Connecting Few-Body Inelastic Decay to Quantum Correlations in a Many-Body System: A Weakly Coupled Impurity in a Resonant Fermi Gas

We study three-body recombination in an ultracold Bose-Fermi mixture. We first show theoretically that, for weak interspecies coupling, the loss rate is proportional to Tan’s contact. Second, using a ${}^7\mathrm{Li}/{}^6\mathrm{Li}$ mixture we probe the recombination rate in both the thermal and dual superfluid regimes. We find excellent agreement with our model in the BEC-BCS crossover. At unitarity where the fermion-fermion scattering length diverges, we show that the loss rate is proportional to $n_f^{4/3}$, where $n_f$ is the fermionic density. This unusual exponent signals nontrivial two-body correlations in the system. Our results demonstrate that few-body losses can be used as a quantitative probe of quantum correlations in many-body ensembles.

Figure 1

Sketch of inelastic decay of an impurity immersed in a tunable Fermi gas. On the BEC side, $\uparrow$ and $\downarrow$ fermions are paired in tightly bound molecules and the decay mechanism is a two-body process involving the impurity (green disk) and a molecule. The loss rate scales as $1/a_{ff}$ [20, 24]. On the BCS side, the loss occurs through a three-body process and it scales as $a_{ff}^2$ in the mean-field limit [20]. The extrapolation of these two asymptotic behaviors towards the strongly correlated regime yields contradictory results (grey area).

Figure 2

Remaining fraction of bosons (blue symbols) and fermions (red symbols, inset) after a 1 s and 1.5 s waiting time for spin-balanced (filled symbols), resp. 90% polarized (open symbols) fermions. The blue dash-dotted (red dashed, inset) curve is a coupled loss model describing the competition between boson fermion-dimer decay ($\propto 1/a_{ff}$) and dimer-dimer decay ($\propto 1/a_{ff}^{2.55}$) [27, 31]. The blue-shaded area represents the $1\sigma$ fluctuations for the remaining fraction of bosons with spin-polarized fermions. The initial atom numbers are $3\times 10^5$ for ${}^6\mathrm{Li}$ and $1.5\times 10^5$ for ${}^7\mathrm{Li}$ at a temperature $T\simeq 1.6\mu \mathrm{K}$ with trap frequencies ${\nu }_z=26\mathrm{Hz}$ and ${\nu }_r=2.0\mathrm{kHz}$.

Figure 3

(a) Boson-fermion loss rate vs molecule fraction. Circles: Experimental data. The vertical error bars represent the statistical errors for $L_{\mathrm{bf}}$ from fitting the loss curves. The horizontal error bars represent the statistical errors on the molecule fraction due to ${}^6\mathrm{Li}$ number fluctuations. The red dashed line is a linear fit to the data. (b) Boson-dimer loss rate vs inverse scattering length. The blue dot-dashed line is a linear fit to the data with $n_f{a}_{ff}^3\le 0.025$ (black circles), providing $\gamma =1.17(11)\times {10}^{-27}{\mathrm{m}}^4·{\mathrm{s}}^{-1}$, see Eq. (3).

Figure 4

Boson loss rate versus fermion central density at unitarity, $n_f=n_f(0)$. Circles: Experimental data. The red line is the $n_f^{4/3}$ prediction of Eq. (6) without any adjustable parameter. The red shaded area represents the $1\sigma$ uncertainty resulting from the error on $\gamma$.