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arXiv:0705.2069 · Physical Review Letters

Spectroscopic Signatures of Nonequilibrium Pairing in Atomic Fermi Gases

Maxim Dzero, Emil A. Yuzbashyan, B. L. Altshuler, Piers Coleman

Published Oct 16, 2007• 31 citations
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Abstract

We determine the radio-frequency (rf) spectra for nonstationary states of a fermionic condensate produced by a rapid switch of the scattering length. The rf spectrum of the nonequilibrium state with constant BCS order parameter has two features in contrast with equilibrium where there is a single peak. The additional feature reflects the presence of excited pairs in the steady state. In the state characterized by periodically oscillating order parameter, the rf-absorption spectrum contains two sequences of peaks spaced by the frequency of oscillations. Satellite peaks appear due to a process where a rf photon in addition to breaking a pair emits or absorbs oscillation quanta.

DOI
10.1103/physrevlett.99.160402

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We determine the radio-frequency (rf) spectra for nonstationary states of a fermionic condensate produced by a rapid switch of the scattering length. The rf spectrum of the nonequilibrium state with constant BCS order parameter has two features in contrast with equilibrium where there is a single peak. The additional feature reflects the presence of excited pairs in the steady state. In the state characterized by periodically oscillating order parameter, the rf-absorption spectrum contains two sequences of peaks spaced by the frequency of oscillations. Satellite peaks appear due to a process where a rf photon in addition to breaking a pair emits or absorbs oscillation quanta.
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.
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.
We employ a time-dependent variational approach to investigate the dynamics of a fermionic atomic gas driven by a radio-frequency (rf) field at zero temperature. Starting from an initial Bardeen-Cooper-Schrieffer (BCS) state with pairing of atoms of two internal levels, an rf field transfers atoms to a third level. Dynamical equations derived from the variational principle are shown to be consistent with the time-dependent Bogoliubov--de Gennes equation. In particular, we show that the short-time dynamics is governed by a set of linear equations, in which an eigenvector associated with a discrete eigenvalue can be identified as the formation of a pair bound state in the final scattering channel. Such a bound state induces characteristic oscillations in the time evolution of the order parameter. At longer times numerical solutions demonstrate complicated dynamics where linear theory breaks down.
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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.
We measure radio frequency (rf) spectra of the homogeneous unitary Fermi gas at temperatures ranging from the Boltzmann regime through quantum degeneracy and across the superfluid transition. For all temperatures, a single spectral peak is observed. Its position smoothly evolves from the bare atomic resonance in the Boltzmann regime to a frequency corresponding to nearly one Fermi energy at the lowest temperatures. At high temperatures, the peak width reflects the scattering rate of the atoms, while at low temperatures, the width is set by the size of fermion pairs. Above the superfluid transition, and approaching the quantum critical regime, the width increases linearly with temperature, indicating non-Fermi-liquid behavior. From the wings of the rf spectra, we obtain the contact, quantifying the strength of short-range pair correlations. We find that the contact rapidly increases as the gas is cooled below the superfluid transition.