Self-Bound Droplets in Two-Component Dilute Bose Gases

Existing in a world in which temperature extremes are limited, it is difficult to envisage systems of high and low temperatures. However, across the world there are experiments capable of cooling matter down to almost absolute zero. Matter begins to behave in many intriguing ways at these temperatures, one example being the Bose-Einstein Condensate (BEC).

All particles possess a wavelength which is intrinsically linked to temperature. At room temperature, this wavelength is negligible and thus within a gas, the particle collisions can be modelled as 'billiard-ball' interactions. Moving into the ultracold regime leads to such wavelengths becoming comparable to the distance between particles. This can be thought of as particles undergoing an 'identity crisis' causing them to act extremely coherently as if in lockstep. This state of matter is a BEC and it is a manifestation of quantum physics with many interesting properties. One such property is superfluidity, in which a fluid possesses no viscosity and hence can theoretically flow forever. The field of ultracold gases is an ever-growing field with many avenues of research from exploring new states of matter through to modelling cosmological mechanisms.

This project will focus on a new state of matter called the quantum droplet. The first prediction of this state came in 2015 with the work of D.S.Petrov, who argued that droplets could be created in two mixed gases of bosons (i.e. atoms). The mechanism behind this would be to force the interaction between the gases to be attractive. However, by causing the interactions between the gases to become dominantly attractive, this would lead to a collapse as there would be no effects to counteract the attraction. The ingenuity of Petrov's work arises from the inclusion of quantum fluctuations.

Quantum fluctuations are present throughout nature, but their effects are often too weak to be detected. In the system explored by Petrov, quantum fluctuations present a repulsive interaction. It was argued that by including quantum fluctuations, the repulsive effects could counter the collapse of the gas mixture. This leads to a stabilised state in equilibrium. The stabilised state would have a large constant density in the centre, with low density tails at the edges, akin to a classical droplet such as a water droplet. Quantum droplets are peculiar objects as they exist in low density gases, yet they can behave as an incompressible fluid.

There has been some experimental and theoretical work looking into quantum droplets, but the field is still young and there is much to explore such as excitations and dynamics. The first quantum droplets in mixtures were created in mixtures of Potassium which were successful but had the drawback of limited lifetimes, thus few time dependent properties were observed. This project will work in conjunction with experimental work at Durham University, attempting to create quantum droplets in mixtures of Caesium and Ytterbium. One major benefit of this mixture will be extended lifetimes and thus it will be possible to model the experimental results.

The techniques employed in this project will be largely numerical and will consist of solving the Gross-Pitaevskii equation - a mainstay in modelling BECs - extended to include the effects of quantum fluctuations. The first goal of this project will be using simulations to aid the direction of the experimentalists to create the droplets. This will include isolating parameter values leading to droplet formation. From there, the project is predicted to work alongside the results of the experiments to compare with known theory.

With the field of quantum droplets being young, there are many properties to be explored and this work will theoretically explore some of these properties. Furthermore, quantum droplets present a system stabilised by quantum fluctuations, a phenomenon so ubiquitous yet often so difficult to detect, making this project both relevant