Nondispersing Wave Packets

We have formed nondispersing wave packets from atomic Li Rydberg eigenstates by adding a small microwave field approximately resonant with the $\Delta n=1$ transition. The orbital motion of the Rydberg electron in states of $70\le n\le 78$ becomes phase locked to a 17.5 GHz microwave field and remains so for 900 ns, roughly 15 000 orbits of the Rydberg electron. A Floquet approach provides a reasonable quantum-mechanical description.

Figure 1

The electron (●) in the two highly eccentric orbits about the ionic core (+) that become phase locked to the weak microwave field. The electron orbits are aligned along the $z$ axis as is the microwave field. When the force of the field on the electron $F_{\mathrm{MW}}$ is at its maximum in the $-z$ direction the electron in the orbits (a) and (b) are at their outer and inner turning points, respectively.

Figure 2

Ionization probability vs fine time delay of the HCP 100 ns after the beginning of the 17.528 GHz, $1\mathrm{V}/\mathrm{cm}$ microwave pulse: (a) HCP amplitude set to ionize $\sim 60\%$ of the atoms, (b) HCP with amplitude set to ionize $\sim 50\%$ of the atoms with the same polarity as (a) and reversed polarity. In all cases the modulation with period 56 ps indicates that the wave packet is phase locked to the microwave field. In (b) the phase of the signal reverses with HCP polarity as expected.

Figure 3

Peak-to-peak amplitude of the detected wave-packet ion signals vs initial $n$ state for a 17.528 GHz, $1\mathrm{V}/\mathrm{cm}$ microwave field (□). The solid line simply connects the points. Fractional $n$-state composition of the highest energy Floquet state, $A$ (dotted line) and the adjacent Floquet state, $B$ (dashed line) calculated with a $4\mathrm{V}/\mathrm{cm}$ microwave field of the same frequency, but shifted in $n$ by 1 as described in the text. The states $A$ and $B$ are labeled in Fig. 4.

Figure 4

Floquet energy vs field for a one-dimensional atom in a 17.528 GHz field. The energies are plotted relative to the energy of the $n=72$ state. The zero-field Floquet energy of state $n$ is shifted from its normal energy by $(72-n)\times 17.528\mathrm{GHz}$.