Written by Angela Foerster and Jon Links.
Our research started a long way from Device and Materials Engineering, as a project in Quantum Integrability. This is a field within Mathematical Physics, where researchers study quantum models offering a level of mathematical tractability. A rich development of this subject over many decades has led to the construction of infinitely-many integrable quantum systems. Within this class, there are some fundamental questions to consider such as
Which systems can be physically realised?
What are the effects of breaking the integrability?
In some instances the special mathematical properties of an integrable model translate to special physical properties, which is the case for the quantum Newton’s cradle. On the other hand, especially in statistical systems, the notion of a "universality class" is one in which many models share common features. An integrable model which can be thoroughly analysed serves as a representative to understand the physical properties of a whole collection of models.
The two questions above were foremost in our minds while Jon was visiting Brazil in 2016. Leandro, Arlei, Angela, and Jon had completed a manuscript on the construction of integrable multi-well tunneling models. Karin had commenced as a research student at this stage, and she began numerical calculations for the three-well case. We were aware that a three-well system bears resemblance to a transistor, and we considered this to be a promising place to start.
The investigations led to the discovery that, for particular parameter values, near-perfect harmonic tunneling oscillations occurred in the system. We studied one form of integrability breaking and, contrary to our expectations, this did not destroy the oscillations. It simply affected the period and amplitude. Moreover, these were quantities that we could analytically calculate and compare with the numerical simulations. The close agreement was beyond anything we imagined.
But it was possible that the model was not physical, and we should not become too excited. To obtain an integrable system required particular long-range interactions, and it was not clear to us how this could be achieved. In time, we discovered that it was feasible to do so through dipole interactions, and the architecture for realising such a system with cold atoms was already in the literature. However, the interaction that we used to break the integrability did not fit with this set-up.
We had to break another egg before we could begin to cook.
Through further investigations, and discussions with laser experts, we discovered that displacing the focus of a laser in the configuration implemented a different form of integrability breaking. We re-did our calculations and simulations to find that harmonic oscillations were still present in this setting, and we could still predict the period and amplitude. In this manner we had uncovered a viable means to physically control the oscillations. By the end, we had designed an atomtronic switch.
Jon returned to visit Brazil in 2018. The photo below was taken the day before we submitted the version which was provisionally accepted for publication. The article appears in Communications Physics.