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.
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 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.
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.
The problem of resonance between light and an atom is treated by solving the wave equation through the method of variation of constants. It is found that an initial degeneracy is removed by the action of the light, and that there occur fluctuations between the two states involved. Calculation of the electric moment of the perturbed atom on the Schr\"odinger density hypothesis shows that when the incident light is linearly polarized the radiation has the same degree of polarization as though the atom were in a weak magnetic field parallel to the electric vector of the light. In the case of circular polarization this fictious field is perpendicular to the plane of polarization. These results confirm the Heisenberg rule deduced from the correspondence principle.
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.
As is well known a linearly polarized resonant laser will cause atoms to generate a magnetic tensor moment (MTM) by polarizing them. When there exists an external magnetic field, it is possible that the moment will precess around the field. In the presence of a radio frequency (RF) exciting source, we investigate theoretically the dependence of time-independent (direct current, DC), the first and second harmonic signal of the MTM precession on magnetic vector field, and obtain its analytical solution by solving the Liouville equation. The results show that the interference of both harmonic components will result in the precession spectrum evidently varying. A detailed explanation is described in the following. For the DC signal, Rabi frequency Ω of 1/(2√2) is a spectral splitting threshold. When it is greater than the threshold, the interference will cause single resonant absorption dip characterized usually to split into two dips, which has not been reported before to the best of our knowledge, and the separation between both the dips may be expressed as √3√Ω2+Ω4 -Ω2-1. For the first harmonic signal including symmetric and antisymmetric component, an interference fringe will appear near the center of antisymmetric part when Ω >1/(2√2), simultaneously its symmetric part behaves like the above dc component, such as splitting threshold and separation between both dips. With regard to the second harmonic signal, it is found that the interference can also lead to the width of the second harmonic decreasing to 38% compared with the case of the first harmonic signal. At the optimum RF Rabi frequency, on the assumption that noise spectral density is constant, it is theoretically shown that the most sensitive magnetometer, realized by the DC component or the first or second harmonic signal of the precession, depends only on the angle between the light polarization and the measured magnetic field.In fact, we are able to obtain the modules of the measured magnetic vector by RF resonant frequency. The angle between the magnetic field and the laser polarization is determined just by the ratio of the intensity of the DC component to the intensity of the second harmonic signal and the ratio between the intensities of the symmetric parts of two harmonic signals in resonance, and another orientation angle between the measured field projection at the plane perpendicular to the light polarization and the direction of RF source depends on the phase difference between the antisymmetric components of both harmonic signals. Consequently, we demonstrate a vectorial atomic magnetometer that is realized by using the RF source and the linearly polarized resonant laser without rotating laser polarization. This kind of atomic magnetometer with simple sensor structure is easy to integrate vector magnetometer array which will be suitable for solving the inverse problem and geomagnetic navigation.
The nonlinear magneto-optical rotation in a medium consisting of $J=1\ensuremath{\rightarrow}J=0$ atoms placed in a static magnetic field is studied. The density matrix approach and irreducible atomic basis are used to describe the state of the atomic system. The stationary propagation equations for two collinear laser beams with perpendicular circular polarizations are derived and analyzed in the case of the magnetic field perpendicular to the light propagation direction. The effect of the linear polarization rotation toward the direction parallel or perpendicular to the magnetic field vector and lossless propagation of the resulting light are predicted. The conversion of the circularly polarized beam into linearly polarized one is shown. The propagation of the leading edges of switched on cw-laser beams and their stationary propagation are analyzed numerically. The dependence of the considered effects on the light detuning and on the additional magnetic field component parallel to the light propagation direction is discussed. The destructive role of the collisional relaxation is demonstrated.