Radio-frequency spectroscopy of a strongly imbalanced Feshbach-resonant Fermi gas

A sufficiently large species imbalance (polarization) in a two-component Feshbach resonant Fermi gas is known to drive the system into its normal state. We show that the resulting strongly interacting state is a conventional Fermi liquid, that is, however, strongly renormalized by pairing fluctuations. Using a controlled $1∕N$ expansion, we calculate the properties of this state with a particular emphasis on the atomic spectral function, the momentum distribution functions displaying the Migdal discontinuity, and the radio frequency (rf) spectrum. We discuss the latter in the light of the recent experiments of [Schunck et al., Science 316, 867 (2007)] on such a resonant Fermi gas, and show that the observations are consistent with a conventional, but strongly renormalized Fermi-liquid picture.

Figure 1

Momentum distribution $n_{\sigma }\left(k\right)$ of the majority (∣1⟩) and minority (∣2⟩) atoms for polarization $P=0.9$ at zero temperature and at resonance. The residues for the majority and minority atoms are, respectively, $Z_1=0.56$ and $Z_2=0.29$.

Figure 2

(Color online) rf spectrum for polarization $P=0.97$: the intensity $I_3\left(\nu \right)$ (arbitrary units) vs the detuning from the resonance frequency $\nu$ measured in units of the Fermi energy ${ϵ}_F$. In free space, the resonance would be at $\nu =0$. The shift in the resonance frequency above is due to strong interactions between fermions in the nonsuperfluid ground state of a polarized Fermi gas. Our primary claim is that such a shift is present even while the ground state remains a Fermi liquid, with the discontinuities in the momentum distribution function shown in Fig. 1.

Figure 3

Self-energy diagram ${\Sigma }_{\sigma {\sigma }^{\prime }}$ to leading order in $1∕N$.

Figure 4

Quasiparticle Fermi-liquid properties: (a) residue $Z_{\sigma }$ [Eq. (25)], (b) effective mass $m_{\sigma }^{*}$ [Eq. (26)], and (c) the chemical potential shift $\delta {\mu }_{\sigma }$ [Eq. (16)] of the hyperfine state ∣1⟩ (dashed line), ∣2⟩ (solid line), and ∣3⟩ (dash-dotted line).

Figure 5

(Color online) Vertex correction to the rf spectrum for $P=0.97$. The axes are the same as in Fig. 6. The plain red line includes the vertex correction, while the dashed black line does not. The contribution of the correction $X_{32}^{\left(b\right)}(\mathbf{0},\nu )$ is less than 0.1%.

Figure 6

(Color online) rf spectrum for polarization $P=0.93$: the intensity $I_3\left(\nu \right)$ (arbitrary units) vs the detuning from the resonance frequency $\nu$ measured in units of the Fermi energy ${ϵ}_F$. The peak frequency relative to the noninteracting line (black vertical line at $\nu =0$) is smaller than for the $P=0.97$ case shown in Fig. 2. The linewidth broadens for lower polarizations due to the increase in pairing fluctuations.