Figure 1

Proposal for experimental demonstration of the quantization of the average work performed by the electric field $E(t,x)$. The top panel shows acceleration profile in a space-time unit cell obtained by integration of the classical equations of motion (9). For each initial condition, the resulting classical trajectory allows one to calculate the acceleration by differentiation of the trajectory with respect to time twice. In the middle panel we show the same profile obtained by plotting the total force acting on an atom. In the bottom panel the contribution from the electric field force $E(t,x)$ is plotted only. The integration of $E(t,x)$ over a single space-time cell results in a quantized value which can be also obtained when one estimates the integral with the help of the points presented in the top panel. In the latter case, one has to first subtract the other contributions to the total force which are known from the theoretical description, cf. Eq. (9). Here, $\mu =0.5$ and $m=1$. The Chern number is 4. Moreover, we take $\hslash =1$.