Pauli Blocking Effect on Efimov States near a Feshbach Resonance

In this Letter we study the effect of Pauli blocking on Efimov states in a quantum Fermi gas and illustrate that the universal Efimov potential is altered at large distances. We obtain the universal spectrum flow of Efimov trimers when the Fermi density is varied and further consider the effect of scattering of trimers by the Fermi sea. We argue that the universal flow is robust against fluctuating particle-hole pairs that result in an infrared catastrophe in impurity problems.

Figure 1

Effective potentials $u_{\mathrm{L}}/k_{\mathrm{F}}^2$ versus $k_{\mathrm{F}}R$. From top to bottom we plot the potential for $k_{\mathrm{F}}{a}_{\mathrm{HL}}=-1$, $\infty$, 1. At resonance, $u_{\mathrm{L}}(R)=-{\Omega }^2/R^2$ if the Pauli blocking effect is absent (dashed line); the dotted line is the estimated potential due to the scattering of trimers by the Fermi sea (see discussion near the end of this Letter).

Figure 2

A subset of eigenvalue trajectories at resonance ($a_{\mathrm{HL}}=\infty$) in the $Z=\mathrm{sgn}(u_{\mathrm{B}})\sqrt{|u_{\mathrm{B}}|}{r}_0$ versus $X=k_{\mathrm{F}}{r}_0$ plane; the thin red trajectories are for trimers dressed in fluctuating particle-hole pairs estimated in the leading order. The ray $Z=\sqrt{Y^{\infty }}X$ (dashed line) represents the dimer-atom threshold. The termination points along this threshold $X_n^{\infty }$ are discussed in Eq. (10). Here $\beta =\sqrt{\gamma /\mu }=10$, $r_0$ is the hard-core size of Bose atoms. Only Efimov states are shown, and we take $\delta =\pi /4$ [19].