Observation of quantum equilibration in dilute Bose gases

We investigate experimentally the dynamical relaxation of a nonintegrable quantum many-body system to its equilibrium state. A Bose-Einstein condensate is loaded into the first excited band of an optical lattice and let to evolve up to a few hundreds of milliseconds. Signs of quantum equilibration are observed. There is a period of time, roughly 40 ms long, during which both the aspect ratio of the cloud and its momentum distribution remain constant. In particular, the momentum distribution has a flat top and is not a Gaussian thermal distribution. After this period, the cloud becomes classical as its momentum distribution becomes Gaussian.

Figure 1

(a) Aspect ratios of the atomic cloud at different holding times with the lattice strength $V=8E_{\mathrm{r}}$. The TOF image at 50 ms is shown in the inset to show how the aspect ratio is extracted. Each point is the average over five experiments and the error bar is the standard error. The red solid line indicates the plateau during which the aspect ratio remains constant while the red dashed line shows the transition period between two stages. (b) The starting (blue) and ending times (red) of the plateau for different lattice strengths.

Figure 2

The TOF images (left column) and the corresponding integrated one-dimensional distribution (right column) at five typical times: $t=2\mathrm{ms},t=40\mathrm{ms},t=50\mathrm{ms},t=200\mathrm{ms}$, and $t=400\mathrm{ms}$. The red dashed lines in the right column are the best thermal distribution fit. $V=8E_{\mathrm{r}}$.

Figure 3

The momentum distribution at the beginning (red solid line), in the middle (black dotted line), and at the end (blue dashed line) of the quantum equilibrium plateau for (a) $8E_{\mathrm{r}}$ and (b) $14E_{\mathrm{r}}$. The momentum distribution averaged over the entire equilibrium plateau is shown in (c) for $8 E_{\mathrm{r}}$ and (d) for $14 E_{\mathrm{r}}$ with solid blue lines while the thermal fitting is shown with red dashed lines.

Figure 4

(a) Oscillations of the aspect ratio $r$. The dashed line is a theoretical fitting. The oscillation frequency is about twice the trapping frequency along the direction of optical lattice. (b) Decay of amplitude of the oscillations. The solid line represents an exponential fit. $V=8E_{\mathrm{r}}$.