Saturated absorption and DAVLL-observed Zeeman shifts at 780 nm in 85,87Rb
J. Peter Campbell
Davidson College, Davidson NC 28035
The 780 nm absorption peaks in 85, 87Rb provide an excellent model for studying saturated absorption
spectroscopy and Zeeman shifts in electronic transitions. Using a tunable diode laser, we excited the 5 2P3/25S1/2 (F=2,1) transitions in 87Rb and the 52P3/2-5S1/2 (F=3,2) in 85Rb and observed the induced absorption
using FMS spectroscopy. Using several ring magnets we explored the effect an axial magnetic field along
the direction of propagation of the laser. Using the Dichroic-Atomic-Vapor-Laser-Locking technique
(DAVLL) we compared the Zeeman shifts with the theoretical ΔE= g*μ b*B. Finally, we created a model
using gaussian interference to model the DAVLL signal.
I. INTRODUCTION
Atomic absorption spectroscopy is ordinarily limited
by Doppler broadening due to the random motion of the
atoms in the sample. Saturated absorption spectroscopy
allows spectral resolution below the usual limits of
Doppler broadening.i
By introducing a counterpropagating pump beam that is 90% more powerful than
the probe beam, most of the 5S electrons in each Rb atom
will be saturated into their first excited state (5P). This
saturation significantly decreases the absorption of the
probe beam at the resonant energies. Thus, non-absorbing
peaks appear within each broadened absorption peak that
are below the Doppler spectral limit. A saturated
spectrum would contain vertical peaks in the middle of
each absorption peak where the energy of the pump beam
exactly matches the resonant energy of the electronic
transition.
One advantage to using saturated absorption
spectroscopy is that it can illuminate spectral features that
would otherwise be buried in a Doppler-broadened
spectrum.
Specifically in this case, the hyperfine
structure of the 5P state in Rb splits into three different
energy levels (one for each projection of mf). This is
similar to fine structure due to LS coupling, but three
orders of magnitude smaller. Thus, unless one can
eliminate the broadening, these hyperfine splittings will
be unobservable. For more information on energy
splittings in Rb, visit: http://hubble.physik.unikonstanz.de/jkrueger/thesis/thesis.html.
Figure 1. Fine and Hyperfine structure for Rb. Each
isotope has a similar plot. The 780 nm transition
observed in this experiment occurs from (5)2P3/2- (5)2S1/2.ii
Since the simplest description of electronic spin
approximates the electron as a spinning charged particle
with resultant magnetic moment, it seems intuitive that an
external magnetic field would somehow change the
stability (and thus energy) of the electron. The energy of
the electron can also change due to coupling with the
magnetic moment of the orbital (fine structure) and of the
nucleus (hyperfine structure). Each of these effects can
be amplified and studied through the introduction of an
external magnetic field. The change in energy as result of
an introduced magnetic field is referred to as a Zeeman
shift. In general, for mf =+/-1 the shift is represented as:
ΔE=g*μb*Biii
(1)
where g is a gyrometric ratio characteristic of each
coupling (fine, hyperfine, etc) and μb is the Bohr
magneton.
Due to quantum mechanical considerations, there are
only certain allowable optical transitions within the
numerous possible splittings. Specifically, only mf = +/1,0 are allowed. It turns out that the various transitions
interact with polarized light differently (analogously to
the interaction of plane-polarized light with chiral
molecules). Transitions with Δmf = +1 only absorb rightcircularly-polarized light (σ+), and Δmf = -1 only absorb
left-circularly polarized light (σ-). The signals can thus be
separated using a quarter-wave plate with its fast axis
oriented at 45 degrees. Using a polarizing beam splitter,
the laser can then be separated into two signals, one for
each of the allowable Δmf transitions.
The DAVLL plot takes advantage of the ability to
separate these signals. Since the Zeeman shift for σ+ will
be opposite of that for σ- as the magnetic field increases
the plot for σ+ will shift in the opposite direction as the
plot for σ-. By subtracting one signal from the other, an
error plot is obtained that changes as a function of energy
level splitting.
Saturated Absorption in Rb
II. SATURATED ABSORPTION
The most difficult portion of the saturated absorption
experiment was aligning the optics to maximize signal.
As shown in Figure 2, the scanning laser beam was split
into two beams, a probe and a pump (or saturating) beam,
by means of a thick lens. Most of the light passed
through the lens and ended up in the pump beam, which is
important for the saturated absorption signal (since most
electrons need to be in their excited state).
Trans. (arb. units)
4
3
2
1
0
-1
-2
0
500
1000
1500
2000
2500
Energy (arb. units)
Figure 3. Saturated Absorption in Rb85, 87. The energy
scale is approximately 2.5 GHz per division. The dark
plot represents the unpumped Doppler broadened
absorption spectrum, whereas the lighter plot displays the
pumped spectrum. The resonant energies are clearly
visible as narrow transmission peaks within the Dopplerbroadened absorption valleys.
