Observation of high-order quantum resonances in the delta kicked rotor

Quantum resonances in the delta kicked rotor\footnote{F.L. Moore, J.C. Robinson, C.F. Bharucha, B. Sundaram, M.G. Raizen, {\it Phys. Rev. Lett.} \textbf{75} 4598 (1995). } are characterized by a dramatically increased energy absorption rate in direct contradiction to the momentum localization generally observed. These resonances exist where the scaled Planck's constant $\tilde{\hbar}=\frac{r}{s}\cdot4\pi$, for integers $r$ and $s$. However only the $\tilde{\hbar}=r\cdot2\pi$ resonances are easily observable. We report on the observation of high-order quantum resonances ($s>2$) utilizing a sample of low temperature, non-condensed atoms and a pulsed optical standing wave. Resonances are observed for $\tilde{\hbar}=\frac{r}{16}\cdot4\pi$ for integers $r=2-6$. The behavior of the resonances with variation of kick number and kick strength is examined. Quantum numerical simulations suggest that our observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample.