# Research topics

# Dipolar quantum gases

Cooling down matter to nanokelvin range (billionths of a degree above absolute zero) results in some spectacular physics. Many historical experiments have been done with dilute gases of short-range contact-interacting atoms such as rubidium or lithium, yielding exotic forms of matter, such as Bose-Einstein condensation (BEC) and superfluidity.

Strongly magnetic atoms, such as erbium and dysprosium, have now also been used in ultracold matter experiments. These atoms, which behave like tiny magnets, have additional long-range anisotropic interactions and can be collectively polarized by an external magnetic field.

Under the right conditions, magnetic superfluids act like a quantum-mechanical ferrofluid, and can also form a supersolid phase of matter. A supersolid paradoxically combines the crystal structure of a typical solid with the frictionless flow of a superfluid.

Dipolar gases can be also combined (with dipolar or non-dipolar species) to form mixtures. These mixtures can also form multi-component supersolids like those to the left.

# Non-equilibrium quantum systems

How does information propagate in quantum systems? Is there a speed limit? What kinds of universality exist in dynamics of many-particle systems? How does temperature fit into all this? These are the broad and fundamental questions I try to answer in some of my research.

The time-evolution history of non-equilibrium systems can be divided into multiple steps. At early times, systems are governed by their chaotic or non-chaotic behaviour. Using measures such as the "out-of-time-ordered correlator", we can measure quantum-mechanical analogues to classical chaos such as the Lyapunov exponent.

Before thermalization, out-of-equilibrium systems may show a kind of universality at "non-thermal fixed points" -- where drastically different systems, at least from a microscopic perspective, can behave the same way.

As systems relax toward equilibrium, they tend to thermalize, and so the concept of temperature emerges. Systems near equilibrium tend to have observables which obey random matrix theory.

# Caustics in quantum mechanics

Caustics are regions where the underlying classical theory (usually described by rays) become singular. In light, these become bright lines that might be familiar in a coffee cup, or at the bottom of a swimming pool.

Zooming in to the scale of wave mechanics, these singularities become smoothed out by interference, and results in beautiful diffraction patterns like the one shown on the right.

There is an even smaller scale wherein lies the realm of quantum mechanics. At this level, the smoothness of diffraction patterns is broken by the discretization of nature itself. Examples of these quantum caustics can be seen in dynamics of quenched Bose-Einstein condensates (left), or as "quantum light cones" in spin chains.

Throughout our research, we use the mathematics of catastrophe theory to categorize these caustics and to describe their universal features.