Laser cooling of an atomic gallium beam
S. J. Rehse, K. M. Bockel, and S. A. Lee
Department of Physics, Colorado State University, Fort Collins, CO 80523
We have laser cooled a gallium atomic beam in one dimension using the lin 
lin polarization gradient technique.
Operating on the cycling 4p2P3/2(F=3) 
4d2D5/2(F=4) hyperfine transition at 294.45 nm, the full-angle divergence of the
beam was reduced to 0.35 mrad, corresponding to a transverse velocity of 13 cm/s,
about one-half the Doppler cooling limit. The dependence of the cooling efficiency
on the laser detuning, interaction length and power was investigated. Optical
pumping of the atoms out of the 4p2P3/2(F=3) state by the cooling laser was
observed.
Repumping schemes were investigated and found to successfully
repopulate the cooled F=3 hyperfine state.
PACS numbers:
I.
Introduction
Laser standing waves have been used to focus neutral atoms into nano-scale
features during their deposition onto a substrate. This direct atom lithographic scheme
has been demonstrated in sodium1, chromium2,3, aluminum4 and cesium5. In order to
achieve the smallest feature size in direct laser focusing, the incident atomic beam must
be collimated transversely to a very high degree, typically less than 1 mrad. 6,7 Laser
cooling was used to provide a high degree of collimation without a significant loss of
atom flux. In this technique, two counter-propagating laser beams intersect the atom
beam at right angles to generate a one dimensional optical molasses.8,9 If the polarization
of the optical molasses varies across the path of the atoms, an additional force is exerted
on the atoms. This force, termed the polarization gradient force, can cool the atoms to a
lower level than the optical molasses alone.10,11 Through interactions with the laser
beams, the atoms experience these two forces which act together to cool the atoms to
below the Doppler limit.
In this paper, we report on the one-dimensional laser cooling of a Ga atomic beam
with the lin  lin polarization configuration. Gallium is particularly interesting because it
is a key building block of modern III-V semiconductor diode lasers. The ability to
directly focus Ga with laser light during molecular beam epitaxy (MBE) growth of III-V
heterostructures offers a unique method for forming periodic regions of high and low Ga
density within the growth plane.12 Thus, the technique has the potential for forming large
numbers of quantum wires and quantum dots in a controlled manner.
II.
Gallium
2
Ga has two stable isotopes:
69
Ga and
71
Ga, with an isotopic ratio of 60.4% to
39.6%. Both isotopes have nuclear spin I = 3/2, yielding a rich hyperfine structure. 13
Fig. 1 is an energy level diagram showing the lower-lying states of Ga. A cycling
transition suitable for laser cooling is the 4p2P3/2(F=3)  4d2D5/2(F=4) hyperfine
transition at 294.45 nm, with a natural linewidth /2 = 25 MHz. The frequency splitting
between 69Ga and 71Ga for this hyperfine transition is 81.4 MHz, thus only 69Ga is cooled
efficiently. The Doppler cooling limit is TD = 600K, corresponding to an rms velocity
of 27 cm/s in one dimension.
The lower state of the transition, the 4p2P3/2 state, is metastable and lies 0.103 eV
above the 4p2P1/2 ground state. With an oven operating around 1300º C and taking the
isotopic ratio into consideration, 13% of the atoms in a thermal beam will be
69
Ga in the
4p2P3/2(F=3) state.
III.
Experimental arrangement
A schematic of the experimental arrangement is shown in Fig. 2. A beam of Ga
atoms was generated by a resistively heated effusive oven source operating near 1300º C.
The most probable (longitudinal) speed of the atom beam was 750 m/s. An aperture 0.8
mm x 1.0 mm pre-collimated the beam to 6.2 mrad. This corresponded to a nominal
transverse velocity of 2.3 m/s, about 90x the Doppler cooling limit. The Ga atoms
interacted with the cooling laser and traveled 34 cm where they were illuminated by a
weak probe laser beam to measure the amount of collimation.
The laser-induced
fluorescence from the probe laser was imaged onto a liquid nitrogen cooled UV sensitive
CCD camera.
3
Both the cooling beam and the probe beam were derived from a frequency
doubled cw ring dye laser. A BBO crystal in an external power enhancement cavity
produced the tunable UV light required for this experiment.14 In this configuration, the
probe laser and the cooling laser were always detuned from resonance by the same
amount. The cooling laser beam had a 1 mm x 5.5 mm elliptical cross-section (1/e2 fullwidths). It was linearly polarized and passed through a quarter-wave plate on the far side
of the cooling region prior to retroreflection.
These orthogonally polarized beams
generated a lin  lin polarization gradient in the cooling region. Typical powers in the
cooling laser ranged from 40 mW to 70 mW. The probe laser, also linearly polarized,
was circular in cross section with a 1/e2 diameter of 1.6 mm and was tens of W of
power. The UV laser was frequency stabilized by offset locking the fundamental dye
laser to a nearby iodine hyperfine transition in a saturated absorption apparatus. 14 This
apparatus used a double-passed acousto-optic modulator (AOM) to shift the laser
frequency into resonance with iodine. Changing the drive frequency to the AOM allowed
up to 40 MHz of UV tuning while the laser remained locked.
