Duncan H.J. O'Dell

Willkommen! Et bienvenue! Welcome! (I'm cabaret, au cabaret, to cabaret!)

I am a theoretical physicist and lead a research group that is broadly interested in quantum dynamics. Our work is motivated by experiments in the fields of ultra-cold atoms, quantum optics and condensed matter physics. One of our favourite systems is a Bose-Einstein condensate (BEC) with dipole-dipole interactions. Dipolar interactions are novel in BECs because they are long-range and anisotropic, in contrast to the short-range s-wave interactions usually considered in these systems. New effects my co-workers and I have predicted in the presence of dipolar interactions include a roton minimum in the Bogoliubov excitation spectrum. We also showed that by irradiating a cloud of atoms with lasers from different directions one can realize a 1/r interatomic potential, a type of electromagnetically-induced gravity, opening the door to doing "astrophysics in the lab".

Another system with long-range interactions is provided by ultra-cold atoms confined in optical cavities which realize cavity-QED. The cavity mediates an infinite range coupling between the atoms. We have studied how such a system relaxes to equilibrium and shown that it undergoes a quantum version of violent relaxation a phenomenon well known in classical gravitationally bound systems. Another nice feature of optical cavities is that the light leaking out of them can be used to continuously and non-destructively monitor the dynamics of the atoms inside. We have used this to propose a method for making sensitive measurements of forces, such as real gravity this time, by monitoring the Bloch oscillations of atoms moving in the joint potential provided the intra-cavity optical field and the external force.

A thread that runs through my research is the phenomenon of quantum catastrophes [1, 2, 3, 4, 5], an endeavour in which I was greatly inspired by the pioneering contributions by Ulf Leonhardt, Michael Berry and Mark Dennis. These are singularities in classical fields (e.g. mean-field theory of many-body systems such as the Gross-Pitaevskii equation, or Maxwell's theory of electromagnetism) that are regularized by quantization, somewhat like Planck's original quantization of the blackbody spectrum to avoid the ultraviolet catastrophe. It turns out that dynamics following a sudden quench (a typical scenario in cold atom experiments) generically leads to such singularities, and, furthermore, the behaviour close to the singularity is universal, taking on one of a set of characteristic shapes that were first described by the mathematician René Thom in his catastrophe theory. Each catastrophe has its own set of scaling exponents (the Arnold and Berry indices) and are an example of universality in quantum dynamics (it is general rule in physics that singularities lead to universality, another well known example being phase transitions).

Catastrophes are in fact an everyday wave phenomenon: in optics they are known as caustics with examples including rainbows, the bright lines on the bottom of swimming pools and in coffee cups on a sunny day, and the twinkling of starlight. They also occur in hydrodynamics in the form of tidal bores and wave blocking. As shown in the figure below, there are three levels of structure in a wave catastrophe: at large scales there is a geometric caustic; zooming down to the wavelength scale one finds an intricate pattern of interference fringes and zooming down further there is a network of nodes that come in vortex-antivortex pairs that organize the interference pattern. The goal of my research on this topic is to study a new fourth scale that appears when the wave is quantized (in optical examples this means including the photon nature of light). We have studied such catastrophes in the dynamics of coupled BECs (bosonic Josephson junctions) and also spin chains where we showed that the light-cone like spreading of correlations that has been seen in many experiments (and is described by the Lieb-Robinson bound) is in fact an example of a catastrophe.

The cusp catastrophe. From left to right: At large scales we see the geometric cusp, familiar as the lines in a coffee cup on bright day. It can be understood using ray theory which predicts a diverging intensity along the cusp. Zooming in to the wavelength scale we find that interference smoothes the singularity and decorates it with a characteristic pattern (the Pearcey function). Zooming in further reveals a network of nodes that occur in vortex-antivortex pairs. Lastly, a quantum catastrophe is discrete (the horizontal axis could be the difference in the number of atoms between two coupled BECs and the vertical axis time).

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