Observation of Elastic Doublon Decay in the Fermi-Hubbard Model

We investigate the decay of highly excited states of ultracold fermions in a three-dimensional optical lattice. Starting from a repulsive Fermi-Hubbard system near half filling, we generate additional doubly occupied sites (doublons) by lattice modulation. The subsequent relaxation back to thermal equilibrium is monitored over time. The measured absolute doublon lifetime covers 2 orders of magnitude. In units of the tunneling time $h/J$ it is found to depend exponentially on the ratio of on-site interaction energy $U$ to kinetic energy $J$. We argue that the dominant mechanism for the relaxation is a simultaneous many-body process involving several single fermions as scattering partners. A many-body calculation is carried out using diagrammatic methods, yielding fair agreement with the data.

Figure 1

Stability of highly excited states in the single-band Hubbard model. Doubly occupied lattice sites are protected against decay by the on-site interaction energy $U$. The average kinetic energy of a single particle in a periodic potential is half the bandwidth $6J$. Thus the relaxation of excitations requires several scattering partners to maintain energy conservation.

Figure 2

Comparison of the time evolution of the double occupancy and total atom number for different ratios $U/6J$. The data were recorded using the ($-9/2$, $-5/2$) spin mixture, with $U/h=3.9\mathrm{kHz}$ (3.1 kHz) and $J/h=140\mathrm{Hz}$ (200 Hz) for the triangular (round) data points. The lines show fits of the integrated population equations of Eq. (1). The total atom numbers are scaled to the initial values. The inset shows a magnification for short times. Error bars denote the statistical error of at least four identical measurements.

Figure 3

Semilog plot of doublon lifetime ${\tau }_D$ vs $U/6J$. The lifetime is extracted from data sets as shown in Fig. 2. Solid and hollow circles denote the ($-9/2$, $-5/2$) and ($-9/2$, $-7/2$) spin mixture, respectively, while the dashed line shows the theoretical result at half filling. The solid line is a fit of Eq. (2) to the experimental data, yielding $\alpha =0.82\pm 0.08$, whereas for the theory curve the asymptotic slope at large $U/6J$ is ${\alpha }_T=0.80$. The shaded corridor was obtained by varying the filling factor in the calculation by $\pm 0.3$ (which has only a weak effect on the slope). The inset shows the parameters used to realize the different values of $U/6J$. Error bars denote the confidence intervals of the lifetime fits and the statistical errors in $U/6J$. The systematic errors in $U/6J$ and ${\tau }_D/(h/J)$ are estimated to be 30% and 25%, respectively.

Figure 4

The double lines represent doublon propagators, and the single lines fermion propagators. (a) Typical doublon propagator diagram showing the creation of particle-hole pairs by both the doublon and the projected fermions as well as annihilation of the doublon into a pair of single fermions. (b) Typical example for a neglected diagram type.