Decoherence of Impurities in a Fermi Sea of Ultracold Atoms

We investigate the decoherence of ${}^{40}\mathrm{K}$ impurities interacting with a three-dimensional Fermi sea of ${}^6\mathrm{Li}$ across an interspecies Feshbach resonance. The decoherence is measured as a function of the interaction strength and temperature using a spin-echo atom interferometry method. For weak to moderate interaction strengths, we interpret our measurements in terms of scattering of K quasiparticles by the Fermi sea and find very good agreement with a Fermi liquid calculation. For strong interactions, we observe significant enhancement of the decoherence rate, which is largely independent of temperature, pointing to behavior that is beyond the scattering of quasiparticles in the Fermi liquid picture.

Figure 1

Interferometric method for measuring the decoherence of K in a Li Fermi sea. The upper illustration shows a schematic of the rf pulse sequence. The atoms in the $\mathrm{K}|3⟩$ state interact with a Fermi sea of $\mathrm{Li}|1⟩$ atoms, as indicated by the shaded region. The graph shows the fraction of the K atoms transferred to the $\mathrm{K}|3⟩$ state as a function of the relative phase of the final $\pi /2$ rf pulse for various interaction times $\tau$ and for $-1/{\kappa }_{F}a=2.1$, $T=0.16$ ${\epsilon }_F/k_B$.

Figure 2

Contrast $C$ as a function of interaction time $\tau$. In (a), we show results for moderately attractive interspecies interactions ($-1/{\kappa }_{F}a=2.1$), corresponding to Fig. 1. In (b), we probe the system in the strongly interacting regime ($-1/{\kappa }_{F}a=0.15$) for $T=0.20{\epsilon }_F/k_B$ by rapidly shifting the interaction parameter from 2.2 to 0.15 during the interaction time. The solid lines are exponential fits to the points with $\tau >7\mu \mathrm{s}$. The dotted line is an extrapolation to $\tau =0$.

Figure 3

Decoherence rate of K in a Li Fermi sea as a function of the interaction parameter for an average temperature $T=0.16$ ${\epsilon }_F/k_B$ (see text). The measurements with (without) rapid shifting of the FR are shown as the red circles (black squares). The measurements from Fig. 2 are indicated by open symbols. The solid upper (blue) and lower (black) lines correspond to the prediction of the Fermi liquid theory with and without medium corrections, respectively. The dashed lines incorporate corrections due to decay to Feshbach molecules. The shaded areas show the $1\sigma$ effect of the experimental uncertainties on the theoretical predictions.

Figure 4

Decoherence rate of K in a fermionic Li cloud as a function of temperature. The data for $-1/{\kappa }_{F}a=0.2$, ${\kappa }_F{R}^{*}=0.94$, ${\overline{n}}_{\mathrm{K}}/{\overline{n}}_{\mathrm{Li}}=0.2$ ($-1/{\kappa }_{F}a=2.4$, ${\kappa }_F{R}^{*}=0.89$, ${\overline{n}}_{\mathrm{K}}/{\overline{n}}_{\mathrm{Li}}=0.3$) measured with (without) rapid shifting of the FR is shown as red circles (black squares). The solid blue and black lines correspond to the predictions of the Fermi liquid theory for $-1/{\kappa }_{F}a=2.4$ with and without medium corrections, respectively. The shaded areas show the $1\sigma$ effect of the experimental uncertainties on the theoretical predictions.