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arXiv:cond-mat/0504394 · Physical Review A

Radio-frequency spectroscopy and the pairing gap in trapped Fermi gases

Yan He, Qijin Chen, Kathryn Levin

Published Jul 15, 2005• 59 citations
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Abstract

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 ${T}_{c}$. 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.

DOI
10.1103/physreva.72.011602

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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.
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.
We provide a comprehensive theoretical study of the radio-frequency (rf) spectra of a two-component Fermi gas with balanced populations in the normal region of the temperature-vs-coupling phase diagram. In particular, rf spectra are analyzed in terms of two characteristic peaks, which can be either distinct or overlapping. On the BEC side of the crossover, these two contributions are associated with a fermionic quasi-particle peak and a bosonic-like contribution due to pairing. On the BCS side of the crossover, the two peaks are instead associated with interactions between particles occurring, respectively, at high or low relative momenta. Through this two-peak analysis, we show how and to what extent the correlation between the widths of the rf spectra and the pair size, previously identified in the superfluid phase at low temperature, can be extended to the normal phase, as well as how the temperature-vs-coupling phase diagram of the BCS-BEC crossover can be partitioned in a number of distinct physical sectors. Several analytic results for the shape and widths of the rf spectra are also derived in appropriate temperature and coupling limits.
Strong evidence for pairing and superfluidity has recently been found in atomic Fermi gases at the BCS–BEC crossover both in collective modes and radio frequency (RF) excitation energies. It is argued that the scale for the effective pairing gaps measured in RF experiments is set by the lowest quasiparticle in-gap excitation energies. These are calculated at the BCS–BEC crossover from semiclassical solutions to the Bogoliubov–deGennes equations. The strong damping of the radial breathing mode observed in the BCS limit occurs when the lowest quasiparticle excitation energies coincide with the radial frequency, which indicates that a coupling between them takes place.
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.
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.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.