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Journal of Experimental and Theoretical Physics

Two-scale angular-momentum evolution induced by elliptically polarized resonance radiation for a two-level atom with J g → J e =J g +1 optical transition in a constant magnetic field

K. A. Nasyrov

Published Mar 1, 2004• 0 citations
Publisher

Abstract

The dynamics of a two-level atom with optical transition J g → J e =J g + 1 under the action of elliptically polarized resonance radiation in the presence of a constant field directed along the radiation wave vector is studied in the approximation of a semiclassical description of the angular momentum orientation. It is shown that the atomic distribution over the angular momentum orientation exhibits a two-scale time evolution. At the first stage, after the beginning of irradiation, the angular momenta of atoms get oriented (over comparatively short time intervals) along the magnetic field, as well as in the opposite direction, depending on their initial orientation and the ellipticity of radiation. At the second (longer) stage, the redistribution of atoms takes place, as a result of which they are oriented predominantly in one of the above directions. The duration of the second stage is an exponential function of angular momentum J.

DOI
10.1134/1.1705700

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The dynamics of a two-level atom with optical transition J g → J e =J g + 1 under the action of elliptically polarized resonance radiation in the presence of a constant field directed along the radiation wave vector is studied in the approximation of a semiclassical description of the angular momentum orientation. It is shown that the atomic distribution over the angular momentum orientation exhibits a two-scale time evolution. At the first stage, after the beginning of irradiation, the angular momenta of atoms get oriented (over comparatively short time intervals) along the magnetic field, as well as in the opposite direction, depending on their initial orientation and the ellipticity of radiation. At the second (longer) stage, the redistribution of atoms takes place, as a result of which they are oriented predominantly in one of the above directions. The duration of the second stage is an exponential function of angular momentum J.
The Wigner representation of angular-momentum orientation in the classical limit on $J\ensuremath{\gg}1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\stackrel{\ensuremath{\rightarrow}}{J}J$ or $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, 1/J,1/\sqrt{J},1/J​, of the angular-momentum orientation. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ or $\stackrel{\ensuremath{\rightarrow}}{J}J,$ transition particles come into ``dark'' states while for the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition they occupy the ``brightest'' state. In the presence of a nonzero magnetic field, particles with $\stackrel{\ensuremath{\rightarrow}}{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition the directions of the angular momentum form a cone around the magnetic field.
The interaction of laser light of arbitrary polarization with systems of high angular momentum is considered. We show that elliptically polarized light creates an anisotropic spatial distribution of atomic and molecular angular momentum which is qualitatively different from the alignment and orientation induced by light of circular or linear polarization. Multilevel coherent population trapping within a manifold of ground-state magnetic sublevels results in a nonclassical behavior of a high-JJJ molecular rotor. The classical approximation for the angular momentum distribution is compared with the exact quantum calculations, and is shown to fail in cases of long interaction times and high intensities of the exciting light. In these limits, the quantum uncertainty defines the spatial width of the angular distribution. The applicability of the classical treatment is analyzed and found to be different in the cases of $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ and $\stackrel{\ensuremath{\rightarrow}}{J}J$ transitions. A biaxial spatial orientation with two preferential axes of rotation is experimentally created in sodium atoms via coherent population trapping by elliptically polarized light. A method for producing an arbitrary orientation of atomic angular momentum by magnetic field assisted coherent population trapping is proposed.
The problem of the interaction of radiation with arbitrary polarisation and intensity with the resonance transitions 1/2-1/2 and 1-0 is solved. Exact expressions for the orientation vectors of the ground and excited states for the transition 1/2-1/2 and for the orientation vector and alignment tensor of the transition 1-0 have been obtained. In the case of longitudinal propagation the system of equations for the absorption of an elliptically polarised wave is obtained. It is shown that, irrespective of the initial state, the polarisation at the transition 1-0 tends either to the linear or to the circular form as it propagates depending on the times of collisional relaxation of orientation and alignment and on the magnetic field value. In the case of transverse propagation the dependence of the saturation intensity of a linearly polarised wave on the magnetic field value and on relaxation widths is obtained.
In recent years interest has significantly quickened in investigation of nonlinear optical and spectroscopic phenomena in such unique objects as Rydberg atoms (the atoms in the energy states near the ionization limit) and van der Waals complexes (dimers). These objects are characterized, in particular, by that their energy states are strongly degenerate due to a large value of angular (rotational) momentum. Here, the problem arises of adequate theoretical description of experimental results, especially when polarization peculiarities of nonlinear radiation processes are considered. The problem is caused by the existence of a huge number of quantum magnetic sublevels of energy states, which are, in the general case, coherently coupled to each other and take part in the radiation processes. Figure 1 gives a vivid presentation of the problem arising even in such a seemingly simple case when one need describe the radiation transitions caused by a strong monochromatic field between two energy levels with large values of the angular momentum J. If the field polarization is arbitrary, the whole set of the magnetic sublevels turn out to be coupled by radiative transitions. Formally, the problem becomes essentially multilevel. In this case not only the hope fades of solving it analytically using the traditional quantum-mechanical approach, but the problems of numerical solution grow abruptly with increasing quantum number J as well. On the other hand, as is often the case, every cloud has a silver lining. With large J we approach the situation when the rotational motion of particles can be described classically. It turns out that the transition from the quantum description of orientation states of the angular momentum to the classical one simplifies the problem radically: it reduces to the problem of radiation processes in the simplest model of nondegenerate states. In this case the rotational motion manifests itself in a dependence of the density matrix elements on orientation angles of the angular momentum as on a parameter.
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.
We have studied the transition probabilities and the photofragment energy and angular distributions in a resonant two-photon transition to the continuum with an elliptically polarized radiation field. The general formalism applies both to ionization of atoms within the framework of a single-electron model and the dissociation of diatomic molecules with the involvement of \ensuremath{\Sigma} states only. Detailed calculations for an initial J=0 state give the observable quantities as functions of detuning, intensity, and the polarization parameter for several combinations of the system parameters such as bound-bound and bound-continuum couplings and the Fano q parameter. For sufficiently intense fields the Raman-like coupling between the two coherently excited magnetic sublevels of the resonant J=1 state (one of which can be decoupled from the ground state by a linear transformation) causes a significant enhancement of the transition probability near the Fano minimum obtained for linearly or circularly polarized fields. The evolution of the photofragment kinetic-energy distribution changes with the ellipticity parameter of the radiation. The angular distribution becomes intensity dependent for general ellipticity parameters; the shapes of the resultant distribution in different space-fixed planes are discussed.