Optical Pumping
Optical pumping denotes the redistribution of population within
atomic multiplets by state-selective optical excitation in an electronically
excited state and the subsequent spontaneous emission (see the references [1,2]
for the original papers). In most cases the considered multiplets consist
of Zeeman substates. This allows to achieve huge nonlinear effects with
very modest (down to micro Watts) power levels. The simplest case is the
one of a J=1/2 to J'=1/2-transition with a two-fold degeneracy
in both the ground and in the excited state.
Due to the selection rules for angular momenta circularly polarized
light will couple only to one of the Zeeman substates of the ground state
and thus the population of this level will be reduced. Since spontaneous
emission occurs also into the unpumped sublevel, there will be a net accumulation
of population in this sublevels. Optical pumping is particularly effective,
if the population in the excited state is rapidly equalized between the
Zeeman sublevels due to collisions with a buffer gas because then the spontaneous
emission is isotropic. Note that the direction of the pumping will depend
on the sign of the helicity of the pumping light. Linearly polarized light
will not induce pumping because it contains sigma+ and sigma_
light of equal strength.
The induced population difference between the two Zeeman substates
is called orientation and often denoted by w (normalized to [-1,1]).
If the population of the excited state can be neglected, it obeys the following
equation of motion:
The last term is the source term for the optical pumping. P+/_
denotes a pump rate which is proportional to the intensity of the sigma+,
respectively sigma_ component. As mentioned above, the two components pump
in different directions. Gamma denotes relaxation due to collisions and
is very small (of the order of s-1). The damping term proportional
to the pump rate represents saturation. The diffusion term models the thermal
motion of the sodium atoms in the buffer gas atmosphere.
The optical properties of the medium now depend on the orientation
and - via w=w(P) - on the intensity of the light field.
If the linear absorption coefficient is alpha0 and the linear
refractive index 1+n0, the nonlinear absorption coefficient
is
and the nonlinear refractive index is
For circularly polarized light the vapor is bleached by the pump beam.
For very high intensity, one sublevel will be completely empty, the orientation
reaches one. Then the absorption drops to zero and the refractive index
is one. The beam will essentially propagate as in vacuum. Note that an
increase in optical density for the sigma+ component means a
decrease for the sigma_ one and vice versa.
It turns out that the simple model of a homogeneously broadened J=1/2
to J' =1/2-transition is not only of academic interest but a very
appropriate description for the sodium D1-line if a buffer gas
of sufficient pressure (typically 200 to 300 hPa argon or nitrogen) is
introduced so that the homogeneous broadening is larger than the
hyperfine splitting and the Doppler broadening. It is simple enough
to allow for analytical investigations as well as extensive numeral studies
on state of the art workstations. Since these are prerequisites for a thorough
understanding of spatially extended nonlinear system the J=1/2 model
is used in most of our theoretical studies.
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