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

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can be used for studies of collisional perturbations of
Rydberg states with much greater precision than that
of earlier photoabsorption experiments.
4. Gas lasers
Magneto-optical rotation of a weak probe light passing
through a gas discharge is a useful tool for studying
amplifying media in gas lasers. Early examples of this
are the papers by Aleksandrov and Kulyasov (1972) who
observed large rotations in a 136 Xe discharge and by Menzies
(1973) who determined population and polarization
relaxation rates of the Ne levels making up the 3.39 µm
laser transition. The technique is applicable to transitions
which exhibit light absorption as well as amplification
depending on particular population ratios. Since
the Faraday angle is proportional to the population difference
for the two levels of a transition and changes sign
when population inversion is achieved, such studies allow
precise determination of population differences and their
dependencies on parameters such as gas pressure and discharge
current. An example is the work of Winiarczyk
(1977) who studied the 632.8-nm Ne line. Due to its sensitivity,
this method is useful for optimizing the efficiency
of gas lasers, particularly those utilizing weak transitions.
5. Line identification in complex spectra and search for “new”
energy levels
We have already mentioned the utility of magnetooptical
rotation for identification of molecular spectra
and for distinguishing atomic resonances from molecular
ones. Another, more unusual, application of Faraday
rotation spectroscopy was implemented by Barkov
et al. (1989b, 1987, 1988b). They were looking for optical
magnetic-dipole transitions from the ground term of
atomic samarium to the levels of the first excited term of
the same configuration whose energies were not known.
A study of the spectrum revealed hundreds of transitions
that could not be identified with the known energy levels
(most of these were due to transitions originating from
thermally populated high-lying levels). Drawing an analogy
with infrared transitions between the ground term
levels for which unusually small pressure broadening had
been observed by Vedenin et al. (1986, 1987), Barkov
et al. predicted small pressure broadening for the soughtafter
transitions as well. They further noticed that in
the limit of γ ≫ Γ D (where γ and Γ D are the Lorentzian
and Doppler widths, respectively), the peak Faraday rotation
is ∝ γ −2 (in contrast to absorption, for which the
amplitude is ∝ γ −1 ). In fact, at high buffer gas pressures
(up to 20 atm), the magneto-optical rotation spectra
showed that almost all transitions in the spectrum
were so broadened and reduced in amplitude that they
were practically unobservable. The spectrum consisted
of only the sought-after transitions, which had unusually
small pressure broadening.
6. Applications in parity violation experiments
Magneto-optical effects have played a crucial role in
experiments measuring weak-interaction induced parityviolating
optical activity of atomic vapors. 9 Parityviolating
optical activity is usually observed in the absence
of external static fields near magnetic-dipole (M1)
transitions with transition amplitudes on the order of a
Bohr magneton. The magnitude of the rotation is typically
10 −7 rad per absorption length for the heavy atoms
(Bi, Tl, Pb) in which the effect has been observed.
The Macaluso-Corbino effect allows calibration of the
optical rotation apparatus by applying a magnetic field
to the vapor. On the other hand, because the parityviolating
optical rotation angles are so small, great care
must be taken to eliminate spurious magnetic fields, since
sub-milligauss magnetic fields produce Macaluso-Corbino
rotation comparable in magnitude to the parity-violating
rotation, albeit with a different lineshape. The lack of
proper control over spurious magnetic fields apparently
was a problem with some of the early measurements of
parity-violating optical activity in the late 1970s whose
results were inconsistent with subsequent more accurate
measurements. 10
The origin of the parity-violating optical rotation lies
in the mixing, due to the weak interaction, of atomic
states of opposite parity, 11 which leads to an admixture
of an electric-dipole (E1) component to the dominant
M1 amplitude of the transition. The observed effect
is the result of the interference of the two components
of the amplitude. In general, there is also an electric
quadrupole (E2) component of the transition amplitude.
However, there is no net contribution from E1–E2 interference
to the parity-violating optical rotation, since the
effect averages to zero for an unpolarized atomic sample.
Nevertheless, knowledge of the E2 contribution is
crucial for accurate determination of the parity-violating
amplitude, as it affects the sample absorption and the
Macaluso-Corbino rotation used for calibration. In addition,
this contribution is important for interpretation of
the parity-violation experiments, since the E2/M1 ratio
can serve as an independent check of atomic theory. Fortunately,
investigation of Macaluso-Corbino lineshapes
allows direct determination of the E2/M1 ratio (Bogdanov
et al., 1986; Majumder and Tsai, 1999; Roberts
et al., 1980; Tregidgo et al., 1986). These measurements
exploit the difference in the selection rules for these two
9 See, for example, a review of early experiments by Khriplovich
(1991), and more recent reviews by Bouchiat and Bouchiat
(1997) and Budker (1999).
10 The most accurate optical rotation measurements to date
(Meekhof et al., 1995; Vetter et al., 1995) have reached the level
of uncertainty of ∼1% of the magnitude of the effect.
11 Parity-violating interactions mix states of the same total angular
momentum and projection. As a consequence of time-reversal
invariance, the mixing coefficient is purely imaginary, which is
the origin of the chirality that leads to optical rotation.