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Physica Scripta

Role of trap states in forward scattering of resonance light

Bogdan Lobodzinski, Wojciech Gawlik

Published Jan 1, 1997• 5 citations
Publisher

Abstract

Forward scattering of laser light by atoms in a magnetic field is analyzed nonperturbatively within a standard | F , m > and the coupled-uncoupled (trap) state representations along the lines of recent theory of forward scattering [B. Lobodzinski and W. Gawlik, Phys. Rev. A54 , 2238 (1996)]. It is shown that the main features of the forward scattering signals can be associated with the number of trap states and their evolution in a magnetic field. In particular, when two traps are possible, as a result of the competition between them, not all light-induced multipole moments affect the scattering signal.

DOI
10.1088/0031-8949/1997/t70/019

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Forward scattering of laser light by atoms in a magnetic field is analyzed nonperturbatively within a standard | F , m > and the coupled-uncoupled (trap) state representations along the lines of recent theory of forward scattering [B. Lobodzinski and W. Gawlik, Phys. Rev. A54 , 2238 (1996)]. It is shown that the main features of the forward scattering signals can be associated with the number of trap states and their evolution in a magnetic field. In particular, when two traps are possible, as a result of the competition between them, not all light-induced multipole moments affect the scattering signal.
We perform nonperturbative analysis of forward scattering of resonance laser light on atoms in magnetic field when the laser drives transitions between states with total angular momenta F=1,2 and study the role of the induced higher-order multipole moments in the forward-scattering signal. It is shown how the multipole moments affect these signals and why not all possible multipoles are revealed for some transitions. The analysis is performed in terms of density-matrix formalism and in terms of coupled and uncoupled (trap) states. Evolution of the trap states in a magnetic field is found to be responsible for specific dependencies of the forward-scattering signals on the multipoles of various ranks. The general theory is applied to the case of the Na D1{\mathit{D}}_{1}D1​ line. We also present a pump-probe method for studying multipoles in systems with states of high angular momenta and with complex transitions overlapping within their Doppler width. \textcopyright{} 1996 The American Physical Society.
The theoretical formulation of the nonlinear optical activity is utilized to describe the signal intensity in forward scattering. For cases in which the ratio of the Rabi frequency of an isolated transition to its relaxation rate is less than one, a perturbation procedure in this parameter is presented. The successive terms in the resulting series are interpreted as higher-order coherences or induced multipole moments. Application is made to the hyperfine components of the sodium D transitions where experimental data is described by a third-order calculation. Good agreement is obtained without invoking an induced hexadecapole moment as was proposed originally.
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.
Laser and microwave fields can be mixed in paramagnetic samples in a coherent Raman process. The radiation scattered in the forward direction contains frequency components at the sum and difference frequency. We consider the details of this scattering process in a static magnetic field, where two types of signals appear: magnetic-resonance transitions give rise to signals at fixed magnetic fields, independent of the laser frequency. Another set of resonances is determined by the optical transition frequencies. These resonances are particularly prominent in samples with narrow optical absorption lines. We derive a comprehensive theory that describes both contributions and compare it with experimental data from the R lines of ruby.
Recent studies of the decoherence induced by the quantum nature of the laser field driving a two-state atom [J. Gea-Banacloche, Phys. Rev. A 65, 022308 (2002); S. J. van Enk and H. J. Kimble, Quantum Inf. Comput. 2, 1 (2002)] have been questioned by Itano [W. M. Itano, Phys. Rev. A 68, 046301 (2003)] and the proposal made that all decoherence is due to spontaneous emission. We analyze the problem within the formalism of cascaded open quantum systems. Our conclusions agree with the Itano proposal. We show that the decoherence, nevertheless, may be divided into two parts---that due to forwards scattering and to scattering out of the laser mode. Previous authors attribute the former to the quantum nature of the laser field.
The forward scattering of a resonant intense and broad-band (of the order of 1 GHz) laser light on sodium atoms is described. The experimental results for the D 1 and D 2 sodium lines (the 3 2 S 1/2 -3 2 P 1/2 and 3 2 S 1/2 -3 2 P 3/2 transitions) are compared with those of the scattering of the light from a conventional spectral lamp and from a monochromatic laser. The observed differences are explained by taking into account the Zeeman coherences created in the irradiated atoms and the concept of the 'hyperfine uncoupling' is proposed for describing the interaction of atoms with the broad-band laser light.