When an atomic medium is irradiated with (circularly or linearly) polarized light that is resonant with a transition between states of angular momenta
the medium becomes spin polarized. The origin of this polarization is a transfer of populations
between the magnetic sublevels
by subsequent cycles of light absorption and emission. In this module, the dynamics of the optical pumping process is addressed by showing the time dependence of the
obtained by solving rate equations. Upward transitions are driven at a rate
, and allowance for sublevel relaxation at a rate
is made, so that the optical pumping can be parametrized in terms of a dimensionless variable
that is proportional to the light intensity.
The light polarization can be chosen as
(linear polarization) or
(left-/right-handed circular polarization) which implies the selection rules
, and ±1, respectively. The transitions between sublevels are shown by vertical (or skewed) lines whose intensity is proportional to the product of the sublevel population and the relative transition strength (itself proportional to a squared 3j-symbol). In this way one sees how the absorbed (and hence also the reemitted) light intensity changes as the pumping proceeds.
Sublevel populations are represented by vertical bars.
Depending on the relative sublevel populations, the polarized medium may either absorb less light than the unpolarized medium (dark state) or more light than the unpolarized medium (bright state). The former case occurs in
transitions, while the latter case is encountered in
transitions (both with linear and circularly polarized light).
In thermal equilibrium, i.e., in the absence of light, all levels have an identical population of
. Optical pumping leads to a non-equilibrium population distribution and the medium is said to be polarized. The polarization of a medium can be defined in terms of its longitudinal multipole moments
(see also Polarized Atoms Visualized by Multipole Moments
). The only longitudinal multipole moments to which light on an electric dipole transition couples are the orientation
and the alignment
which can be defined in terms of the sublevel populations
, for the orientation, and
The state of polarization can also be represented in terms of a probability surface
, which represents the probability to find the system in the state
, when making a measurement with the quantization axis oriented along the spherical direction given by (
). In thermal equilibrium (
) this surface is a sphere of radius
. Note that the probability surface reflects the (rotational and reflection) symmetry of the light polarization. For states with a pure longitudinal polarization (no coherences) the probability surface has a rotational symmetry around the
axis and can be expressed in terms of the sublevel populations
and specific matrix elements of the Wigner rotation matrices
Note also that for pumping with circularly polarized light the quantization axis (
axis) is oriented along the direction of light propagation, while for pumping with linearly polarized light the quantization axis is along the direction of oscillation of the optical field.