## Transverse optical patterns

Before we discuss the details of our experimental scheme, it is important to define a few useful terms. We often refer to the patterns that we see in the experiment as "transverse optical patterns." We use the word transverse to specify that the patterns can be seen on a screen or camera whose surface is perpendicular (at a 90° angle) to the direction the light is moving. All of the patterns we see are the result of beams of light shining on a camera so "transverse optical pattern" is the specific term for the pictures we take.

Now that we know more about how a transverse pattern can be seen, we should look at how it is created. When we shine laser beams on atoms, the bright laser light can scatter off the atoms in many interesting ways. Depending on the type of atom and the wavelength (or color) of the light, the scattering can change the direction, wavelength, or polarization of the light. Similar ideas help explain why the sky is blue and why sunglasses are often polarized to reduce glare.

A large number of atom-light interactions are what we call linear. That means that what comes out is linearly related to what you put in. If you shine 10 mW of power onto some atoms and see 2 mW scattered in a new direction, then when you shine 20 mW then you may first expect to see 4 mW scattered in the new direction. The relationship between in and out in this example is: Out = 0.2 * In. This is a linear relationship. There can be different relationships depending on the details of how the light and atoms interact. In some cases, like in a laser, you can get a lot more light out than you put in. As an example, if the amount you get out is the amount you put in raised to some power (Out = Inn, n ≠ 1) then the interaction is said to be nonlinear.

 In rubidium-87 (one of the two natural Rb isotopes), counterpropagating beams (red) induce an instability giving rise to the generation of new light, along a cone (blue). The transverse optical pattern (red ring) can be observed on a screen perpendicular to the pump beams. © Andrew Dawes, 2005

We use rubidium atoms in our experiment because they are known to have several types of nonlinear optical interactions. Specifically, if we use two laser beams pointing in opposite directions and overlapping (shown in the figure as red arrows), then interactions between the laser beams and the atoms generate new light that is emitted along a cone about the original beams (shown in blue). This phenomena is known as a counterpropagating beam instability, where instability refers to the fact that the generated light is due to the amplification of small amounts of light present in the system. Certain conditions must be met for this generation of light to take place and the set of these conditions defines the threshold for the instability, and we see that for well-aligned beams and atoms at the right temperature, there is a specific level of optical power that must be reached before light is generated along the cones.

## Symmetry Breaking

 When the pump beam power is near threshold, the symmetry of the generated light is weakly broken resulting in a transverse pattern containing two spots. This corresponds to two distinct output beams. © Andrew Dawes, 2005

If we use just enough pump light to generate a pattern (that is to say we are operating close to the instability threshold), then we observe a transverse optical pattern consisting of a pair of spots. In our experiment, the orientation of these spots does not change when we turn the pump beams off and on.

The fixed orientation of this pattern suggests the symmetry of the system is slightly broken. Symmetry is the idea that with perfect alignment of the pump beams, our experiment looks the same if we rotate it around the pump beams (red arrows). In this case, we would expect to find beams emitted in pairs but anywhere along the cone of emission. Thus we would expect the orientation of the spots to change upon turning the pump beams off and on.

Of course symmetry is never perfect in the laboratory so even with the two pump beams very well aligned, there can be enough symmetry breaking to give rise to the fixed orientation two-spot pattern. The key principle in our experiment is that we can also break the symmetry in a controlled way by sending another beam through the atoms. This third beam, our "switching" beam, will influence the orientation of the generated two-spot pattern. This is discussed in the Switching section.