III. DAVLL AND ZEEMAN SHIFT
Figure 2. Experimental setup for saturated absorption
experiment. Both the probe and saturating beams were
frequency scanned about the 780 nm absorption peaks for
Rb.iv
In order to achieve an ideal saturated absorption
signal, the pump beam must overlap as much of the probe
beam as possible. This can be obtained as diagrammed in
Figure 2 by directing the pump beam back to the middle
of the reflective lens, splitting the reference and probe
beams. Care must be taken not to reflect the beam back
into the diode laser however, as it may affect the stability
of the laser.v
The amplitude of the ramping voltage affects the
range of frequencies over which the laser scans, and thus
the transition energies observable in the Rb. The 780 nm
transitions in Rb were at the outside range of the Vortex
diode laser that we employed so care had to be taken not
to maximize signal without exceeding the stable ramping
frequency of the piezo element.
The Nirvana photodetector was set to Auto Bal mode,
which compares the signal beam (probe) with the
reference beam to determine differential absorption. We
plotted the linear output from the photodetector on the
oscilloscope.
Without the pump beam, a Doppler
broadened spectrum was easily observed. With the
saturating pump beam, the resonant energies are easy to
observe. Figure 3 displays both spectra.
Observation of the DAVLL spectra required a
different experimental setup. After much trial and error
experimentation, we found a configuration that allowed
observation of the DAVLL signal and measurable
Zeeman shifts under the influence of a controllable
magnetic field.vi
Figure 4 displays the DAVLL
configuration.
Figure 4. Experimental setup for DAVLL technique. The
magnetic field was created by ring magnets oriented
axially above (i.e. out of the page), not surrounding, the
Rb cell and laser beam.vii
The first polarizing beam splitter ensures that the
light entering the magnetic field is vertically polarized.
Once the light has traveled through the magnetic field and
sample it enters a quarterwave plate, which separates the
left from the right-circularly polarized light. Specifically,
we aligned the fast axis of the quarterwave plate at 45 o
from vertical, so the two rotating polarizations would be
offset by 90o, with one exiting the quarterwave plate
oriented vertically and the other horizontally. The two
polarizations were then separated using a polarizing beam
splitter, and directed into the Nirvana photodetector.
The Nirvana photodetector was set on Auto Bal,
which subtracted the two signals and equalized their
relative DC amplitudes. Thus, in the absence of a
magnetic field, since there is no difference in the
absorption of the light in the cell, the difference between
the two signals produces a baseline signal at 0 V. As the
field increases, however, the DAVLL signal was observed
as the two absorptions began to deviate according to Eq.
1.
We took eight data points from 0-200G, which was
the maximum field that we could create given the
experimental setup. Figure 5 displays three of the eight
plots that we obtained, which evidences the effect of the
magnetic field on the DAVLL plot, and indirectly, on the
relative absorptions of the two directions of polarized
light.
Once we had obtained DAVLL plots for several
different magnetic field strengths, we attempted to
measure the Zeeman shift as a function of magnetic field
strength. The magnetic field was measured for each
sample at the center of the Rb tube with an axial Gauss
meter. Due to experimental limitation, the field varied by
almost 10% over the area of the tube, which should be
negligible.viii
To measure the Zeeman shift, I plotted the difference
between each peak position (in energy) as a function of
the magnetic field strength. Since the oscilloscope
provided the energy as a time, this required a conversion
from seconds to GHz, using the calibration of the laser as
a reference.
IV. SATURATED ABSORPTION RESULTS
Presumably due to imprecise optical alignment,
the complete hyperfine structure of the excited state
of Rb remained unseen. Only the first peak in Figure
3 suggests that the Doppler-broadened peaks contain
more than one spectral feature. For more information
on the observable hyperfine structure in the 5P
excited state of 85,87Rb, visit: http://hubble.physik.unikonstanz.de/jkrueger/thesis/thesis.html.
V. DAVLL MODEL RESULTS
Error Plot (arb. units)
DAVLL plot vs. Energy
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
12
13
14
Energy (arb. units)
15
16
38.6 G
In order to qualitatively understand the effect of
a peak energy change (in this case due to a Zeeman
shift) on the shape of a DAVLL plot, we created a
mathematical model to mirror the effects of shifting
peaks. We approximated each absorption peak as a
gaussian curve, and then visually adjusted the width
and height of each curve until each peak (1-4)
approximately matched the observed spectra. The
DAVLL plot was obtained by subtracting one
gaussian from another, each one offset in opposite
directions about a center peak (determined from the
absorption spectrum). For example:
92.7 G
194.4 G
Figure 5. DAVLL plot for peak 3 (Rb85 F=2) for three
different magnetic field strengths. Zeeman shift, indicated
by peak deviation, is barely observable, but the shape of
the plot clearly changes with increasing magnetic field.
 ( E E)
DAVLL = A  e
2

2
 ( E E)
 Ae
2
2

(2)
where: E is the energy of each peak in the absence of
a magnetic field, A is a normalization constant, ΔE is
the energy shift to model the Zeeman shift, and σ
modifies the width of the gaussian to fit the data.
