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Journal of Physics B Atomic Molecular and Optical Physics

Coherent elliptic states of atoms in non-orthogonalEandBfields

Lars Kristensen, Erik Horsdal-Pedersen, Peter Sørensen

Published Mar 14, 1998• 11 citations
Publisher

Abstract

The dynamics of coherent elliptic states in time-dependent electric and magnetic fields has been studied and it is shown that a linear Stark state may be transformed adiabatically into a circular Zeeman state through a continuous range of coherent elliptic states provided the fields vary slowly and are not parallel. The orientation vectors of the elliptic states rotate relative to the fields during the adiabatic transformation except when the fields are orthogonal. The condition for adiabatic behaviour is established for an easily realizable choice of field variation.

DOI
10.1088/0953-4075/31/5/012

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The dynamics of coherent elliptic states in time-dependent electric and magnetic fields has been studied and it is shown that a linear Stark state may be transformed adiabatically into a circular Zeeman state through a continuous range of coherent elliptic states provided the fields vary slowly and are not parallel. The orientation vectors of the elliptic states rotate relative to the fields during the adiabatic transformation except when the fields are orthogonal. The condition for adiabatic behaviour is established for an easily realizable choice of field variation.
The dynamics of the n = 25 shell of Li atoms in weak electric, E , and magnetic, B , fields was studied experimentally as a function of the rate of change of the electric field strength, , the strength, B , of a constant magnetic field and the angle between the two fixed field directions, . Prior to the variation of E , it was held constant at with strong enough to dominate the Stark-Zeeman manifold for the shell. The uppermost state, which is a coherent elliptic state (CES), was populated selectively by pulsed laser excitation. The field was subsequently varied without rotation from to at the constant rate . It is shown experimentally, in accordance with theory, that the dynamics is described by a single dimensionless parameter given by in atomic units. When the variation of E is so slow that the electron has time to adjust and the population then remains in the uppermost state of the manifold (adiabatic transformation), for smaller the population shifts to an interval of states centred near the middle of the manifold and at the wavefunction is almost frozen and the lowermost part of the manifold populated (diabatic transformation). The experimental findings for near-adiabatic evolution of the CES agree with theoretical results obtained in a non-relativistic, hydrogenic model but discrepancies are seen when non-hydrogenic states are populated for .
Oriented elliptic Rydberg atoms have been formed in a thermal beam of Li atoms by the adiabatic crossed-field method. All coherent elliptic quantum states from linear to circular can be produced by this method. The orientation and eccentricity is controlled by the external fields. While the formation of circular states by the crossed-field method has already been established experimentally, the radiative decay of the Rydberg atoms formed here was measured and compared with theory to verify that highly eccentric elliptic quantum states may also be formed.
The well-known Zeeman and Stark effects can lead to unusual atomic state dynamics when both magnetic and electric fields are present. In this paper we analyze quantum mechanical and classical models of the time evolution of the angular momentum of an atom in the presence of weak, orthogonal electric and magnetic fields. The anisotropic electric polarizability of the atom plays a crucial role in the dynamics. The classical model leads to nonlinear evolution equations, and we investigate how quantum mechanics ‘‘avoids’’ the nonlinearity. Finally, we note that the classical equations of motion are identical to those used to describe the time evolution of Stokes vectors for polarized light propagating in an optically nonlinear medium. The treatment is appropriate for an undergraduate course in quantum mechanics.
The dependencies of the polarization rotation on the probe ellipticity and the longitudinal magnetic field have been studied both experimentally and theoretically in a V-type electromagnetically induced transparency for 87Rb vapour. The angle of rotation varies periodically with the change in the probe ellipticity and non-linearly with the variation of the magnetic field. We have observed that the plane of polarization is rotated maximum for linearly polarized light and have obtained angle of rotation 0.32° ± 0.01° for B = 0.036 ± 0.001 mT while it was 0.0267° ± 0.0002° without magnetic field. Thus our measurement becomes sensitive to the low magnetic field. A four-level system is considered and the corresponding density matrix equations have been solved analytically to explain these observations theoretically with the help of degenerate and non-degenerate magnetic sub-levels.
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.