Electric field ionization of excited Na atoms by microwave fields between 12 and 15 GHz exhibits several interesting phenomena. The
∣m∣=0and1 states may be ionized with a very low microwave field, $\ensuremath{\sim}\frac{1}{{3n}^{5}}$, corresponding to the point at which the
n and
n+1 Stark manifolds of principal quantum numbers
n and
n+1 intersect. The ionization occurs by an atom's making a succession of Landau-Zener transitions to higher-lying states, finally reaching the classical ionization limit. The
∣m∣=2 states, on the other hand, ionize at a very high microwave field, $\ensuremath{\sim}\frac{1}{{9n}^{4}}$. Both these observations and the more familiar static or low-frequency result of ionization by a field of $\ensuremath{\sim}\frac{1}{{16n}^{4}}$ are all consistent with ionization in a completely classical fashion. The apparent differences are due to the dynamics of passing from zero field to a high ionizing field.
Near threshold the microwave ionization rates of Na \ensuremath{\Vert}m\ensuremath{\Vert}=0,1 Rydberg states within a Stark manifold n show a strong dependence on the location of the state within the manifold. In particular, the rate-limiting step for ionization of states with the smallest Stark shifts (\ensuremath{\Vert}k\ensuremath{\Vert}\ensuremath{\ll}n) is different from the field-limited step of making the n\ensuremath{\rightarrow}n+1 transitions at threshold fields
FT\ensuremath{\simeq}1/3
n5 (a.u.). This variation in the ionization rates as a function of manifold location or Stark shift may be understood in terms of the variation in the transition probability to the bluest Stark states from the other members of the manifold.
We have measured the ionization fields for Na Rydberg states of $n\ensuremath{\ge}26$ by a 79-GHz microwave field. At low
n, where the microwave frequency $\ensuremath{\omega}$ is one-third the classical Kepler frequency ${\ensuremath{\omega}}_{K}$, which is equal to the
1/n3 spacing between
n states, the ionization field is $\ensuremath{\approx}1/3{n}^{5}$, in atomic units. As
n is raised ${\ensuremath{\omega}}_{K}$ decreases, and the ionization field rises above
1/3n5, reaching a constant value when $\ensuremath{\omega}={\ensuremath{\omega}}_{K}$. At very high
n, where $\ensuremath{\omega}>1/2{n}^{2}$, single photoionization is possible, and the measured rate agrees with the calculated value. These measurements, together with those done previously, connect the processes of field ionization and photoionization in Na. At low
n and radio frequencies ionization is simply field ionization, and at very high
n it occurs by photoionization, single-photon absorption. These measurements also show that microwave ionization of Rydberg atoms at 79 GHz results in significant populations' being left in the very high-lying states.
We have measured the microwave ionization threshold electric fields for ns-state Na Rydberg atoms from n=24--33 as a function of the duration of the ionizing microwave pulse. Pulses as short as 2.8 ns were used, containing fewer than 25 cycles of 8.55-GHz radiation. While the fields required to produce the onset of ionization were independent of pulse duration and exhibited the ${\mathit{n}}^{\mathrm{\ensuremath{-}}5}$ scaling characteristic of ionization by diffusion through higher-energy states, the fields required to produce nearly complete ionization increased dramatically as the pulse was shortened. Additional measurements of the populations of bound states after the shortest microwave pulses showed that up to \ensuremath{\sim}10% of the atoms were excited to states above the initially populated ns state and the adjacent (n-1) manifold of higher angular momentum states, while most either ionized or remained in these states. From this observation we conclude that the rate-limiting process for ionization is the transition from the initially populated ns states or the adjacent manifold to the next higher manifold, not the diffusion through higher-lying states.
In circularly polarized microwave fields of frequencies in the vicinity of 10 GHz ionization of Na Rydberg atoms occurs at a field E=1/16n4, up to principal quantum number n=50. This field is equal to the classical field for ionization and the static field required to ionize a Na atom. On the other hand, this field is far below the linearly polarized 10 GHz field required to ionize Na atoms, E=1/3n5. If the problem is transformed to a frame rotating with the microwave field, the field becomes a static field. In this case it is straightforward to calculate the ionization field classically. However, it is far lower than the experimentally observed field, a discrepancy which may be due to an angular momentum barrier.
The ionization of Na atoms by 8-GHz electric fields from principal quantum number n=16--42 exhibits a threshold for the \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states of E\ensuremath{\approxeq}1/3
n5, and two thresholds for the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states of E\ensuremath{\approxeq}1/9
n4 and E\ensuremath{\approxeq}1/21
n4 depending upon the n state. The \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 thresholds show a departure from a 1/
n5 scaling at high n which we interpret as being due to the fact that the relatively slower atomic frequencies at high n no longer match the 8 GHz microwave frequency. The E=1/21
n4 \ensuremath{\Vert}m\ensuremath{\Vert}=2 threshold has not to our knowledge been observed before, and we interpret it as arising from the ionization of the highest energy, or blue, Stark state at the classical limit for ionization.