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.
We report the first observation of the ionization of Rydberg atoms by a circularly polarized 8.5-GHz microwave field. The observed threshold field for ionization is E=1/16
n4, a value higher than that required for ionization by a linearly polarized microwave field. The origin of this threshold can be understood by transforming to a frame rotating at the microwave frequency. In the rotating frame no transitions occur, and level mixings alone are responsible for the ionization.
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.
We have measured the 17.3 GHz circularly polarized microwave ionization (CPMI) threshold fields for Na Rydberg atoms and compared them to the previous 8.5 GHz measurements. In both cases the ionization fields are near for low n and fall below this value at high n. A small ellipticity in the polarization and a small static field in the plane of the rotating microwave field both lead to ionization at substantially lower fields, approaching . In addition, elliptically polarized microwave ionization (EPMI) of Rydberg atoms and CPMI in the presence of a small static field have much lower threshold fields for ionization and unexpected resonant peaks at microwave fields below the CPMI threshold fields are observed in both cases at 8, but not at 17, GHz. Sequences of resonant microwave transitions are proposed to explain these resonant structures.
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 studied in detail the continuous evolution from static field ionization to ionization by a circularly polarized microwave field by combining a z-polarized static field with a circularly polarized microwave field in the x-y plane. We have measured the ionization threshold for Na states of
27< n< 50 in the precessing total field
Ft, as a function of its angle \ensuremath{\theta} from the z axis. For low n, ${F}_{t}\ensuremath{\cong}{1/16n}^{4},$ independent of \ensuremath{\theta}. For
n> 45, Ft decreases from
1/16n4 to
0.8/16n4 as \ensuremath{\theta} is increased from 0\ifmmode^\circ\else\textdegree\fi{} to 25\ifmmode^\circ\else\textdegree\fi{}, and it remains at this value until $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}.$ We also observe ionization at quite low values of
Ft, which we attribute to resonantly enhanced ionization, with the resonances driven by a stray static field in the x-y plane.
Here we present experimental results connecting field ionization to photoionization in Li Rydberg atoms obtained with 17- and 36-GHz microwave fields. At a low principal quantum number
n, where the microwave frequency $\ensuremath{\omega}$ is much lower than the classical, or Kepler frequency, ${\ensuremath{\omega}}_{K}=1/{n}^{3}$, microwave ionization occurs by field ionization, at
E=1/9n4. When the microwave frequency exceeds the Kepler frequency, $\ensuremath{\omega}>1/{n}^{3}$, the field required for ionization is independent of
n and given by $E=2.4{\ensuremath{\omega}}^{5/3}$, in agreement with dynamic localization models, which cross over to a Fermi's Golden Rule approach at the photoionization limit. A surprising aspect of our results is that when $\ensuremath{\omega}\ensuremath{\approx}1/2{n}^{2}$, the one- and multiphoton ionization rates are similar, and even at the lowest microwave powers, all are 10 times lower than the perturbation theory rate calculated for single-photon ionization. Further, we show that when the Rydberg atoms are excited in the presence of the microwave field, the probability of an atom's being bound at the end of the microwave pulse passes smoothly across the limit. This microwave stimulated recombination to bound Rydberg states can be well described by a simple classical model. More generally, these results suggest that the problem of a Rydberg atom coupled to a high-frequency microwave field is similar to the problem of interchannel internal coupling in multilimit atoms, a problem well described by quantum defect theory.