It should be noted that for an uncooled atom beam the CCD images did not
reproduce the true geometrical beam size. The spatial information was convoluted with
the Doppler shift due to the transverse velocity and the detuning of the probe laser. At
zero detuning, atoms near the central portion of the beam contributed more significantly
to the fluorescence signal than the atoms in the wings, and the CCD image width was
narrower than the geometrical beam width. As the red detuning of the probe laser
increased, the CCD images became asymmetric and broadened. However, when the
4
atoms were cooled and the Doppler frequency shift is negligible, all the atoms responded
equally to the probe and the CCD images represented the actual geometrical sizes.
To determine the divergence and the size of the un-cooled Ga beam, the atoms
were deposited onto glass slides at various distances along the beam axis and the
deposited spots were measured with an optical microscope. In the horizontal dimension,
the full angle divergence was measured to be 6.2  0.1 mrad. The atom beam full width at
half maximum (FWHM) was found to be 1.79  0.03 mm at the center of the cooling
laser region and 3.91  0.06 mm at the center of the probe laser region. The measured
results were in full agreement with a computer simulation based on the configuration of
the oven and aperture geometry. The simulation also reproduced the CCD observed
lineshapes and asymmetry with detuning of the uncooled atom beam, as discussed above.
IV.
Collimation results
The effect of laser cooling is presented in Figs. 3 and 4. CCD images of the atom
beam illuminated by the probe laser are shown. In the fluorescence images, the atoms
traveled from top to bottom and the probe laser illuminated the atoms from left to right,
as shown in Fig. 3(c). To the right of the CCD images are intensity profiles taken
through the middle of the fluorescence images. In Fig. 3(a) the cooling laser was on and
the atom beam was collimated. This cooling was done with 68 mW of power (I/I0 =
13.7) in the cooling laser and a detuning of –20 MHz. The observed image was a real
measurement of the spatial distribution of the atoms in the beam. In Fig. 3(b) the cooling
laser was off and the beam was uncollimated. The asymmetry in the fluorescence image
of the uncooled beam due to the probe detuning is evident. The measured FWHM of the
cooled atom beam was 1.800.08 mm. The noise in the CCD image limited the accuracy
5
of the measurement. Recall that 1.79 mm was the atom beam’s horizontal dimension at
the center of the cooling region. In the limit of zero divergence of the atom beam, this
would be the size of the atom beam in the probed image. This size is denoted as the
geometrical limit, and is indicated by the horizontal mark in each case. Figure 3 indicates
very little divergence of the atom beam occurred over the 342 mm flight path from the
cooling region to the probe region.
Fig. 4 illustrates the effect of polarization gradient cooling. The cooling laser
power was 52mW (I/I0 = 10.5) and was detuned –12 MHz from resonance. The top
image, Fig. 4(a), shows the uncollimated, normally diverging atom beam. Fig. 4(b)
shows the atom beam with the cooling laser on, but the quarter-waveplate removed. This
cooling was from the Doppler molasses only. Fig. 4(c) shows the atom beam cooled with
the lin  lin polarization gradient configuration. The atom beam was more collimated
and brighter on axis than the Doppler molasses cooled beam. This was direct evidence of
the polarization gradient technique extending the cooling into the sub-Doppler regime.
The cooling efficiency as a function of detuning was investigated. The detuning
of the laser was accomplished by manually changing the drive frequency of the double
pass AOM in the saturated absorption apparatus. Since the Ga transition in the atomic
beam was typically 35 MHz wide, the setting of the zero detuning had an uncertainty of ~
2 MHz. The results of cooling vs. detuning are shown in Fig. 5. The cooling laser power
was 68 mW. The collimation improved with laser detuning down to approximately -14
MHz. Afterwards, the collimation was relatively independent of the detuning up to -24
MHz (~ ).
6
Sub-Doppler cooling was achieved for detunings greater than -12 MHz (~/2).
Averaging over the results for detunings from -14 to -24 MHz, the cooled atom beam had
a FWHM divergence of 0.35 mrad (full-angle), corresponding to a nominal transverse
velocity of 13 cm/s, about half of the Doppler cooling limit. The one-dimensional
kinetic energy of the atoms was reduced to ~6 neV. This should be sufficient for laser
standing wave focusing of neutral atoms.
The cooling efficiency as a function of interaction distance was investigated. by
translating a razor blade through the cooling laser. Fig. 6(a) shows the results for two
different detunings. Because the cooling laser was Gaussian in intensity, moving the
razor 1 mm at the edge of the beam had less effect than moving it 1 mm at the center of
the beam. Thus this graph actually contains information about the cooling dependence on
the laser power. The cooling efficiency as a function of the total power in the truncated
laser beam is shown in Fig. 6(b). For the smaller detuning (-12 MHz) only 50 mW was
needed before the collimation of the beam ceased at a beam FWHM of 2.05 mm. For a
larger detuning (-18 MHz) it required at least 70 mW to cool the atoms all the way to the
minimum (1.79 mm).
