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Physical Review A

Suppression of angular-momentum mixing in precision solutions of the Schrödinger equation for photoexcitation of Rydberg states

Harm Geert Muller

Published Apr 24, 2002• 4 citations
Publisher

Abstract

Numerical integration of the Schr\"odinger equation for the resonant single-photon excitation from the $1s$ to $10p$ state in atomic hydrogen has been used to produce solutions converged to a precision of a few parts per million. At all intensities investigated (in the range $10--100{\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}),$ the population in the states having angular momentum higher than $\mathcal{l}=1$ after a narrowband (500 fs) laser pulse are found to be neglible. This shows that off-resonant states can effectively suppress Raman-like transitions to degenerate states of higher angular momentum. Instead of such mixing, strong Rabi-like oscillations between $1s$ and the $\mathrm{np}$ Rydberg series are observed.

DOI
10.1103/physreva.65.055402

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Numerical integration of the Schr"odinger equation for the resonant single-photon excitation from the 1s1s1s to 10p10p10p state in atomic hydrogen has been used to produce solutions converged to a precision of a few parts per million. At all intensities investigated (in the range 10−−100TW/cm2),10--100{\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}),10−−100TW/cm2), the population in the states having angular momentum higher than l=1\mathcal{l}=1l=1 after a narrowband (500 fs) laser pulse are found to be neglible. This shows that off-resonant states can effectively suppress Raman-like transitions to degenerate states of higher angular momentum. Instead of such mixing, strong Rabi-like oscillations between 1s1s1s and the np\mathrm{np}np Rydberg series are observed.
When the Rydberg atom prepared in an n0s state (n0≫1) is exposed to a sufficiently intense laser pulse of a duration not exceedingly short compared with the initial-state Kepler period, the resulting photoelectron angular distributions are not only governed by the p partial wave but are shown to be shaped by higher-order waves as well, provided that the frequency assumed permits the higher-angular-momentum Rydberg states about the initial n0s state to be involved in the process owing to multiple resonant Raman transitions.
When optical frequency fields are used to couple a ground state to a Rydberg state, the resonant dipole coupling is to a low angular momentum state. Higher angular momentum states are typically thought not to play a role in the excitation. The extremely large dipole matrix elements coupling Rydberg states of the same nnn but differing lll, however, allow optical fields of modest strengths to produce Rabi frequencies larger than optical frequencies. We demonstrate that these optical fields can therefore readily excite the higher angular momentum states, and we examine the consequences of this coupling.
An analytical study is presented of two models of intense-laser ionization from an isolated initial state via a band of high-Rydberg states in a system which bears many features of the hydrogen atom. The models differ in the way the population from the directly excited Rydberg states can migrate to the states of higher angular momenta. In one of them it migrates via nonresonant and in the other via resonant degenerate Raman coupling. Within these models we draw conclusions about the efficiency of migration, the initial-state lifetime, the redistribution of population, the laser intensities stabilizing the atom against ionization, the effect of the initial state on the threshold stabilizing intensity, as well as about stabilizing mechanisms versus the initial-state choice.
The process of resonant multiphoton ionization of a hydrogen atom in the ground 1 s state is studied by direct numerical integration of the nonstationary Schrödinger equation for a quantum system in an electromagnetic field. The dependence of photoionization probability on the radiation intensity is found to be nonmonotonic. It is established that the minima of ionization correspond to multiphoton resonances between the ground state and one of the excited (Rydberg) atomic states perturbed by the laser field. It is shown that ionization is suppressed due to rearrangement of Rydberg states in a strong electromagnetic field and is accompanied by efficient Raman Λ transitions, which connect a set of closely lying Rydberg states via the continuum.
Cold, dense Rydberg gases produced in a cold-atom trap are investigated using spectroscopic methods and time-resolved electron counting. Optical excitation on the discrete Rydberg resonances reveals long-lasting electron emission from the Rydberg gas ( >20 ms). Our observations are explained by lm-mixing collisions between Rydberg atoms and slow electrons that lead to the population of long-lived high-angular-momentum Rydberg states. These atoms thermally ionize slowly and with large probabilities.