The last two decades have witnessed huge expansion of the field of ultracold atoms; cutting edge experiments can now not only cool these atoms down to within billionths of a degree of absolute zero, such that their quantum nature becomes apparent, but also apply unprecedented levels of control using magnetic fields and laser light to manipulate the atoms' quantum state. The combination of unprecedented experimental control and the quantum many-body nature of these systems makes them an ideal way to create "quantum simulators": configurable test systems that reproduce complex phenomena for study under controlled conditions. They are also at the forefront of progress towards future quantum sensing and computing technologies. One of the most notable phenomena accessible to these experiments is the Bose-Einstein condensate: a state of matter in which bosonic (integer spin) atoms enter a collective quantum state, becoming a single wave-like entity. These condensates display the remarkable property of superfluidity, flowing indefinitely without resistance. In displaying superfluidity, they are similar to low temperature liquid Helium, which also enters a superfluid state containing a Bose-Einstein condensate, but the atomic condensates have the advantage that they can be experimentally measured and manipulated at a microscopic, quantum level.
At the heart of the so-called dirty boson problem is a simple question: how do interacting bosons behave when we put them in a random disordered environment? This can be investigated by pouring liquid Helium into a porous substance like aerogel, but this system is difficult to study directly on a microscopic footing. Instead, cutting-edge experiments can realise the dirty boson problem can by creating atomic condensates in disordered potentials made using laser light; this can be thought of as putting the bosons in a random hilly landscape. The core of the dirty boson problem is the competition between the bosons' natural tendency to form a condensate at the lowest point in the landscape, and the interactions' tendency to push the bosons further apart. This competition generates a rich equilibrium phase diagram, with normal, superfluid and exotic Bose-glass phases.
However, the out-of-equilibrium dynamics of dirty bosons remain relatively unexplored. As well as being of fundamental theoretical interest, a better understanding of the dynamics of dirty bosons will help optimize future experiments using atomic condensates for quantum sensing or information processing. This research project will address these questions by creating new theoretical and numerical techniques to study the out-of-equilibrium dirty boson problem in atomic condensates. We will investigate what happens dynamically when dirty bosons undergo a phase transition, and what happens when a flow of dirty bosons becomes turbulent.