Classical phase locking in adiabatic rapid passage

When a Rydberg atom is slowly swept through a dipole allowed resonance with an oscillating field adiabatic rapid passage (ARP) from one state to the other can occur. By measuring the time resolved momentum of a Rydberg electron with a half cycle pulse we demonstrate that during ARP the classical oscillating dipole due to the orbital motion of the electron becomes phase locked to the microwave field driving the resonance. Depending on the direction of the sweep through resonance, the atom is in one or the other of the two Floquet eigenstates in which the electron is phase locked in or $\pi$ out of phase with the driving field. In contrast, in Rabi oscillations the electron motion oscillates between leading and lagging the driving microwave field.

Figure 1

Schematic diagram of the Floquet energies of the two level system vs tuning electric field $E_s$ with no microwaves $(\cdots )$ and with a microwave field (—). In both (a) and (b) the solid curves are the experimental signals. The broken lines are sinusoidal curves obtained by fitting the experimental curve in (a) and inverting the fit curve from (a) for (b).

Figure 2

Schematic diagram showing the central features of the apparatus.

Figure 3

(Color online) HCP ionization signal vs fine time delay (a) when the atoms are brought to the avoided crossing along the upper curve of Fig. 1, and (b) when they are brought to the avoided crossing along the lower curve of Fig. 1. The signals are $\pi$ out of phase, corresponding to the oscillating dipoles being locked in and $\pi$ out of phase with the field. Dotted curves are fits of the data with the sinusoidal functions.

Figure 4

Experimentally observed (—) and calculated $(\cdots )$ amplitudes of HCP ionization signals vs the tuning field $E_s$.

Figure 5

(Color online) (a) Rabi oscillation between the $6s54s$ and $6s54p$ states in a 0.1 mV/cm, 17.316 microwave field. (b) HCP ionization signals vs fine time delay at the coarse delay times $\mathit{A}$ through $\mathit{E}$ shown in (a). The dipole oscillates between leading and lagging the field, corresponding to energy going from the field to the atom and vice versa.