Photons—the elementary particles of light—very rarely talk to each other which can be both a blessing and a curse. When you’re trying to send an email across the Atlantic, it is a good thing. You don’t have to worry about your email getting mixed up with another message sent through the same optical fibre at the same time. It also helps when describing how light behaves mathematically. But other problems become difficult.
This regime of linear optics is not very interesting for quantum physics. You can still do beautiful quantum experiments but linearity gives you a tight constraint. You can’t build a quantum computer or protect entanglement from losses in a network. Only when photons start being affected by other photons around does the weirdness (and usefulness) of quantum physics appear in full.
How does one make photons talk to each other? The first thing you need is a medium. A photon will not talk to another photon directly. But if a photon talks to an atom and that atom talks to another photon, the second photon might be influenced by the first.
The second thing you need is many photons. Even with atoms around, the effect is usually weak and difficult to see. But if you have many photons, it will be easier to measure their nonlinear interaction. But then we come to a new problem: It will be hard to make all these photons behave quantum mechanically.
We can solve this conundrum by using microwave photons talking to a superconductor. Electrons behave strangely in a superconductor and are much more eager to talk to photons than in normal atoms. But we need microwaves because the photons cannot have large energy. Otherwise, they would destroy the fragile superconductivity.
Working with nonlinear quantum optics presents two problems that a physicist has to solve. The first one is finding out what kinds of intractions one can achieve and how to describe them. We need these to be easy to describe or we can’t make accurate predictions about any experiments. At the same time, they must be interesting and have useful applications. Some nonlinearities can be useful for quantum computing, others for measuring various quantities. It is my goal to understand which tools we have available with superconducting circuits and how best we can put them to a good use.
The second problem is confirming that we have a given nonlinearity and not another. We need to measure all photons precisely to confirm that what happpened to them is what we expected. This becomes challenging when there’s any noise or many photons. To solve this problem, I try to find new ways how to measure the quantum state of these nonlinear microwave fields. One strategy I’m particularly interested in is based on overlap measurements. These are nonlinear transformations which allow us to measure the overlap of our unknown field with another one that we have good control over. I’m trying to work out how best to perform these measurements and what information they can give us.