Ballistic and Localized Transport for the Atom Optics Kicked Rotor in the Limit of a Vanishing Kicking Period

We present mean energy measurements for the atom optics kicked rotor as the kicking period tends to zero. A narrow resonance is observed marked by quadratic energy growth, in parallel with a complete freezing of the energy absorption away from the resonance peak. Both phenomena are explained by classical means, taking proper account of the atoms’ initial momentum distribution.

Figure 1

The function $G$ vs $x=t(k\tau {)}^{1/2}$ for $J_0\in [0,0.1)$. The inset shows a portion of the classical phase space of the map (3), for $\tau =0.1$, $k=2.5$. The dashed lines mark the position of the initial momenta, corresponding to a uniform distribution of quasimomenta in $[0,1)$.

Figure 2

Results from experiments (circles) and classical simulations (solid lines) showing energy vs $\tau$ for $k=2.5$ and $t=3$, 4, 5, 6, 7, 8 for panels (a)–(f), respectively. The error bars shown in (a) and (f) correspond to statistical fluctuations over three experimental shots (they do not take into account systematic effects such as power fluctuations of the kicking laser).

Figure 3

Data as in Fig. 2, for $k=4.9$ and $t=3$, 5, 7, 12, 16, 20 for panels (a)–(f), respectively. The dotted line in (a) shows the measured energy after just one kick.

Figure 4

Mean energy vs $\tau$ from experiments (circles) and from classical (crosses) and quantum simulations (using a Gaussian initial ensemble centered at $p=0$; solid line) for $k=4.9$, ${\sigma }_p=8$, and $t=5$. The inset shows how the energy varies with $t$ for $\tau =0.2$ and $\tau =0.033$ ($T=0.32\mu \mathrm{s}$, for which the $\delta$-pulse approximation just remains valid for $t<20$ [9, 16]). We note the immediate onset of the freezing effect for $\tau =0.2$; dynamical localization would set in on a time scale larger than one kick for this kick strength [2].