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Physical Review Letters

Coherent Anticrossing Signals

B. Budick, Joseph Snir

Published Jan 29, 1968• 7 citations
Publisher

Abstract

Anticrossing signals have been observed in resonance fluorescence in which the two repelling levels are both excited from the same level in the ground state. The two anticrossed levels both decay to the same ground-state level as well. This extension of the anticrossing technique is successfully applied in a state of the hfs of the ytterbium atom.

DOI
10.1103/physrevlett.20.177

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Anticrossing signals have been observed in resonance fluorescence in which the two repelling levels are both excited from the same level in the ground state. The two anticrossed levels both decay to the same ground-state level as well. This extension of the anticrossing technique is successfully applied in a state of the hfs of the ytterbium atom.
The level-crossing technique of atomic spectroscopy utilizes the spatial interference in the scattering of resonance radiation which can occur when two Zeeman levels of an atom are brought into coincidence ("crossed") by the application of an external magnetic field. "Anticrossing" refers to the case where the two levels involved are coupled by a small static interaction. In this paper the general expression for an anticrossing signal is given and its predictions compared with signals observed in the 22P2 ^{2}P22P term of Li. It is shown that anticrossings produce signals in many experimental situations for which there would be no signal from a normal level crossing.
We report the observation of anticrossing signals arising from the interaction of 300-K blackbody radiation with Rydberg atoms near avoided crossings of Stark levels. The role of the blackbody radiation is roughly analogous to that of the resonance fluorescence in traditional anticrossing spectroscopy. We present preliminary results for avoided crossings of ns\mathrm{ns}ns states with $n\ensuremath{-}2$ Stark states in potassium for nnn in the range 18-21.
We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105-\AA{} zero-phonon transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\leftrightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$ of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in a YAlO3{\mathrm{O}}_{3}O3​ crystal at 2\ifmmode^\circ\else\textdegree\fi{} K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction VVV between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened $2\ensuremath{\leftrightarrow}3$ transition. Ground- and excited-state gyromagnetic ratios ${\ensuremath{\gamma}}_{i}(i=X,Y,Z)$ and the interactions VVV are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for 141Pr3+^{141}\mathrm{Pr}^{3+}141Pr3+ which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of \ensuremath{\sim} 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed.
An interaction Hamiltonian analogous to that in a coupled Lee model is used to calculate the transition matrix appropriate for the description of the anticrossing effect in optical resonance fluorescence. The transition matrix is found to contain two terms (in addition to those for resonance scattering through each of the coupled states) which exist in the amplitude only because the damping matrix in the coupled representation is not diagonal. This matrix is diagonal when the uncoupled states have equal radiative widths, and the resonance scattering intensity is then given by the Breit formula. This result justifies the application by Eck, Foldy, and Wieder of the Breit equation to their initial discovery of the anticrossing effect even though this formula would not be expected to apply to the general anticrossing situation. The crossing effect can also be discussed as a special case of the approach presented.
A discussion is given of the requirements for observing strong level-crossing signals in stepwise fluorescence, where the state under investigation is optically excited via an intermediate state, the atom absorbing in the process two photons of different wavelengths. Data obtained using this technique are presented for fine-structure crossings in the 32D{3}^{2}D32D term of Li.