Probing quasiparticle states in strongly interacting atomic gases by momentum-resolved Raman photoemission spectroscopy

We investigate a momentum-resolved Raman spectroscopy technique which is able to probe the one-body spectral function and the quasiparticle states of a gas of strongly interacting ultracold atoms. This technique is inspired by angle-resolved photoemission spectroscopy, a powerful experimental probe of electronic states in solid-state systems. Quantitative examples of experimentally accessible spectra are given for the most significant regimes along the BEC-BCS crossover. When the theory is specialized to rf spectroscopy, agreement is found with recent experimental data. The main advantages of this Raman spectroscopy over existing techniques are pointed out.

Figure 1

(Color online) (a) geometrical configuration of the Raman laser beams. (b) scheme of the atomic levels involved in the Raman process.

Figure 2

(Color online) Contour plot of the calculated rf intensity for a degenerate gas of noninteracting fermions at $T/T_F=0.18$. The color scale indicates the rate of transfer into a state of momentum $\mathbf{k}$ of the $\beta$ state as a function of the (rescaled) rf frequency $E_s={\epsilon }_{\mathbf{k}\beta }-\omega$. The left (a) panel refers to a spatially homogeneous system. The (b) and (c) panels have been calculated within the local-density approximation: the central (b) panel refers to the case where both $\alpha$ and $\beta$ atoms experience the same harmonic trap potential. The right (c) panel refers to the case in which only the $\alpha$ atoms are trapped. The rf field is spatially uniform over the whole system.

Figure 3

(Color online) Momentum-integrated rf signal for a trapped gas; as in the central panel of Fig. 2b, the trap potential is assumed to act in the same way on the two $\alpha$ and $\beta$ atomic states. Differently from Eq. (4), the momentum integration is here performed along lines of fixed $E_s$. The calculated spectrum is in good agreement with the experimental observation by the Boulder group (Fig. 5b of Ref. [33]).

Figure 4

(Color online) Contour plot of the Raman rate for a trapped gas with the same parameters as in the Boulder experiment and a beam transverse size $\sigma =15/k_F$. Left panel: raw data in the $\left(k,\omega \right)$ plane. Right panel: translated data in the $\left(\left|\mathbf{k}-\mathbf{q}\right|,E_s\right)$ plane.

Figure 5

(Color online) Left (a) panel: pseudogap model for a Fermi gas in the unitary limit. The black line is the free particle dispersion while the $E_{\mathbf{k}}^{\pm }$ curves are the BCS quasiparticle branches. Upper (b) and lower (c) panels: contour plots of the rf rate for a spatially homogeneous system at low $T/T_F=0.05$ and intermediate $T/T_F=0.4$ temperatures.

Figure 6

(Color online) Photoemission signal for a strongly interacting, trapped Fermi gas at unitarity $\left(1/k_F{a}_s=0\right)$ at a temperature $T=0.18T_F$. The left panel shows the rf signal. The right panel shows the Raman signal for a spatially selective process with $\sigma =15/k_F$. For a comparison of the left panel to experiment, see Fig. 3b of Ref. [33].

Figure 7

(Color online) Momentum-integrated rf signal for a trapped, strongly interacting Fermi gas at unitarity. Same system as in the left panel of Fig. 6. As in Fig. 3, momentum integration has been performed along lines of constant $E_s$. For a comparison to experiment, see Fig. 5c of Ref. [33].

Figure 8

(Color online) Photoemission spectroscopy signal for ${\left(k_F{a}_s\right)}^{-1}=1$ on the BEC side at a temperature $T/T_F=0.5$. Left (a) panel: rf signal for a homogeneous system. Central (b) panel: rf signal for a trapped system with the parameters of the experiment of Ref. [33]. Right (c) panel: Raman signal with a spatially selective probe $\sigma =15/k_F$ focused onto the cloud center.

Figure 9

(Color online) Photoemission spectroscopy with $q=0$ for different temperatures $T=0.05T_F$ (upper panels), $T=0.4T_F$ (lower panels) and for different initial populations of $\beta$ atoms $k_{F\beta }=0$ (left panels), $k_{F\beta }=1.73k_F$ (right panels). In all panels, the purple background color corresponds to a vanishing photoemission and photoabsorption intensity. The yellow color indicates the occurrence of direct photoemission processes from $\alpha$ into $\beta$; the blue color indicates the occurrence of reverse photoabsorption processes from $\beta$ into $\alpha$.

Figure 10

(Color online) Photoemission spectroscopy for different temperatures $T=0.05T_F$ (upper panels), $T=0.4T_F$ (lower panels), and for initial population of $\beta$ atoms $k_{F\beta }=0.5k_F$. The transfer momenta are $q=0.5k_F$ (left panels) and $q=k_F$ (right panels). Same color code as in Fig. 9.