Beyond Linear Response Spectroscopy of Ultracold Fermi Gases

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.

Figure 1

The rf field breaks a pair of atoms in internal states $g^{\prime }$ and $g$ by driving a transition to a third state. At the single-atom level, the energy cost of creating an excitation in the superfluid, $\delta E_k$, has to match the rf field detuning $\omega$, causing a shift of the spectral peak. Higher order perturbation theory allows processes where energy is conserved at the many particle level, e.g., resonant transfer of the two atoms above even when they are individually out of resonance.

Figure 2

In the sequential transfer (solid arrows) of $N=4$ atoms, the (time) order in which the atoms are transferred can be chosen in $N!$ different ways. An $N$-atom transfer (one example shown by dashed arrows) can be done in $N{!}^2$ different ways. The process is called virtual if an auxiliary vertical line (example shown as a dotted line) cuts two or more arrows [15].

Figure 3

Rf spectra in the higher order theory using parameters given in the text. At finite temperatures, an additional peak appears at the zero detuning. For comparison, the spectrum from the linear response theory is shown as a solid line.