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

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field; after 30 such measurements Isayama et al. (1999)
obtained a precision of 0.18 µG in the determination of
the applied magnetic field. It is expected that by using
atomic fountains (Narducci, 2001) or far-off-resonant
optical dipole traps (Davidson et al., 1995), the observation
time and overall sensitivity to magnetic fields can be
considerably improved.
B. Electric-dipole moment searches
The existence of a permanent electric-dipole moment
(EDM, reviewed by, for example, Khriplovich and Lamoreaux,
1997) of an elementary or composite particle such
as an atom would violate parity- (P ) and time-reversal
(T ) invariance. The nonrelativistic Hamiltonian H EDM
describing the interaction of an EDM d with an electric
field E is given by
H EDM = −d · E ∝ F · E. (34)
Under the parity operator ˆP (the space-inversion operator
that transforms r → −r), the axial vector F does not
change sign, whereas the polar vector E does. Therefore,
H EDM is P -odd, i.e., violates parity. Under the timereversal
operator ˆT , E is invariant and F changes sign,
so H EDM is also T -odd.
Ever since the discovery in 1964 of CP -violation in the
neutral kaon system (C is charge-conjugation), there has
been considerable interest in the search for EDMs of elementary
particles. (CP -violation implies T -violation if
the combined CP T symmetry is valid, as is generally
believed). Many theoretical attempts to explain CP -
violation in the neutral kaon system, such as supersymmetry,
predict EDMs of the electron and neutron that
are near the current experimental sensitivities (see discussion
by Khriplovich and Lamoreaux, 1997). Measurements
of the EDM of paramagnetic atoms and molecules
(that have unpaired electrons) are primarily sensitive to
the electron EDM d e . It is important to note that due to
relativistic effects in heavy atoms, the atomic EDM can
be several orders of magnitude larger than d e .
If an atom has an EDM, its Zeeman sublevels will experience
linear electric-field-induced splitting much like the
usual Zeeman effect. Most methods of searching for an
EDM have thus been based on detection (using magneticresonance
methods or light absorption) of changes in the
Larmor precession frequency of polarized atoms when a
strong electric field is applied, for example, parallel or
anti-parallel to a magnetic field.
Another (related) way of searching for EDMs is to use
induced optical activity. As was pointed out by Baranova
et al. (1977) and Sushkov and Flambaum (1978),
a vapor of EDM-possessing atoms subject to an electric
field will cause rotation of the polarization plane of light
propagating along the direction of the electric field—the
analog of Faraday rotation. Barkov et al. (1988a) demonstrated
that, just as in magneto-optics, nonlinear optical
rotation is significantly more sensitive than linear optical
rotation to the EDM of an atom or molecule (see also discussion
by Hunter, 1991; Schuh et al., 1993; Weis et al.,
1993b).
Kimball et al. (2001); Yashchuk et al. (1999a) recently
investigated the possibility of performing a search for the
electron EDM d e using nonlinear optical rotation in a
paraffin-coated Cs-vapor cell subjected to a longitudinal
electric field. In addition to Cs, which has an enhancement
factor for the electron EDM of ∼120, the cell would
also contain Rb, which has much smaller enhancement
factor and would be used as a “co-magnetometer.” The
estimated shot-noise-limited sensitivity to d e for such
an experiment is ∼10 −26 e cm Hz −1/2 (for a 10 kV cm −1
electric field). This statistical sensitivity should enable
a NMOR-based EDM search to compete with the best
present limits on d e from measurements in Tl (Regan
et al., 2002), which has an enhancement factor of ∼600,
and Cs (Murthy et al., 1989). However, in order to reach
this projected sensitivity, there are several problems that
must be overcome. The first is a significant change in
the atomic density when electric fields are applied to the
cell. The second is a coupling of the atomic polarizations
of Cs and Rb via spin-exchange collisions, which
would prevent Rb from functioning as an independent
co-magnetometer. These issues are discussed in more detail
by Kimball et al. (2001).
There are also molecular beam experiments (Sauer
et al., 2001) searching for an electron EDM using a separated
light pump and probe technique that is a variant of
the Faraday-Ramsey spectroscopic method (Sec. VIII.C).
In another class of experiments, one searches for EDMs
of diamagnetic atoms and molecules. Such experiments
are less sensitive to the EDM of the electron than those
employing paramagnetic atoms and molecules. However,
they probe CP -violating interactions within nuclei, and
are sensitive to EDMs of the nucleons. Romalis et al.
(2001a,b) have conducted the most sensitive experiment
of this kind in 199 Hg. A cylindrical quartz vapor cell at
room temperature (vapor concentration ∼5×10 13 cm −3 )
is subjected to an electric field of up to 10 kV cm −1 , applied
via conductive SnO 2 electrodes deposited on the inner
surfaces of the flat top and bottom quartz plates. The
entire inner surface of the cell including the electrodes is
coated with paraffin. The cell is filled with a N 2 /CO
buffer-gas mixture at a total pressure of several hundred
Torr. The buffer gas is used to maintain high breakdown
voltage, and to quench metastable states of mercury that
are populated by the UV light employed. The nuclearspin-relaxation
time (I = 1/2 for 199 Hg) is ∼100–200 s.
The experiment utilizes the 6 1 S 0 → 6 3 P 1 transition at
253.7 nm, excited with light from a home-made cw laser
system. A magnetic field of 17 mG and the electric field
are applied to the cell, and circularly polarized resonant
light, chopped at the Larmor frequency, illuminates the
cell in a direction perpendicular to that of the fields. After
the atoms are pumped for ∼30 s with 70 µW of light
power to establish transverse circular polarization, optical
rotation of linearly polarized probe light, detuned