Quasiparticle Lifetime in Ultracold Fermionic Mixtures with Density and Mass Imbalance

We show that atomic Fermi mixtures with density and mass imbalance exhibit a rich diversity of scaling laws for the quasiparticle decay rate beyond the quadratic energy and temperature dependence of conventional Fermi liquids. For certain densities and mass ratios, the decay rate is linear, whereas in other cases, it exhibits a plateau. Remarkably, this plateau extends from the deeply degenerate to the high temperature classical regime of the light species. Many of these scaling laws are analogous to what is found in very different systems, including dirty metals, liquid metals, and high temperature plasmas. The Fermi mixtures can in this sense span a whole range of seemingly diverse and separate physical systems. Our results are derived in the weakly interacting limit, making them quantitatively reliable. The different regimes can be detected with radio-frequency spectroscopy.

Figure 1

Zero temperature decay rate $1/{\tau }_p$ (units of $|U{|}^2{m}_{\uparrow }{m}_{\downarrow }^2{\epsilon }_{F\downarrow }^2/8{\pi }^3$) of an $\uparrow$ quasiparticle as a function of excitation energy ${\xi }_{p\uparrow }$, with $m_{\downarrow }/m_{\uparrow }=173/6$ and $k_{F\uparrow }/k_{F\downarrow }=2$. The solid black curve is the result of a numerical integration of Eq. (3), and the dashed red curves are given by Eqs. (5, 6).

Figure 2

Decay rate $1/{\tau }_{k_{F\uparrow }}$ in units of $|U{|}^2{m}^3{\epsilon }_{F\downarrow }^2{k}_{F\downarrow }/8{\pi }^3{k}_{F\uparrow }$ as a function of temperature with $m_{\uparrow }=m_{\downarrow }=m$ for different density imbalances $k_{F\uparrow }/k_{F\downarrow }=1$, 3, 6, 10. The solid black (dark) curves are the numerical integration of Eq. (3), while the solid red (light) curves in (a) and (b) are given by Eqs. (8, 11), respectively.

Figure 3

Decay rate $1/{\tau }_{k_{F\uparrow }}$ in units of $|U{|}^2{k}_F^4{m}_r^2/32{\pi }^3(m_{\uparrow }{m}_{\downarrow }{)}^{1/2}$ as a function of temperature for $n_{\uparrow }=n_{\downarrow }$ obtained from a numerical integration of Eq. (3). The left figure shows the appearance of a plateau for $m_{\downarrow }\gg m_{\uparrow }$. The right figure compares the numerical results (solid curves) with Eqs. (8, 12, 14) (dashed curves) in the low, intermediate, and high temperature limits, respectively. It also shows the contributions of the forward and backward scattering terms of Eq. (1).