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

33
ization in the electric field (Fig. B.2). The maximum
ellipticity induced in the light field due to the coherence
effect is proportional to ∆ s /γ rel .
While much of the recent work on coherence NMOE
has been done with alkali atoms, these are not necessarily
the best choice for NEOE because tensor polarizabilities
are suppressed for states with J = 1/2 as discussed in
Sec. XII.D.
Herrmann et al. (1986) studied a different kind of
NEOE in which an electric field is applied to a sample
of atoms, and normally forbidden two-photon transitions
become allowed due to Stark mixing. The large polarizabilities
of Rydberg states make two-photon Stark spectroscopy
of transitions involving Rydberg levels an extremely
sensitive probe for small electric fields.
XI. EXPERIMENTAL TECHNIQUES
In this Section, we give details of some of the experimental
techniques that are employed for achieving long
ground-state relaxation times (atomic beams with separated
light-interaction regions, buffer-gas cells, and cells
with antirelaxation wall coating), as well as the techniques
used for sensitive detection of NMOE and NEOE,
especially spectropolarimetry (Sec. XI.B).
We begin the discussion by describing a representative
experimental setup (Sec. XI.A). Using this example
we formulate some general requirements for experimental
apparatus of this sort, [for example, laser frequency tunability
and stability (Sec. XI.E), and magnetic shielding
(Sec. XI.D)], and outline how these requirements have
been met in practice.
A. A typical NMOE experiment
Here we give an overview of the Berkeley NMOE apparatus,
which has been used to investigate various aspects
of the physics and applications of narrow (∼2π ×1-Hz,
Budker et al., 1998a) resonances, such as alignment-toorientation
conversion (Budker et al., 2000a), self rotation
(Rochester et al., 2001), and reduced group velocity
of light (Budker et al., 1999a). The setup has also been
used to investigate NEOE and to conduct exploratory
experiments whose ultimate goal is testing fundamental
symmetries (Kimball et al., 2001; Yashchuk et al., 1999a).
Due to the large enhancement of small-field optical rotation
produced by the narrow resonance, this setup is a
sensitive low-field magnetometer (Budker et al., 2000b).
With a few modifications, this apparatus can also be applied
to extremely high-sensitivity magnetometry in the
Earth-field range (Budker et al., 2002b).
The Berkeley apparatus is shown in Fig. XI.A.
Rubidium and/or cesium atoms are contained in a vapor
cell with paraffin coating (Alexandrov et al., 1996),
used to suppress relaxation of atomic ground-state polarization
in wall collisions (Sec. VIII.E). The experiments
FIG. 19 Schematic diagram of the modulation polarimetrybased
experimental setup used by Budker et al. (1998a) to
investigate NMOE in paraffin-coated alkali-metal-vapor cells.
are performed on the D1 and D2 resonance lines. A
tunable extended-cavity diode laser is used as the light
source. The laser frequency is actively stabilized and can
be locked to an arbitrary point on the resonance line using
the dichroic-atomic-vapor laser-lock technique (Sec.
XI.E). The laser line width, measured with a Fabry-
Perot spectrum analyzer, is ≤7 MHz. Optical rotation is
detected with a conventional spectropolarimeter using a
polarization-modulation technique (Sec. XI.B). The polarimeter
incorporates a crossed Glan prism polarizer and
polarizing beam splitter used as an analyzer. A Faraday
glass element modulates the direction of the linear polarization
of the light at a frequency ω m ≃ 2π×1 kHz with
an amplitude ϕ m ≃ 5×10 −3 rad. The first harmonic of
the signal from the photodiode in the darker channel of
the analyzer, is detected with a lock-in amplifier. It is
proportional to the angle of the optical rotation caused
by the atoms in the cell, ϕ s (Sec. XI.B). This signal,
normalized to the transmitted light power detected in
the brighter channel of the analyzer, is a measure of the
optical rotation in the vapor cell.
A coated 10-cm-diameter cell containing the alkali vapor
is placed inside a four-layer magnetic shield and
surrounded with three mutually perpendicular magnetic
coils (Yashchuk et al., 2002a). The three outer layers
of the shield are nearly spherical in shape, while the innermost
shield is a cube (this facilitates application of
uniform fields to the cell). The shield provides nearly
isotropic shielding of external dc fields by a factor of
∼10 6 (Yashchuk et al., 2002a). Although a very primitive
degaussing procedure is used (Sec. XI.D), the residual
magnetic fields averaged over the volume of the vapor
cell are typically found to be at a level of several microgauss
(before compensation with the magnetic coils).