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Physical Review A

Microwave ionization rates of Na Stark states

J. M. Hettema, Panming Fu, Thomas F. Gallagher

Published Jun 1, 1990• 8 citations
Publisher

Abstract

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 ${\mathit{F}}_{\mathit{T}}$\ensuremath{\simeq}1/3${\mathit{n}}^{5}$ (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.

DOI
10.1103/physreva.41.6555

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Physical Review A•Aug 1, 1991•33 citations
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.
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.
The authors have observed the ionization of Na Rydberg states by strong microwave fields and have found that the field required for ionization is 1(3.7n5)\frac{1}{(3.7{n}^{5})}(3.7n5)1​ (in atomic units) for $n=20\ensuremath{-}37$. This field is close to the field 1(3n5)\frac{1}{(3{n}^{5})}(3n5)1​ at which the Stark manifolds of principal quantum numbers nnn and n+1n+1n+1 intersect. The ionization can be shown to arise from transitions occurring near these intersections.
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.
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}1/3n5{n}^{5}n5, and two thresholds for the \ensuremath{\Vert}m\ensuremath{\Vert}=2 states of E\ensuremath{\approxeq}1/9n4{n}^{4}n4 and E\ensuremath{\approxeq}1/21n4{n}^{4}n4 depending upon the n state. The \ensuremath{\Vert}m\ensuremath{\Vert}=0 and 1 thresholds show a departure from a 1/n5{n}^{5}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=1/21n4{n}^{4}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.
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.