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Physical Review A

Short-pulse microwave ionization of Na Rydberg atoms

M. Gatzke, Bernard Broers, Lambertus D. Noordam, R. B. Watkins, Thomas F. Gallagher

Published Sep 1, 1994• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.2502

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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 n\ensuremath−5{\mathit{n}}^{\mathrm{\ensuremath{-}}5}n\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.
We have observed the microwave ionization of Na sss and ddd states with 8-GHz pulses as short as 600 ps full width at half maximum, i.e., pulses containing five cycles. We find the ionization probability to be strongly dependent on pulse length. For the shortest pulses, ionization probability of ∣m∣=0|m|=0∣m∣=0 and 1 states is approximately zero if a requirement for the minimum number of cycles is not met, even when the microwave amplitude exceeds the long-pulse threshold of E=1/3n5{E=1/3n}^{5}E=1/3n5. For the ∣m∣=2|m|=2∣m∣=2 states, which are approximately hydrogenic, essentially no ionization occurs with the shortest pulse until the microwave amplitude equals 1/9n4{1/9n}^{4}1/9n4. We also find that as many as 50% of the ∣m∣=0|m|=0∣m∣=0 and 1 atoms not ionized by the microwaves are left trapped in higher nnn levels than the one initially excited.
Ionization of Rydberg atoms by short, half-cycle electrical pulses is investigated experimentally in the intermediate-pulse duration regime where the ionization threshold fields are determined both by the slew rate of the ionizing pulse and its duration. Electrical pulses with durations ranging from 140 ps to 9 ns and amplitudes up to are applied to rubidium and lithium atoms prepared in high Rydberg states by laser excitation (n ranges from 42 to 82). The amplitude of the 140 ps pulse required for ionization of the Rb and Li Rydberg population is found to be a factor of two higher than the expected amplitude based on diabatic field ionization and recent theoretical calculations by Reinhold et al (1993 26 L659). Using the longer pulses we studied the transition from the diabatic/adabatic ionization towards ionization in the impulse-kick regime.
Electric field ionization of excited Na atoms by microwave fields between 12 and 15 GHz exhibits several interesting phenomena. The ∣m∣=0and1|m|=0 \mathrm{and} 1∣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 nnn and n+1n+1n+1 Stark manifolds of principal quantum numbers nnn and n+1n+1n+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|m|=2∣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 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 1/16n4{\mathit{n}}^{4}n4 and 1/9n4{\mathit{n}}^{4}n4. At 670 MHz \ensuremath{\Vert}m\ensuremath{\Vert}=0, 1, and 2 states are all ionized at fields between 1/3n5{\mathit{n}}^{5}n5 and 1/9n4{\mathit{n}}^{4}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=1/3n5{\mathit{n}}^{5}n5, but the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states are unlikely to ionize at this field, with ionization occurring mostly at higher fields, 1/3n5{\mathit{n}}^{5}n5E1/9n4{\mathit{n}}^{4}n4, approaching the 15-GHz behavior of ionization at E=1/9n4{\mathit{n}}^{4}n4. At 4 GHz, Li n=20 \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 states ionize at E=1/3n5{\mathit{n}}^{5}n5, but at n\ensuremath{\simeq}45, \ensuremath{\Vert}m\ensuremath{\Vert}=1 states ionize at E=1/9n4{\mathit{n}}^{4}n4, and the \ensuremath{\Vert}m\ensuremath{\Vert}=0 states ionize at E>1/3n5{\mathit{n}}^{5}n5. The \ensuremath{\Vert}m\ensuremath{\Vert}=2 states appear to ionize at E=1/9n4{\mathit{n}}^{4}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=1/9n4{\mathit{n}}^{4}n4 occurs at lower n. When a small static field is applied, the Li ionization threshold fields drop from 1/9n4{\mathit{n}}^{4}n4 to fields somewhat above 1/3n5{\mathit{n}}^{5}n5. Together the Na and Li measurements show that microwave ionization depends on a rate-limiting step, which is a resonant multiphoton transition.
We have measured the ionization fields for Na Rydberg states of $n\ensuremath{\ge}26$ by a 79-GHz microwave field. At low nnn, where the microwave frequency $\ensuremath{\omega}$ is one-third the classical Kepler frequency ${\ensuremath{\omega}}_{K}$, which is equal to the 1/n31/{n}^{3}1/n3 spacing between nnn states, the ionization field is $\ensuremath{\approx}1/3{n}^{5}$, in atomic units. As nnn is raised ${\ensuremath{\omega}}_{K}$ decreases, and the ionization field rises above 1/3n51/3{n}^{5}1/3n5, reaching a constant value when $\ensuremath{\omega}={\ensuremath{\omega}}_{K}$. At very high nnn, 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 nnn and radio frequencies ionization is simply field ionization, and at very high nnn 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.
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{\mathit{F}}_{\mathit{T}}FT​\ensuremath{\simeq}1/3n5{\mathit{n}}^{5}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.