Density matrix and irreducible tensor operator formalism have been used to describe optical pumping or similar experiments by electronic excitation in an atomic gas. The authors show that this theory may be extended to diatomic molecules. Experimental possibilities are considered.
Optical pumping of the electronic ground state of molecules has been investigated under conditions of plane, elliptically, and circularly polarized light broadband excitation. The analysis has been performed assuming arbitrary angular momentum values, and applying the apparatus of polarization moments, the latter forming the coefficients in the expansion of the density matrix over irreducible tensor operators, including simplifications due to asymptotic limits for large momentum values. In addition to accounting for the external magnetic field, attention has been also given to the dynamical Stark effect arising from the absence of coincidence between the centers of the exciting line and the absorption line. An alternative classical description is also proposed using multiple moments as coefficients of the expansion of a classical quasidensity of states over spherical harmonics. The equivalence of both approaches of description in the limit of infinitely large angular moments is demonstrated, and the meaning of the origin of coherence is clarified, as well as its destruction by the magnetic field in the classical description of the system.
The absorption of light by optically pumped atoms undergoing magnetic resonance is calculated from expressions based on a simplification of Barrat and Cohen-Tannoudji's theory of optical pumping. The density matrix for the system is first derived in orders of approximation which correspond to successive cycles of pumping. The off-diagonal elements of the matrix, and consequently the absorption of light, are modulated. The amplitudes of modulation are resonance functions which are, in general, more complicated than solutions of the Bloch equations. The selection rules for electric dipole radiation limit the possible frequencies of modulation to ω0 and 2ω0 for primary interactions (ω0 is the applied frequency), but modulation at higher frequencies can arise through the circulation of coherence in optical pumping cycles. The functions which represent the amplitude of modulation at 4ω0 are derived in first and second order, for comparison with experiment.
Recent experiments (Dodd, Fox, Series & Taylor, I959; Colegrove, Franken, Lewis & Sands, i959) have shown that coherence effects can be observed between the Zeeman components of an optical line provided some coherence exists in the excited state. This coherence may be due to a radio-frequency field inducing transitions between the Zeeman sublevels of this excited state, or to the excitation process itself or to both. These effects are actually more or less a generalization of the well-known Hanle's experiments on the polarization of resonance radiation.: In the case of 'double resonance' experiments (Dodd et al. I959), they appear as a modulation of the intensity of the fluorescence radiation at one of the harmonics of the r.f. field; they can be interpreted as interference between the radiations of different frequencies emitted by the atoms which are submitted to the 'double resonance' ('light beat'). These coherence effects are related to those observed in the trapping of resonance radiation. In this paper, the methods used in former papers (Barrat I959 a, b and c, hereafter referred to as I, II, III) for the problem of light trapping are applied to the light beats experiments, using a density matrix formalism. The expression for the density matrix representing the states of the atoms just after the excitation will first be derived; then the intensity of the re-emitted light will be calculated. It will be shown finally how this method can be applied to practical problems. Notation unexplained in this paper is the same as in papers on coherence in light trapping (papers I, II and III).
The optical pumping of atoms by a multimode gas laser, in the presence of a magnetic field, is studied theoretically. The atoms are described by their density matrix, which is expanded on an irreducible tensorial set. The atomic relaxation is assumed to be isotropic. In order to avoid the usual perturbation theory, we use the so-called "Broad-Line approximation" (BLA). BLA is valid when the width of the "Bennett hole" created by one laser mode in the velocity distribution of the excited atoms is comparable to the spacing between modes; under these conditions, the atomic response does not depend on the velocity and the multimode laser irradiation is equivalent to a broad-line excitation. For the atomic system, BLA leads to a set of coupled equations which is valid at arbitrary intensities of the laser field and which depends on this field through a unique parameter, $\ensuremath{\gamma}$. This parameter can be understood as a laser-induced transition probability. In this article, we analyze the nonlinear effects which can be deduced from this theory, for any value of the angular momenta involved in the laser transition: Hanle-effect broadening, alignment coupling, saturation resonances on the populations are shown. The exact calculations, valid at arbitrary laser intensities for $J=1\ensuremath{\leftrightarrow}J=0$, $J=1\ensuremath{\leftrightarrow}J=1$, and $J=1\ensuremath{\leftrightarrow}J=2$ transitions, and the corresponding experimental results will be presented in forthcoming papers.
Real and virtual absorption of weak monochromatic light is analyzed with semiclassical radiation theory. The influence of the light on the atoms is described by an effective ground-state Hamiltonian operator, and the effect of the atoms on the light is described by a dielectric susceptibility operator. These operators are expressed explicitly in terms of familiar ground-state observables, angular factors, oscillator strengths, and plasma dispersion functions. The theory gives a comprehensive description of optical pumping, light shifts, and light modulation due to real and virtual absorption of light, and several new effects are predicted. Repopulation of the atomic ground state from a polarized excited state is not considered in this paper.
The nature of resonance emission of light, which appears as a mixture of (coherent) resonance scattering and (incoherent) resonance fluorescence, is considered. The basic conceptual elements which distinguish the scattering and fluorescence components for the linear excitation limit are developed in terms of a simple formulation whereby a molecule interacts with a coherent Lorentzian light pulse which increases exponentially with time for t<0 and is turned off at t = 0. These results together with the ideas, currently existing in the literature, that stochastic modulation of a molecule by its medium is essential for the appearance of fluorescence provide the basis for the further formulation of a theory which does not require the ad hoc introduction of a random potential. The theory developed considers the microscopic origins of manifest stochastic modulation effects in terms of a bath potential for the molecule–medium (bath) degrees of freedom. This potential, termed the sudden potential, is associated with the change in interaction with the medium that a molecule experiences upon intramolecular state transitions which are induced by external interactions (e.g., by light). Development of the reduced molecule–field density operator leads naturally to a separation of terms which describes scattering and (the propensity for) fluorescence. Critical to the theory is a four-time correlation function for the bath (sudden) potential. The difficulties inherent in defining absorption (spectrum) resonances and the corresponding distinctions between resonance and relaxed emission are discussed. Implications are considered for the further understanding of experimental results on molecular excitation dynamics in the gas phase and in supersonic jets. Sources of stochastic modulation other than material media are mentioned. In particular, the possibility is suggested of the pervasive existence of stochastic modulation through interaction of a molecule with the vacuum state of the radiation field. This raises questions concerning the fundamental relations between quantum mechanics and thermodynamics.