Thermal crossover, transition, and coexistence in Fermi polaronic spectroscopies

We investigate the thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using self-consistent frameworks of strong-coupling diagrammatic approaches, both the ejection and the reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to the Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp transition near unitarity and to double-peak coexistence of attractive and repulsive branches in the strong-coupling regime. Our theory provides semiquantitative descriptions for a recent experiment on the ejection RF spectroscopy at unitarity [Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Phys. Rev. Lett. 122, 093401 (2019)] and suggests the importance of beyond-two-body correlations in the high-temperature regime due to the absence of Pauli-blocking effects.

Figure 1

Schematic diagram for polarized Fermi gases at a finite temperature near unitarity obtained from ejection RF spectra, where AP (BG) is the regime of attractive polarons (Boltzmann gas). Solid and dashed lines show the transition and the boundary for the coexistence regime (AP $+$ RP), respectively.

Figure 2

Calculated ejection RF spectra $I_{\mathrm{E}}\left(\omega \right)$ [panels (a1) and (a2)] and reverse RF spectra $I_{\mathrm{R}}\left(\omega \right)$ [panels (b1) and (b2)] in arbitrary units. Panels (c1) and (c2) show the line shapes of $I_{\mathrm{E}}\left(\omega \right)$ [the inset is $I_{\mathrm{R}}\left(\omega \right)$]. The interactions are set at ${\left(k_{\mathrm{F}}a\right)}^{-1}=0$ [panels (a1), (b1), and (c1)] and ${\left(k_{\mathrm{F}}a\right)}^{-1}=0.4$ [panels (a2), (b2), and (c2)]. ${\varepsilon }_{\mathrm{F}}$ and $T_{\mathrm{F}}$ are the Fermi energy and the Fermi temperature of the majority atoms, respectively. The common line styles are used in each figure.

Figure 3

Peak positions ${\omega }_{\mathrm{peak}}$ of (a) ejection and (b) reverse RF spectra at different interaction strengths. The common line symbols are used in each figure.

Figure 4

FWHM of the ejection RF spectra at different interaction strengths. The dashed (long-dashed) line represents the high (low)-temperature fitting $\gamma /{\varepsilon }_{\mathrm{F}}=1.75\sqrt{T_{\mathrm{F}}/T}$ $[\gamma /{\varepsilon }_{\mathrm{F}}=1.61{(T/T_{\mathrm{F}})}^2]$ at ${\left(k_{\mathrm{F}}a\right)}^{-1}=0$ [50, 68, 69, 70, 71].

Figure 5

Comparisons of peak positions and FWHM (inset) in ejection RF spectra between our results (solid circle, ETMA; open square, SCTMA; open diamond, TMA) and recent experiments at the unitarity limit. The downward and upward triangles represent the experimental value from Ref. [50] and that with the subtraction of the mean-field shift with respect to the final state interaction given by ${\mathrm{\Sigma }}_{\mathrm{f}}=0.09{\varepsilon }_{\mathrm{F}}$, respectively.

Figure 6

Feynman diagrams describing examples of (a) three-body and (b) four-body correlations which are absent in the TMA, where the solid (double-solid) lines represent $G$ ($\mathrm{\Gamma }$). While the ETMA involves three-body correlations (a), the SCTMA involves both three-body (a) and four-body (b) correlations.