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Physical Review A

Rydberg-atom photoionization with and without the single-nmanifold approximation

R. Parzyński, Michał Sobczak, Antoni Wójcik

Published May 16, 2001• 6 citations
Publisher

Abstract

In a wide basis of bound hydrogenic states $(20<~n<~80,l<~29),$ we simulate redistribution of the initial $50s$ state population by a nonresonant, optical-frequency pulse of the strength at which Rydberg-to-Rydberg Rabi frequencies exceed the pulse frequency. A small transient flow of the population out of the $50l$ manifold $(l=0,1,2,3,\dots{})$ is observed and the effect of this $n\ensuremath{\ne}50$ redistribution on the formation of the photoionization signal from Rydberg states is calculated in the limit of weak bound-free coupling. This $n\ensuremath{\ne}50$ redistribution is found to totally cancel the predictions of the single-n manifold approximation $(n=50$ in this case) in photoionization.

DOI
10.1103/physreva.63.063413

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In a wide basis of bound hydrogenic states (20< n< 80,l< 29),(20<~n<~80,l<~29),(20< n< 80,l< 29), we simulate redistribution of the initial 50s50s50s state population by a nonresonant, optical-frequency pulse of the strength at which Rydberg-to-Rydberg Rabi frequencies exceed the pulse frequency. A small transient flow of the population out of the 50l50l50l manifold (l=0,1,2,3,…)(l=0,1,2,3,\dots{})(l=0,1,2,3,…) is observed and the effect of this n\ensuremath≠50n\ensuremath{\ne}50n\ensuremath=50 redistribution on the formation of the photoionization signal from Rydberg states is calculated in the limit of weak bound-free coupling. This n\ensuremath≠50n\ensuremath{\ne}50n\ensuremath=50 redistribution is found to totally cancel the predictions of the single-n manifold approximation (n=50(n=50(n=50 in this case) in photoionization.
Assuming the initial population in the hydrogenic 50s state, we simulate Rydberg-state redistribution and photoionization by a nonresonant optical-frequency pulse versus the number of different n manifolds included. The inclusion of additional n manifolds, around the n = 50 manifold distinguished by the initial-state choice, is shown to invalidate the photoionization predictions based on the single-n manifold approximation. The calculations are performed assuming a linearly polarized, 620 nm pulse, turned on and off suddenly, of ten-optical-period duration and peak intensity 109 W cm-2 ensuring effective transient mixing of both-parity Rydberg states around n = 50.
Our recent approximate analytical results on the evolution of the initial state and the excitation from this state of a band of high Rydberg states by an optical pulse [Phys. Rev. A 55, 2144 (1997)] are compared with more exact numerical results. The difference between the two approaches is that the approximations of representative atom-field couplings and equidistant spacing of high Rydberg states, applied in the analytical model, are removed in the numerical model. We find that the approximate analytical model is not able to reproduce all the results of the more exact numerical model, if the laser pulse is very short (i.e., much shorter that the Kepler period of the resonantly excited high Rydberg state) or very intense (i.e., when the Rabi period for the resonant transition is substantially shorter than the above Kepler period). This mainly concerns the redistribution of the population over different Rydberg states. The analytical model predicts a symmetric distribution centered around the resonantly excited Rydberg state, irrespective of the pulse duration and intensity, while the numerical model allows an asymmetric distribution with its maximum shifted towards lower Rydberg states. Despite the above-stated difference, the analytical model is able to give preliminary results for the total population of all the excited Rydberg states and the evolution of the initial state, imitating at least qualitatively the results of the numerical model in certain time and intensity scales.
Stimulated by a recent experiment [L. D. Noordam et al., Phys. Rev. Lett. 68, 1496 (1992)], we present a model of Rydberg-atom photoionization whose essential feature is the resonance between the initially populated Rydberg state and an additional state lying below Rydberg quasicontinuum. Despite the infinite number of discrete states involved in our model we have obtained the expressions for photoionization yield and discrete-state populations in completely analytical form. These expressions cover both short- and long-time scales, i.e., when laser-pulse duration is shorter or longer than the classical round-trip time of the Rydberg electron. The short-time scale corresponds to the conditions met in the experiment of Noordam et al. and, on the basis of our expressions, we have gained at least qualitative understanding of their observations. In the case of long pulses, which in our considerations are never longer than 54 ps, near resonance is shown to be the origin of a profound ionization suppression, particularly for some specific frequencies, which we identify as those ensuring the formation of a perfectly dark dressed state of zero width and thus unionizable. This dark state is shown to be populated with a probability increasing when laser gets stronger. We discuss the connection between stabilization and formation of this perfectly dark state as well as of additional dressed states, which are dark in the sense that they have the property of becoming very narrow as laser intensity increases. The undamped perfectly dark state, created at specific laser frequencies, has given us rise to introduce what we call the zero-pole approximation for ionization yield, which, as we have shown, works well if duration and intensity of laser pulse are appropriately combined.
Expanding the wave function in terms of eigenstates, we calculated the population redistribution of high-Rydberg hydrogen atoms under the interactions of external time-dependent electromagnetic fields. Our numerical results show that populations of Rydberg atoms can be driven down to lower nnn levels with a train of half-cycle pulses. Oscillations of the Rydberg population through both nnn levels and lll levels are observed during these interactions. The approach may have applications in providing an effective mechanism for producing near ground-state atoms from the initially high-Rydberg distributions found in recombining ultracold plasmas such as encountered in the antihydrogen trapping experiments at CERN.
Following the experiment of Jones et al. [Phys. Rev. Lett. 71, 2575 (1993)], we present a theory of coherent redistribution of population in a model Rydberg atom exposed to a sequence of two identical laser pulses separated in time and shorter in duration than the Rydberg-electron Kepler period. For different initial-population conditions, we solve the problem of redistribution in a fully analytical and rigorously nonperturbative way, thus obtaining discrete-state population amplitudes, dependent on laser intensity, and a time delay between the pulses. Using this solution, we study the population in a given state versus pulse delay (Ramsey fringes), as well as the corresponding Fourier spectrum, for both low and high laser intensities. From the number of frequency components and their positions in the Fourier spectrum, we deduce the redistribution of the initial-state population over a number of states by the first pulse. Within our model calculations we achieve qualitative agreement with the experimental observation of Jones et al. that an increase in laser intensity results in a general increase in the number of frequency components in the Fourier spectrum. Our theoretical results are also consistent with the experimental finding of Noordam et al. [Phys. Rev. Lett. 68, 1496 (1992)] that Raman transitions via the continuum between different Rydberg states are essential for population redistribution. We suggest new experiments to measure the effect of the initial-state depletion on the Fourier spectrum. As follows from our model calculations, some frequency components (both low and optical) present in the low-intensity Fourier spectrum should vanish in the high-intensity spectrum due to complete depletion of the initial state by the first pulse.