Resonant nonlinear magneto-optical effects in atoms∗ - The Budker ...

26
tion along the light path and for the high-light-power
effects (see Sec. V.C), was developed by several authors
(e.g, Matsko et al., 2002a; Rochester and Budker, 2002,
and references therein). However, a complete theoretical
description of NMOR in dense media must also consider
radiation trapping of photons spontaneously emitted
by atoms interacting with the laser light. Matsko
et al. (2001b, 2002a) concluded that for densities such
that the photon absorption length is comparable to the
smallest dimension of the cell, radiation trapping leads to
an increase in the effective ground-state relaxation rate.
B. Time-domain experiments
In many NMOE experiments, the same laser beam
serves as both pump and probe light. More complex experiments
use separate pump and probe beams that can
have different frequencies, spatial positions, directions of
propagation, polarizations, and/or temporal structures.
A wealth of pump-probe experimental techniques in the
time and frequency domains have been developed, including
spin nutation, free induction decay, spin echoes, coherent
Raman beats or Raman heterodyne spectroscopy,
to name just a few. 26 In this section, we give an example
of an experiment in the time domain; in Sec. VIII.C
we discuss frequency domain experiments with spatially
separated light fields.
Zibrov and Matsko (2002); Zibrov et al. (2001) applied
two light pulses to a 87 Rb vapor in sequence, the first
strong and linearly polarized and the second weak and
circularly polarized. A particular elliptical polarization
of the transmitted light from the second pulse was detected.
When a longitudinal magnetic field was applied
to the cell, the resulting intensity displayed oscillations
(within the duration of the probe pulse) at twice the
Larmor frequency. The authors interpreted these experiments
in terms of Raman-scattering of the probe light
from atoms with coherent Zeeman-split lower-state sublevels.
Here we point out that the “rotating polarizer” picture
of coherence NMOR discussed in Sec. V.B can be
used to provide an equivalent description of these experiments.
The linearly polarized pump pulse induces alignment
and corresponding linear dichroism of the atomic
medium, i.e., prepares a polaroid out of the medium. The
polaroid proceeds to rotate at the Larmor frequency in
the presence of the magnetic field. Circularly polarized
probe light incident on such a rotating polaroid produces
linearly polarized light at the output whose polarization
plane rotates at the same frequency. This is the same
as saying there are two circularly polarized components
with a frequency offset.
26 For a detailed discussion we refer the reader to a comprehensive
overview of the underlying mechanisms and applications in a
book by Suter (1997).
Light beam
B
z
Pumping
x
y
Atomic beam
Probing
FIG. 15 Faraday rotation technique utilizing separated light
beams and an atomic beam. The resonance line width is
determined by the time-of-flight between the pump and the
probe beams. Variations of this technique include the use of
circularly polarized light both for pumping and probing, and
the detection of absorption or induced ellipticity instead of
polarization rotation.
C. Atomic beams and separated light fields,
Faraday-Ramsey Spectroscopy
In the coherence effects (Sec. V.B), the resonance
width is determined by the relaxation rate of groundstate
polarization. In the transit effect, in particular,
this relaxation rate is given by the time of flight of atoms
between optical pumping and probing. When one laser
beam is used for both pumping and probing, this time can
be increased, narrowing the resonance, by increasing the
diameter of the beam. Another method of increasing the
transit time, however, is to use two beams, spatially separating
the pump and probe regions. For this technique,
the model (Sec. V.B) of the coherence effects in terms
of three sequential steps (pumping, precession, probing)
becomes an exact description.
As this experimental setup (Fig. VIII.C) bears some
similarities to the conventional Ramsey arrangement (see
Sec. VIII.C.3) and as the coherence detection in the
probe region involves polarimetric detection of polarization
rotation, this technique is called Faraday-Ramsey
spectroscopy.
1. Overview of experiments
Several experiments studying NMOE using spatially
separated light fields have been performed, using various
detection techniques. The first atomic beam experiment
of this sort was performed by Schieder and
Walther (1974) with a Na beam using fluorescence detection.
Mlynek et al. (1988) observed Ramsey fringes
in a Sm beam on the 570.68-nm F = 1 → F = 0 transition
using Raman heterodyne spectroscopy, a technique
involving application of both light and rf magnetic fields
to the atoms (as in work by, for example, Suter, 1997),
with light beam separations of up to L = 2.2 cm. The
fringe widths were found to scale as L −1 with the beam