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

27
separation, as anticipated, but signal quality was strongly
degraded as L increased (Mlynek et al., 1987). 27
The first beam experiment with a long (34.5-cm)
precession region was done by Theobald et al. (1991)
using D2-line excitation on a Cs beam with fluorescence
detection. In similar work, using detection of
forward-scattered light rather than fluorescence monitoring,
Schuh et al. (1993); Weis et al. (1993b) applied
pump-probe spectroscopy to a Rb beam using D2-line
excitation. Two experiments were performed with interaction
lengths of L = 5 cm (Schuh et al., 1993) and
L = 30 cm (Weis et al., 1993b), respectively. Improving
the sensitivity by going to longer interaction lengths is
difficult because of signal loss due to the finite atomicbeam
divergence. This can be counteracted by laser collimation
of the beam (this technique is being used in
work towards a 2-m apparatus at U. Fribourg), or by
using atoms that are free-falling from a magneto-optical
trap or an atomic fountain (Sec. VIII.H). Hypersonic
and laser-slowed beams can also be used to increase the
atomic flux and transit time, respectively.
F (arb. units)
B (mG)
FIG. 16 Experimental Faraday-Ramsey signal from a thermal
Cs beam (T = 400 K) and a precession length of L = 30 cm.
Polarimetric detection of the rotation angle ϕ of the probe
beam is used.
2. Line shape, applications
In Faraday-Ramsey spectroscopy, one measures the
magneto-optical rotation angle ϕ of the linearly polarized
probe beam. For a beam with Maxwellian velocity
distribution, the magnetic-field dependence of ϕ is obtained
from the three-step model discussed in Sec. V.B
in a manner similar to that described in Sec. VII.A:
ϕ(B) ∝
∫ ∞
0
( B
sin
B0
R
1
u + 2θ pp
)
u 2 e −u2 du. (26)
where θ pp is the relative orientation of the pump and
probe polarizations, u = v/v 0 is the dimensionless velocity,
and v 0 is the most probable velocity in the atomic
beam oven, and
B R 0 = ¯hv 0
2gµL
(27)
is a scaling field (L is the distance between pump and
probe beams). The line shape is a damped oscillatory
Ramsey fringe pattern centered at B = 0 (the scaling
field B0 R is a measure of the fringe width). Figure
27 Other examples of early work in the field are the work of Bertucceli
et al. (1986), who used fluorescence detection to observe nonlinear
level-crossing Ramsey fringes in a metastable Ca beam, the
work of Nakayama et al. (1980), who observed Ramsey fringes
on the D1 line in a Na vapor cell using laser beams separated
by up to 10 mm, and an experiment performed by Borghs et al.
(1984) in the time domain using a monokinetic Ba + beam, which
showed a large number of higher-order fringes, normally damped
in thermal beams due to the large velocity spread. This last experiment
determined the ratio of g-factors of the 5d 2 D 3/2 and
5d 2 D 5/2 states of Ba + .
VIII.C.2 shows an experimental Faraday-Ramsey spectrum
recorded with a thermal Cs beam (T = 400 K) with
a precession region of L = 30 cm, for which B0
R = 170 µG.
Faraday-Ramsey spectroscopy has proven to be an extremely
sensitive tool for investigating spin-coherence
perturbations by magnetic and/or electric 28 fields under
collision-free conditions. Any additional external perturbation
which affects spin coherence will lead to an additional
phase shift in the fringe pattern given by Eq.
(26). Faraday-Ramsey spectroscopy has been applied in
a variety of situations, including an investigation of the
Aharonov-Casher effect in atoms (Sec. XII.C), a precision
electric field calibration (Rasbach et al., 2001), and
a measurement of the forbidden electric tensor polarizabilities
(Sec. XII.D) of the ground state of Cs (Rasbach
et al., 2001; Weis, 2001). Applications of the technique
of Faraday-Ramsey spectroscopy with atomic beams to
the search for parity- and time-reversal-invariance violation,
in particular, for a permanent electric dipole moment
(EDM, Sec. XII.B) have also been discussed (Schuh
et al., 1993; Weis et al., 1993b). Note, however, that
a competitive EDM experiment would need a very intense
optically thick atomic beam, such as the source
built for experiments with atomic thallium by DeMille
et al. (1994).
28 Electric interactions do not couple to spin directly; however, they
affect the orbital angular momentum. Thus spin coherences are
affected by an electric field via spin-orbit and hyperfine interactions.