The quasi-stability of highly-exicited H and He atoms in a strong infrared (IR) field is studied based on three-dimensional quantum calculations.The spectra of atoms that survive the IR field show a series of IR-frequency-modulated peaks which extend from deeply bound states all the way to the ionization threshold and above.The atoms that survive mainly consist of highly-excited Rydberg states, even after hundreds of the intense IR cycles.Also they tend to have initial energies which allow emission or absorption of an integer number of IR photons to reach these quasi-stable states.Peaks above the ionization threshold in the survival spectra indicate the existence of multi-photon assisted recombination in the intense IR field.
The 38-GHz microwave field required to effect 50
ionization of Li atoms decreases from 60 V/cm at
n=37, where the microwave frequency is one-third the Kepler frequency, to 45 V/cm at
n=56, where the microwave frequency is equal to the Kepler frequency. For
n>56 the 50
ionization field is constant at $E\ensuremath{\approx}2.4{\ensuremath{\omega}}^{5/3}$ until $\ensuremath{\sim}80$ GHz below the ionization limit, where it begins to decline. In spite of the fact that the pulse is 8000 cycles long, we detect approximately 5
of the initial population in very-high-lying (
n>215) states subsequent to the microwave pulse. We suggest that these atoms are trapped in metastable atom-field states during the microwave pulse and relax to the high-lying states when the field is turned off. The existence of such states is predicted by the simple man's model of above-threshold ionization.
We have studied the ionization of Na ns and nd Rydberg atoms by \ensuremath{\sim}1-\ensuremath{\mu}s pulses of 10-MHz, 670-MHz, 2-GHz, and 4-GHz fields, bridging the gap between the previous measurements of ionization by \ensuremath{\sim}1-\ensuremath{\mu}s rise-time pulses and 8- and 15-GHz microwave fields. We have also studied the ionization of Li ns and nd Rydberg atoms by 4-, 8-, and 15-GHz fields, which, due to the smaller Li quantum defects, represents the high-frequency limit of nonhydrogenic microwave ionization. The Na measurements show that ionization at 10 MHz occurs without change in n at fields of 1/16
n4 and 1/9
n4. At 670 MHz \ensuremath{\Vert}m\ensuremath{\Vert}=0, 1, and 2 states are all ionized at fields between 1/3
n5 and 1/9
n4, indicating that transitions to higher-n states are occurring. As the frequency is raised further, to 2 and 4 GHz, the \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states exhibit an increasingly sharp threshold for ionization at E=1/3
n5, but the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states are unlikely to ionize at this field, with ionization occurring mostly at higher fields, 1/3
n5E1/9
n4, approaching the 15-GHz behavior of ionization at E=1/9
n4. At 4 GHz, Li n=20 \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states ionize at E=1/3
n5, but at n\ensuremath{\simeq}45, \ensuremath{\Vert}m\ensuremath{\Vert}=1 states ionize at E=1/9
n4, and the \ensuremath{\Vert}m\ensuremath{\Vert}=0 states ionize at E>1/3
n5. The \ensuremath{\Vert}m\ensuremath{\Vert}=2 states appear to ionize at E=1/9
n4. As the frequency is raised to 8 and then to 15 GHz, the transition of \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states to ionization at E=1/9
n4 occurs at lower n. When a small static field is applied, the Li ionization threshold fields drop from 1/9
n4 to fields somewhat above 1/3
n5. Together the Na and Li measurements show that microwave ionization depends on a rate-limiting step, which is a resonant multiphoton transition.
In the ionization of Li and Na by a 16.91-GHz microwave field, roughly 20% of the atoms are not actually ionized but trapped in highly excited states within one or, at most, two microwave photons of the ionization limit. The highly excited atoms appear at the same field as the onset of microwave ionization, irrespective of whether ionization occurs at the field
E=1/3n5 or
E=1/16n4. The highly excited atoms are only detected in static fields less than 35 mV/cm, a field which roughly corresponds to field ionization of an atom bound by twice the microwave frequency. We also show that Na
∣m∣=1 atoms require a microwave field of
E=1/9n4 for ionization in zero static field, but the required field for ionization is reduced to
E=1/3n5 if a static field of 1 V/cm is present.
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.
Using a laser intensity modulated synchronously with a 15.9 GHz microwave field we have examined laser excitation of Li atoms to the vicinity of the ionization limit in the presence of the microwave field and a parallel static field. The static field breaks the symmetry of ionization in the two microwave half cycles, and as the intensity modulated laser beam is delayed relative to the microwave field, maxima in the ionization are observed every microwave field cycle, not every half cycle, as in the absence of the static field. When the laser is tuned below the ionization limit there is an unexpected phase reversal of the modulation in the ionization, the origin of which is clarified by a classical model.