Thus, each absorption peak had two terms as in Eq. 2.
The full spectrum was obtained by adding all eight
terms together at their relative energy positions.
Peak Separation vs. "B"
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
0
5
10
15
Energy (arb. units)
20
25
Observed
Model
Figure 6. The DAVLL plot model superimposed onto the
38.6 G observed plot. This superposition demonstrates
that DAVLL plots may be reasonably modeled using sums
of gaussian functions.
Due to the interference of the gaussian curves, the
plot of the ΔE vs. B field is nonlinear until ΔE is
sufficiently large. Figure 7 models the DAVLL plot as a
function of systematically increasing ΔE.
1.0
B1
B2
B3
B4
B5
DAVLL Plot
0.5
Peak Separation (GHz)
DAVLL Plot
DAVLL Plot Model
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
Model
Peak
4
0
50
100
150
200
250
Magnetic Field (G)
Figure 8. Peak separation in DAVLL plot vs. increasing
magnetic field. The nonlinearity of the lower portion of
the graph demonstrates the error in assuming that peak
separation is always linearly related to ΔE.
This mathematical model suggests that peak position
accurately relates ΔE to B only for sufficiently high
Zeeman shifts. The precise shift is a function of the width
of the gaussian (in this case determined by Dopplereffects). The model suggests that as ΔE increases above
2σ, the peak separation is proportional to B. Further
analysis might yield an algorithm for determining ΔE for
DAVLL plots below 2σ.
However, due to time
constraints, the following analysis is based only on data
obtained above that limit.
VI. ZEEMAN SHIFT RESULTS
0.0
-0.5
-1.0
0
200
400
600
800
1000
Energy (arb. units)
Figure 7. Gaussian model of Eq. 2 as a function of
increasing ΔE. The five curves are equally spaced in
energy, but the change in energy for each peak as a
function of B is nonlinear for low B.
Our primary objective was to characterize the effect
of an axial magnetic field on the energy levels of the lone
outer shell electron in Rb. Since there were four
absorption peaks in Rb at 780 nm, we should have been
able to obtain four observations of the Zeeman effect,
described by Eq. 1. Unfortunately, peak 1 ( 87Rb F=2)
and peak 2 (85Rb F=3) are so close energetically that their
spectra interfere so as to disallow an accurate
determination of peak separation at any energy (bounded
on the low side by gaussian limitations and the high side
by peak interference). Therefore, we disregarded the
measurements obtained from those peaks. Figure 9
demonstrates the results of ΔE measurements (determined
by peak separation and converted to GHz) vs. ub*B.
ΔE (Zeeman) vs. μB
ΔE (GHz)
0.55
Peak 3,
g=1.1
0.5
0.45
0.4
Peak 4,
g=1.5
0.35
0.3
0.10
0.15
0.20
0.25
0.30
μ*B (GHz)
Figure 9. Zeeman shift versus ub*B. The slope of this
plot represents the gyromagnetic ratio, g, for this
transition.
VII. CONCLUSIONS
The two experiments discussed here demonstrate
several concepts and experimental techniques. First,
saturated absorption provides a means to reduce the
effects of Doppler-broadening on an absorption signal. In
doing so, it is possible to illuminate the hyperfine
structure of the excited state, which often is lost in the
broadened signal.
Second, the dichroic-atomic-vapor-laser-locking
technique provides a mechanism for observing the
varying effects of differentially polarized light an atomic
orbital. Specifically, the absorption of light is dependent
on the conservation of mf in the transition. This work did
not address the role of DAVLL in laser locking (hence the
name), but its most useful purpose is indeed found there.
Third, as a means to measure Zeeman splitting,
DAVLL fails to be worth the hassle due to the limitations
of extrapolating a useable ΔE from the error plot of two
absorption peaks at low energies. It makes more sense to
directly measure the ΔE of each signal directly, rather
than from the difference between the two signals. This
would eliminate the lower limit on data collection.
Fourth, the DAVLL plot can be used to measure ΔE
once ΔE > 2σ.
Fifth, DAVLL plots can be reasonably estimated
using sums of gaussian functions.
Sixth, obtaining a Nobel Laureate to assist with
experimental setup greatly facilitates data collection.
K. Razdan and D.A. Van Baak, “Demonstrating optical
saturation and velocity selection in rubidium vapor,” Am.
J. Phys., 832-836, (1999).
ii
Copied from
http://austin.onu.edu/~jgray/chem342/rubidium.pdf
i
D. Budker, D. Orlando, and V. Yashchuk, “Nonlinear
laser spectroscopy and magneto-optics,” Am. J. Phys.,
584-592, (1998).
iv
J. Kruger, (1998).
v
J. Kruger, (1998).
vi
Thanks to Dr. Eric Cornell, 2001 Nobel Prize Laureate
in Physics.
vii
J. Kruger, (1998).
viii
J. Kruger, (1998).
iii
0.6