V.
Optical pumping
From the fluorescence images it was observed that the on-axis intensity of the
cooled beam was smaller than it was in the uncooled beam. As the atom/cooling laser
interaction length increased, the total fluorescence decreased in a linear fashion. In the
case of best cooling as in Fig. 6 (= -18 MHz, 70 mW), the total fluorescence had
decreased by 43% after the atoms had traversed the full width of the cooling laser beam.
7
The decrease in fluorescence indicated a loss of atoms from the 4p2P3/2 (F=3)
cooling state. This is attributed to optical pumping by the cooling laser. The F=3  3
transition was only 12.5  to the red of the F=3  4 cooling transition. Off resonant
excitation and subsequent decay to the F=2 lower state resulted in the loss of the cooled
atoms. It should be noted that the F=21 transition was ~2 from the cooling transition
and was also pumped. Thus the net effect of the optical pumping was to transfer atoms
from the F=3 cooled state to the F=1,0 lower states.
To study this pumping, the CCD camera was replaced by a photomultiplier tube
and the UV probe laser was replaced by a 417 nm diode laser tuned to the 4p 2P3/2 
5s2S1/2 transition. This was a better transition for studying the effects of optical pumping
because there were fewer hyperfine lines and they overlapped less. Fig. 7(a) is the laserinduced fluorescence spectrum obtained by 417 nm excitation of the Ga atoms with the
cooling laser upstream turned on and off. The power in the 417 nm beam was 0.6 mW
and the power in the UV cooling beam was 45 mW. Fig. 7(b) is a calculated spectrum
for both isotopes to assist in identifying the transitions. The loss of atoms from the
4p2P3/2(F=3) state to the F=0,1 states was observed by the decrease in intensity of the 3
 2 transition and the accompanying increase in the other transitions.
Two repumping schemes were investigated. In the first case, a repumping laser
tuned to the 4p2P3/2(F=2)  4d2D5/2(F=3) of
69
Ga was used. A portion of the cooling
laser was picked off and frequency shifted +334 MHz by two AOMs in tandem to be in
resonance with the F=23 transition.
The repump beam was overlapped with the
cooling laser beam to interact with the atoms. Laser induced-fluorescence spectra were
taken downstream with the 417 nm laser operating at 0.4 mW. The effect of repumping
8
was shown in Fig. 8. Figure 8(a) was taken with only the cooling laser and no repump.
Fig. 8(b) was obtained when both the cooling and repump lasers were on. The cooing
laser was detuned by –14 MHz and had 20.2 mW of power. The repump laser power was
4.5 mW. It is seen that the repump laser was able to transfer almost all of the F=2 atoms
to the F=3 state. The dependence of the repumping efficiency on power is shown in Fig.
9. Even at very low powers (<1 mW) the repump laser was capable of putting a
significant number of atoms into the F=3 state.
In the presence of a very powerful cooling beam, depopulation of the F=2 state by
the cooling laser to the F=1,0 states (as mentioned above) might disrupt this repumping
scheme. We therefore investigated an alternate scheme that involved pumping the atoms
from the F=0 and F=1 states. The UV repump beam was shifted ~ 400 MHz to the blue
of the cooling transition.
This allowed pumping on both the F=01 and F=12
transitions (separated by only 20 MHz) in
69
Ga.
Several repump detunings were
investigated from +380 to +420 MHz. This scheme was able to increase the population
of the F=3 state but was not as effective as pumping directly on the F=2 F=3 transition.
VI.
Summary
Using the cycling 4p2P3/2(F=3)  4d2D5/2(F=4) hyperfine transition at 294.45 nm,
a Ga atomic beam was collimated to 0.35 mrad (full-angle). The cooling laser was
operated in the lin  lin polarization gradient configuration with at least 60 mW of power
and a detuning between –12 and -24 MHz. The transverse velocity of the atoms was
reduced to ~13 cm/s, about half of the Doppler cooling limit.
The dependence on the cooling laser detuning, interaction length and power was
studied and the pumping of the cooled atoms out of the desired 2P3/2(F=3) state by the
9
cooling laser was observed. To address this depopulation, two repumping schemes
utilizing an additional frequency shifted laser beam at 295 nm were investigated and were
found to be effective at increasing the population of the 2P3/2(F=3) state in the presence of
the cooling laser.
VII. ACKNOWLEDGEMENTS
The authors wish to thank Carmen Menoni for lending us the CCD camera, and
Henry Cook, III and Jason Forsyth for construction of the imaging apparatus. This
research was supported by the National Science Foundation under grants PHY-9732489
and PHY-0140216.
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