Optical Pumping: Visualization of Steady State Populations and Polarizations

When an atomic medium is irradiated with (circularly or linearly) polarized light that is resonant with a transition between states of angular momenta and , 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 Demonstration, the steady-state populations are inferred by solving the rate equations for the populations . Upward transitions are driven at a rate , and allowance is made for sublevel relaxation at a rate , 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- or right-handed circular polarization) that implies the selection rules , or ±1, respectively. The transitions between sublevels are shown by vertical (horizontal or skewed) lines whose intensity is proportional to the product of the sublevel population and the relative transition strength (itself proportional to a squared 3-symbol). In this way one sees how the absorbed (and hence also the re-emitted) 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 and transitions, while the latter case is encountered in transitions (both with linear and circularly polarized light).

In thermal equilibrium, that is, in the absence of light, all levels have an identical population of . Optical pumping leads to a nonequilibrium 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 as

for the orientation, and

for the alignment.

The state of polarization can also be represented in terms of a probability surface that represents the probability of finding 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. It can be expressed in terms of the sublevel populations and specific matrix elements of the Wigner rotation matrices as

.

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.

For more details on probability surfaces see Polarized Atoms Visualized by Multipole Moments.

Snapshot 1: dark state prepared by -pumping

Snapshot 2: bright state prepared by -pumping

Snapshot 3: dark state prepared by -pumping

Snapshot 4: dark state with a pure positive alignment prepared by -pumping

Snapshot 5: bright state with a pure negative alignment prepared by -pumping