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Proceedings of the Physical Society

Interference effects in step-wise fluorescence due to level-crossings

B P Kibble, S Pancharatnam

Published Dec 1, 1965• 23 citations
Publisher

Abstract

The semi-classical derivation of the Kramers-Heisenberg formula describing resonance scattering is extended to the step-wise scattering of light. We consider an atom (such as 198 Hg) which interacts with two polarized beams of light (λ2537 Å and λ4358 Å): starting from a specific initial state 0 (6 1 S 0 ), it undergoes a two-step excitation (6 1 S 0 → 6 3 P 1 → 7 3 S 1 ), and makes a transition to one specific final state F (any magnetic sub-state of the 6 3 P 2.1.0 terms). It thus emits step-wise radiation (λ5461 Å or λ 4358 Å or λ4047 Å). A possible route 0 → r → r' → F taken by the atom in the scattering process is defined by two possible intermediate states (r', r). When there are two routes connecting 0 to F, the fluorescent intensity observed through an analyser differs from that obtained by adding the corresponding transition rates, owing to a quantum-mechanical interference term. Observations on the fluorescent intensity from 198 Hg vapour as a function of applied magnetic field confirm three types of interferences, occurring at the zero-field crossing of Zeeman sub-levels. The first is analogous to that observed in resonance fluorescence. Two new types are (i) a level-crossing signal essentially in the absorption of the second radiation, due to degeneracy of states excited in the first term (6 3 P 1 ), and (ii) a multiplicative level-crossing signal, where mutual coherence between one pair of degenerate states excited in the first step is carried over to a second pair in the next step.

DOI
10.1088/0370-1328/86/6/323

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Quantum Optics Journal of the European Optical Society Part B•Apr 1, 1992•5 citations
The semi-classical derivation of the Kramers-Heisenberg formula describing resonance scattering is extended to the step-wise scattering of light. We consider an atom (such as 198 Hg) which interacts with two polarized beams of light (λ2537 Å and λ4358 Å): starting from a specific initial state 0 (6 1 S 0 ), it undergoes a two-step excitation (6 1 S 0 → 6 3 P 1 → 7 3 S 1 ), and makes a transition to one specific final state F (any magnetic sub-state of the 6 3 P 2.1.0 terms). It thus emits step-wise radiation (λ5461 Å or λ 4358 Å or λ4047 Å). A possible route 0 → r → r' → F taken by the atom in the scattering process is defined by two possible intermediate states (r', r). When there are two routes connecting 0 to F, the fluorescent intensity observed through an analyser differs from that obtained by adding the corresponding transition rates, owing to a quantum-mechanical interference term. Observations on the fluorescent intensity from 198 Hg vapour as a function of applied magnetic field confirm three types of interferences, occurring at the zero-field crossing of Zeeman sub-levels. The first is analogous to that observed in resonance fluorescence. Two new types are (i) a level-crossing signal essentially in the absorption of the second radiation, due to degeneracy of states excited in the first term (6 3 P 1 ), and (ii) a multiplicative level-crossing signal, where mutual coherence between one pair of degenerate states excited in the first step is carried over to a second pair in the next step.
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.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
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.
The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.
The interference spectra arising from the competition between a spontaneous process and an induced one by two laser fields, which interact on two-photon resonance with a three-level atom in the Lambda configuration have been considered. In the low intensity limit of both laser fields, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, respectively, cancel each other out completely at the centre of the line for zero detuning and at the finite values of the detuning as well. At those frequencies, the fluorescent light totally disappears. The interference spectra arising from the absorption of a laser photon by the ground state of the atom consists of two peaks describing the induced processes of absorption and stimulated emission, respectively.