, of the pseudogap and of the effects of superconducting coherence (in passing from above to below the superfluid transition temperature, TcT_cTc​).These issues have a counterpart in the cold Fermi gases and it would be most useful in future to use these atomic systems to address these and the more sweeping question of how to describe that anomalous superfluid phase which forms in the presence of a normal state excitation gap.
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