Light Force Collimation of an Atomic Gallium Beam

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Light Force Collimation of an Atomic Gallium Beam

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.

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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 sodium[1], chromium[2],[3], aluminum[4] and cesium[5]. 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

Ga has two stable isotopes: 69Ga and 71Ga, 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 69Ga 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.

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 full-widths). 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 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 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 (~ ).

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.

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 4p2P3/2  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 laser-induced 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 69Ga 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 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 69Ga. 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 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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