Theory - Optical Pumping
Last updated
Last updated
Our goal is to get all of our atoms into a specific state. This is because atoms are extremely complicated, as we learned a few weeks ago! We can significantly simplify our problems by forcing our atoms into a specific state (or set of states) to accomplish whatever goal we have in mind. As you might expected, getting 100% of our atoms into the desired state is impossible. But we should try to get as many as possible into the right state!
Thankfully, through the process of optical pumping, we can simplify our problem by transferring a sizeable fraction of our population to the states of interest. Optical pumping relies on the use of light to manipulate the internal degrees of freedom of our atoms. The power of this procedure in 1966. The idea relies heavily on selection rules. When the atoms interact with photons of a certain polarization, they must satisfy certain rules to satisfy conservation of energy and conservation of momentum. This is why we don’t expect an atom in a certain excited state to randomly fall into thousands of different states.
More practically, our experiment relies on a cooling cycle that is usually between two states defined by and By applying circularly polarized light, atoms starting in the states are able to be excited to a state with . Once the atom is in this excited state, it can either decay back to it’s original state with , or decay to a lower energy state with hyperfine number . This process can be continuously looped until, via absorption and decay, the atoms are constrained to an effective two-level system.
Figure of pumping schemes between hyperfine states (from Foot chapter 7).
Figure of pumping schemes between hyperfine states (from UMich Notes).
We now have a way to reach our desired state! However, you might be raising some eyebrows. This process might seem too perfect. Remember that atoms are complicated! In the process of optically pumping to our desired states, some of our atoms might veer off of our desired path.
Raman Scattering is a process in which the atom will inelastically scatter photons. The atoms are hit by an incident photon, leading them to advance into a higher energy state. Once here, the atom will eventually relax down to a lower energy state. However, this ending state does not have to be the same state we started in. In this case, the atom now ends in a different state and will release a photon of a different wavelength. Practically, this means that there exists a process that can take us to a “random” state not in our cooling cycle.
We now have a new problem of atoms ending up in states that are blind to our pumping light. We sometimes call these states dark because they cannot be excited by the pumping light we are using. If we did nothing about this, we would lose a large fraction of our atoms simply to getting stuck in the wrong states!
We can fix this through a process known as repumping. From the dark state, we can isolate a path that can excite the atom back within the pumping cycle. While we don’t repump the state exactly into a state in our pumping transition, we repump our atoms into a state that will decay back into the ground state of the cooling cycle.
Foot Chapter 9
(Umich)
