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Physical Review A

Level shift and depopulation by blackbody radiation of a Rydberg atom between two metallic plates

Takashi Nakajima, P. Lambropoulos, HERBERT WALTHER

Published Dec 1, 1997• 31 citations
Publisher

Abstract

We study the level shifts and depopulation of Rydberg states, confined between two parallel metallic plates, due to blackbody radiation. After the derivation of the formal equations for the level shift and the depopulation, we present, as an example, specific calculations for the Rb $24s$ state as a function of plate distance $L$ at three different temperatures 10, 85, and 205 K.

DOI
10.1103/physreva.56.5100

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We study the level shifts and depopulation of Rydberg states, confined between two parallel metallic plates, due to blackbody radiation. After the derivation of the formal equations for the level shift and the depopulation, we present, as an example, specific calculations for the Rb 24s24s24s state as a function of plate distance LLL at three different temperatures 10, 85, and 205 K.
A highly excited (Rydberg) atom bathed in blackbody radiation is perturbed in two ways. A dynamic Stark shift is induced by the off-resonant components of the blackbody radiation. Additionally, electric-dipole transitions to other atomic energy levels are induced by the resonant components of the blackbody radiation. This depopulation effect shortens the Rydberg-state lifetime, thereby broadening the energy level. Calculations of these two effects in many states of hydrogen, helium, and the alkali-metal atoms Li, Na, K, Rb, and Cs are presented for T=300T=300T=300 K. Contributions from the entire blackbody spectrum and from both discrete and continuous perturbing states are included. The accuracy is considerably greater than that of previous estimates.
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal nSnSnS, nPnPnP, and nDnDnD Rydberg states have been calculated in a wide range of principal quantum numbers $n\ensuremath{\le}80$ at the ambient temperatures of 77, 300, and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-induced depopulation rates, which well agree with the numerical data.
Blackbody radiation is expected to produce a temperature-dependent Stark shift in atomic Rydberg states. Unfortunately, in "one-electron" atoms, all the Rydberg levels experience the same shift, and the effect is only observable on an optical transition from the ground state. However, in a many-electron atom the presence of valence-state perturbers leads to unequal shifts of the Rydberg levels. This should make it possible to observe the frequency shift of a transition between two neighboring Rydberg states at a frequency in the radio-frequency range. This eliminates the need for a very stable visible laser, which so far has been the major technical obstacle to the observation and utilization of the effect. We present as an example a specific case in Ba.
The effect of a thermal field on Rydberg states of the nS-, nP- and nD-series in beryllium ions Be+ is investigated. The blackbody radiation-induced depopulation rates caused by transitions to upper (excitations) and lower (decays) bound levels and to the continuum (ionization) are calculated in wide ranges of the principal quantum numbers n and ambient temperatures. Simple and reliable approximations for natural lifetimes and stimulated by thermal radiation depopulation rate components are proposed. The blackbody-radiation-induced shifts of Rydberg levels are also calculated and their qualitative and quantitative properties are analysed.
We consider the Zeeman shift in Rydberg atoms induced by room-temperature blackbody radiation (BBR). BBR shifts to the Rydberg levels are dominated by the familiar BBR Stark shift. However, the BBR Stark shift and the BBR Zeeman shift exhibit different behaviors with respect to the principal quantum number of the Rydberg electron. Namely, the BBR Stark shift asymptotically approaches a constant value given by a universal expression, whereas the BBR Zeeman shift grows steeply with principal quantum number due to the diamagnetic contribution. We show that for transitions between Rydberg states, where only the differential shift between levels is of concern, the BBR Zeeman shift can surpass the BBR Stark shift. We exemplify this in the context of a proposed experiment targeting a precise determination of the Rydberg constant.