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Journal of Experimental and Theoretical Physics

Time reversal during magnetization of gas atoms by a resonant light pulse

A. I. Alekseev

Published Aug 1, 1997• 0 citations
Publisher

Abstract

The optically induced magnetic moment of a stationary atom is calculated as a function of time and the resonance detuning ω-ω ba to within a constant factor having the dimensions of a magnetic moment based on the symmetry of an atom in the field of a resonant light pulse and symmetry with respect to time reversal including the initial conditions. The even dependence of the optically induced magnetic moment on ω-ω ba for an elliptically polarized pulse with an isotropic initial state of the atom and its odd dependence on ω-ω ba in the case of a linearly polarized pulsed with an anisotropic initial state in the atom’s alignment are shown to be consequences of symmetry with respect to time reversal and the initial conditions. This behavior is retained even after passage of the light pulse, when the resulting relaxation destroys the time reversal symmetry. The optically induced magnetization of an atomic gas is found to have analogous properties.

DOI
10.1134/1.558271

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The optically induced magnetic moment of a stationary atom is calculated as a function of time and the resonance detuning ω-ω ba to within a constant factor having the dimensions of a magnetic moment based on the symmetry of an atom in the field of a resonant light pulse and symmetry with respect to time reversal including the initial conditions. The even dependence of the optically induced magnetic moment on ω-ω ba for an elliptically polarized pulse with an isotropic initial state of the atom and its odd dependence on ω-ω ba in the case of a linearly polarized pulsed with an anisotropic initial state in the atom’s alignment are shown to be consequences of symmetry with respect to time reversal and the initial conditions. This behavior is retained even after passage of the light pulse, when the resulting relaxation destroys the time reversal symmetry. The optically induced magnetization of an atomic gas is found to have analogous properties.
It is shown that the even dependence of the light-induced magnetic moment on the detuning ω-ω ba from resonance in the case of a circularly polarized pulse and an isotropic initial state of the atom and the odd dependence on ω-ω ba in the case of a linearly polarized pulse and an anisotropic initial state in the form of alignment of the atom are consequences of the symmetry under time reversal t→−t and of the initial conditions at time t=0. In a number of cases, this fundamental law makes it possible to determine the vector properties of a light-induced magnetic moment and its dependence on the time t and ω-ω ba without solving the equation for the density matrix in detail and without calculating the sum over the projections of the angular momenta in the formula for the magnetization of an atom by light.
The properties of the density matrix and the multipole moments arising in oriented and aligned atoms with zero nuclear spin through the interaction with strong resonant ultrashort pulses with wave vector k 0 and circular or linear polarization have been found. Calculations have been made for the time-dependent light-induced magnetization μ ( t ′) of a gas of pre-oriented and prealigned atoms following the passage of a weak resonant elliptically polarized pulse with frequency ω and wave vector k collinear with k 0 . It is shown that for oriented atoms, μ ( t ′) is an even function of the detuning from resonance, ω-ω ba , and can be split into two terms whose directions are a consequence of symmetry and are determined by the vectors k 0 and k as well as by the direction of rotation of the electric fields corresponding to the pulses. For aligned atoms the vector μ ( t ′) is collinear with k , and the first term is an even function of ω-ω ba . However, the second term is an odd function of ω-ω ba and reverses direction when the sign of ω-ω ba changes, as well as when the orientation of the axes of the polarization ellipse is changed. It is shown that if a series of weak linearly polarized pulses pass through the gas, the light-induced magnetization of the oriented and aligned gas atoms can be decomposed into three factors: the first determines the direction and is a consequence of the symmetry; the second (with the dimensions of magnetic moment) depends on the characteristics of the resonant transitions; and the third is a universal function of t ′ and ω-ω ba that does not depend on the underlying characteristics of the resonant transition. These vector factors and the universal functions are in principle different for oriented and aligned atoms.
Results of a fairly straightforward experiment on resonant magneto-optical rotation by rubidium-87 atoms revealed strong time-dependence of the polarization plane of light emerging from atomic vapors following a sudden irradiation with a laser beam. The rotation of the plane appears as a not direct consequence of the influence of the magnetic field on atoms. Reported measurements conducted using a vapor cell without any buffer gas or an anti-relaxation wall coating show that transmitted light has initially the same (linear) polarization as the incident one. Rotation of the polarization plane caused by an axial magnetic field develops in time scales similar to the pace of establishing the optical pumping/relaxation equilibrium in the atomic ensemble. The traditional passive Faraday rotation picture providing working description for the resonant magneto-optical effects in steady-state conditions does not explain the observed sequence of evolution of the polarization. The picture has to be augmented with analysis of time dependence in the spatial distribution of relevant quantum states within the atomic ensemble as well as longitudinal and transversal intensity profiles of the light beam. Isolation of external effects caused by the optical pumping and relaxation processes from consequences of internal atomic coherences should uncover more details of mechanisms of the latter in the presence of magnetic field. Plentitude of data available from time-dependent polarization measurements provides strong incentives for further development and tests of comprehensive models of coherent interactions of atomic ensembles with radiation and possibly a base for additional advance in understanding and applications of these phenomena.
The optical pumping of Cs atoms with light of the D 1 line under magnetic resonance conditions is numerically calculated. This calculation is done to check the suggestion that an unexpectedly strong influence of the polarization of the pumping light on the resonance signals of transverse alignment, which we observed experimentally, is caused by the coupling between orientation and alignment by means of the magnetic field and/or the pumping light. This suggestion has been confirmed: upon circularly polarized pumping, the shape of the signal line of transverse alignment proved to be similar, as well as in the experiment, to the shape of the signal line of transverse orientation and was sharply different from the shape of the line of alignment observed upon linearly polarized pumping. For metastable 23 S 1 4He atoms, in accordance with the experimental data, the calculated shape of the signal line of transverse alignment is found to be independent of the polarization of the pumping light. The calculations also confirm the possibility of a reverse effect: the influence of alignment on orientation, which manifests itself in the occurrence of orientation upon pumping with unpolarized light under magnetic resonance conditions. For Cs atoms exposed to a field of ∼0.6 Oe, the largest contribution to this effect is yielded by the field coupling of orientation and alignment, whereas, for metastable 23 S 1 4He atoms, the largest contribution is made by the light coupling of these polarization moments.
A general approach to the problem of spontaneous transfer of light-induced anisotropy in the scheme of Raman scattering of resonance elliptically polarized light is developed. Depending on the type of the field-excited ( a )↔( b ) transition, the stationary distribution of atoms over the sublevels of the final level ( c ) coupled with the excited level only by the ( b )→( c ) spontaneous transition is either isotropic and does not depend on field parameters or anisotropic. In the latter case, the anisotropy is determined by both field polarization and (at fairly large level momentum values) field detuning and intensity.
We observe shift in the zero magnetic field resonance as the handedness of resonantly interacting circularly polarized light is changed. The characteristic of the shift resembles with the Zeeman light shift that arises due to interaction of non-resonant circularly polarized light with atom. However many attributes of our observed resonant phenomena like dependence on buffer gas, saturation of the shift with light intensity and involved time constant in evolution of the shift contradicts to the fictitious magnetic field model. We propose collective alignment of atomic magnetic moment giving rise to a real magnetic field as a possible mechanism behind the observed shift. The characteristic changes in the signal profile with respect to the three axis magnetic field have been established that can reveal many subtle issues pertaining to the phenomenon.