Reflected Beam Distribution vs Atomic Mirror Angle

By increasing the incidence angle of the atomic beam on the atomic mirror, the

reflected beam was moved away from the unobstructed beam position. There were two competing processes controlling the shape of the reflected beam.

• The subtended width of the mirror presented to the atomic beam was increased as mirror angle increased. This served to effectively increase the width o f this collimating component.

• The perpendicular atomic velocity incident upon the atomic mirror was increased as the mirror angle increased. The reflected atoms thus reached a higher potential in the atomic mirror before being reflected. Since the atomic mirror was generated using a Gaussian laser beam, the effective reflection area decreased as the regions in the Gaussian wings became unable to provide the potential required for reflection. The reflected flux therefore decreased as the incidence angle increased.

The intensity o f the reflected beam was found to be dominated by the second process. As incidence angle increased, the reflected beam flux became smaller and slightly

Chapter 4 Results and Discussion

broader. In addition, the reflected beam profile became asymmetrical, with greater flux on the low angle side o f the beam. This effect was examined further by Snoad (1993).

A number o f reflected beam profiles are presented in figure 4.2. As with figure 4.1, laser 2 was tuned to maximise the fluoresence signal from the unobstructed atomic beam (A2=+800MHz => va= 1050ms"1) and laser 1 was tuned to A1=+4GHz. The saturation parameter o f the evanescent wave was 3.8x104.

The vertical scale o f figure 4.2 has been selected to present the reflected beam shape. The unobstructed beam (at Omrad) peaks off the scale, and the vertical lines are an artifact o f this. Note the wings on the unobstructed beam (present in figure 4.1) are not present in figure 4.2. The results presented in this figure were observed before the degradation o f the oven pinhole.

In Figure 4.2, the traces A through D represent spatial scans which show the position and shape o f the reflected beam as the atomic mirror is rotated. The atomic mirror angle (or incidence angles of the atomic beam) for the four traces are: [A] 0.3 mrad; [B] 0.6mrad; [C] 1.8mrad; [D] 2.3mrad. Comparison o f the four traces indicates that for greater angles o f incidence, the reflected peaks do indeed become broader and smaller.

As the reflection angle increases the reflected beam profiles become asymmetric, with greater reflected flux at lower deflection angles. One explanation for this asymmetry is presented here. It is understood that the reflected flux will be reduced as incidence angle increases. Within the incident atomic beam, there is a range o f incidence angles upon the atomic mirror due to the finite size o f the beam source. Those atoms incident on the atomic mirror at shallower angles are reflected more effectively than those incident at steep angles. There are therefore more reflected atoms at reflection angles on the low deflection angle side o f the reflected beam profile.

Chapter 4 Results and Discussion

A more complete explanation of this phenomenon was developed by Nigel Snoad (1993). Snoad developed a comprehensive model using a series of simulated atomic trajectories reflected from gaussian shaped evanescent spots. He found that atoms could be reflected from a single gaussian spot at steeper angles than incidence, and that the reflection was quite diffuse. Atoms reflected from a series of adjacent spots, while being turned in their trajectory a little by each spot, were on average reflected according to the law of reflection. For a series of spots, the incidence angle equalled the reflection angle.

The reason for the asymmetry in the reflection from a single gaussian spot may be determined by considering the spatial spread of incident atoms across the spot profile (peak at x=0). There will be some atoms whose closest point to the quartz block (vy=0) is at the centre of the gaussian beam (x=0). Those atoms will ride up the potential hill with vy and vx both reducing. As they move away from the quartz block, they will roll back down the potential hill, so that the final vx remains unchanged, while vy has been reversed. The symmetry’ of this trajectory about x=0 means that these atoms obey the law of reflection.

However, some atoms which skim across the top of the gaussian spot (x>0) will not encounter sufficient intensity to be deflected significantly and may be lost.

Alternatively, those striking the gaussian spot at x<0 will continue to lose vx after the point of reflection (vy = 0) as they move to a more intense part of the gaussian spot. These atoms continue to climb the potential hill, reducing in vx even as they move away from the quartz block in the y direction. The reduction in the final vx will thus lead to an increased output angle, thereby creating an asymmetric reflected beam with a high angle tail.

The evanescent standing wave mirror in this experiment is in fact a series of ~33 gaussian spots arising from the multiple internal reflections in the quartz block (3.3.2). Snoad demonstrated that the presence of multiple spots reduce the asymmetry in the reflected beam, due to the x<0 trajectories being shadowed by adjacent spots.

Chapter 4 Results and Discussion

However, at high incident angles, this shadowing is less pronounced, leading again to an increased asymmetry. The spreading of trajectories in the high angle tail means that the apparent maximum in the reflection peak is shifted to lower angles. This result was shown in both Snoad’s simulations and in the experimental results outlined in the next section.

Omrad

Figure 4.2 : A series of reflected atomic beams. Incidence angles were: [A] 0.3mrad, [B] 0.6 mrad, [C]

1.8 mrad, [D] 2.3 mrad.