A method is proposed for measuring the interval between two atomic energy levels of different parity. The method is related to optical radio-frequency double resonance and level-crossing experiments in that the behavior of atoms in excited states is deduced from observations of the fluorescent light. In contrast with the oscillating electric field ordinarily used to stimulate transitions between states of opposite parity, a small, static electric field is required. The rate at which atoms are excited is required to be modulated; consequently, the fluorescent light will be modulated. The amplitude of modulation will depend on the parameters. A general expression is derived. Two cases are of particular interest: (1) A resonance effect is predicted if the frequency of modulation matches the interval between the perturbed levels. This effect could best be studied for frequencies much greater than the combined natural widths of the levels. (2) For frequencies smaller than the natural width, a level-crossing effect is predicted whose peak occurs at the point of intersection of the unperturbed levels. The method might be applied to measure intervals between the $2s$ and $2p$ levels in hydrogen. Estimates are given of the required fields and frequencies.
A method is proposed for measuring the interval between two atomic energy levels of different parity. The method is related to optical radio-frequency double resonance and level-crossing experiments in that the behavior of atoms in excited states is deduced from observations of the fluorescent light. In contrast with the oscillating electric field ordinarily used to stimulate transitions between states of opposite parity, a small, static electric field is required. The rate at which atoms are excited is required to be modulated; consequently, the fluorescent light will be modulated. The amplitude of modulation will depend on the parameters. A general expression is derived. Two cases are of particular interest: (1) A resonance effect is predicted if the frequency of modulation matches the interval between the perturbed levels. This effect could best be studied for frequencies much greater than the combined natural widths of the levels. (2) For frequencies smaller than the natural width, a level-crossing effect is predicted whose peak occurs at the point of intersection of the unperturbed levels. The method might be applied to measure intervals between the 2s and 2p levels in hydrogen. Estimates are given of the required fields and frequencies.
Abstract A theory is formulated to describe the modulation which has been observed in fluorescent light from atoms subjected simultaneously to optical and radio-frequency radiation. The optical field stimulates one or more of a set of excited states of the atom, between which the radio-frequency field establishes coherence. This coherence is manifest in the fluorescent radiation. Interference between radiations of different frequency leads to modulation. General expressions are given for the intensity of the fluorescent light as a function of time. The Zeeman structure of the transition (63P1 — 6 1S0), A2537 A, in mercury is studied in detail. Modulation at frequencies, 1, 2, 3 and 4 times that of the radio-frequency field, w0, is predicted, and resonant effects at static magnetic fields, 0, 1/2, 1, 3/2, 2 and 3 times H0, the field for which w0 is the Larm or frequency. Resonances at fields other than H0 are due to excitation with light of mixed polarization. Most of the predicted effects have been found experimentally. A ‘frequency diagram’ is introduced and discussed, to represent the combined effects of static and radio-frequency magnetic fields. To each excited state belong a set of r frequencies, where r is the number of states linked by the radio-frequency perturbation. The 9 levels are drawn, as functions of H, for the states mJ = 0, ± 1, of 3P1. The resonances at fields other than H0 may be associated with intersections of frequency levels belonging to different mJ.
A treatment of resonance fluorescence is given in which the properties of the incident and scattered light are expressed in terms of coherency matrices. Calculations are made for two successive scattering processes corresponding to the experiments described in an accompanying paper. For the first process the scattering atoms are subjected to a magnetic field consisting of parallel static and oscillating components. The fluorescent light is frequency-modulated and may also be polarization-modulated. This light excites fluorescence in a second cell in which the atoms are subjected to a static magnetic field. The equations show under what conditions the second fluorescence is intensity-modulated and describe the resonances in the amplitude of modulation which occur when the modulation frequency matches a Zeeman interval of the excited atoms.
Abstract This work is an experimental study of the modulation which has been found in resonance radiation when the fluorescing vapour is subjected to static and radio-frequency magnetic fields, as in the double resonance experiment of Brossel & Bitter. The particular example chosen for study in this work also was the resonance line λ 2537 Å of mercury. The experimental observations are compared with the predictions of a theoretical treatment which has already been published. The phenomenon was studied under a variety of geometrical configurations. When the polarization of the exciting light allowed excitation to only one excited state (a component of a Zeeman multiplet), the depth of modulation was found to depend on the closeness to resonance of the frequency, ω0, of the radio-frequency field to the Larmor precessional frequency, ω = γH , in the static field H. When the polarization of the exciting light allowed excitation to more than one component of the multiplet, resonance effects were found in the depth of modulation and in the mean intensity of the fluorescent light at fields where the applied frequency was equal, not to the Larmor frequency alone, but to combinations of the Larmor frequency with the nutational frequency. From a quantum-mechanical point of view, these new phenomena are related to the interference effects which are found in resonance fluorescence when there is degeneracy between excited states: in the present case the degeneracy is induced by the radio-frequency field. The ease with which the geometrical conditions could be altered allowed the theory to be tested in considerable detail without quantitative assessment of the resonance line contours: nevertheless, a quantitative study was made of one particular feature. The predictions of the theory were confirmed at all points where they were tested.
Abstract This is an investigation, at low frequencies, of the modulation of fluorescent light which has already been found a t higher frequencies in a double resonance experiment. In the earlier work, in which the frequency of magnetic resonance was of order 10 Mc/s, the Zeeman levels of the excited atom s were well separated compared with their natural width (1 M c/s): in the present work they are completely unresolved at the centre of the magnetic resonance, which is studied a t 1 kc/s. The principal resonance phenomena are observed as before under the new conditions: they are centred on a field near to zero, while their width is greater than 1G. New resonance phenomena are also studied, which do not appear when the resonance frequency is greater than the natural width of the levels. A theory, previously published, is applied to predict the form of the new resonance curves. An identical result is predicted by the use of a classical model.
Further experiments are reported in which resonance fluorescence of an atomic vapour is excited by modulated light. The system studied was the 3 P 1 level of cadmium excited by the λ 3261 λ intercombination line modulated at 462 kHz. Resonant changes in the amplitude of modulation of the fluorescent light have been observed in both static and time-dependent magnetic fields whenever the modulation frequency matches a frequency separation between the states of the excited atoms. Quantitative investigations of the shape and position of the observed resonances show good agreement between theory and experiment. The application of the technique to the spectroscopy of excited atoms is considered.
For pt.I see ibid., vol.12, no.12, p.1939 (1979). The modulated fluorescence in an optical double resonance experiment, i.e. when an atom interacts with two intense monochromatic laser beams each of which is weakly modulated in amplitude at frequency Omega , is studied in detail. The modulation rate corresponding to the steady-state population of the highest atomic level exhibits resonant structures at the modulation frequencies Omega =0, +or- alpha 0 , +or-2 alpha 0 due to the dynamical Stark splitting of the various energy levels; alpha 0 being related to the Rabi frequencies alpha 1 and alpha 2 associated with the two lasers and the two atomic transitions, by alpha 0 2 = mod alpha 1 mod 2 + mod alpha 2 mod 2 . The peak at Omega =+or- alpha 0 is the most intense and exhibits splitting when the applied fields are detuned from exact resonance with the respective atomic frequencies. Resonances are observed in the modulation rate of the intermediate-level population at the modulation frequencies Omega =0, +or-2 alpha 0 . In the presence of detunings of the applied fields, additional resonant structures occur at Omega =+or- alpha 0 which increase in magnitude with higher detunings and split. Explicit expressions for the positions, widths and weights of these resonant components are obtained analytically for intense, resonant fields. Numerical results for general values of the laser field strengths and the detunings are given.