Dilute Quantum Fluids Beyond the Mean-Field

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If we peer deep inside nature to a microscopic level, we find a strange world governed by quantum mechanics where our intuition breaks down. In this fascinating regime, the position of a particle has inherent uncertainty and is perpetually fluctuating. Such quantum fluctuations lie at the heart of a number of physical phenomena, ranging from the van der Waals force to Hawking radiation in black holes, and may provide the ultimate limit to technologies based on quantum effects. However, quantum fluctuations are difficult to observe experimentally and to describe theoretically.Since their realization in 1995, Bose-Einstein condensates (BECs) have provided a unique window through which to view the quantum world. A BEC is a gas of identical atoms cooled down to less than a millionth of a degree above absolute zero. At this point the uncertainty in an individual atom's position becomes greater than the separation between atoms and it is impossible to identify individual atoms. Instead, the gas behaves like a giant wave of matter dominated by quantum mechanics, and displays a range of striking quantum properties such as the ability to interfere with another BEC and the ability to flow without viscosity (superfluidity). In addition, BECs are amenable to a high degree of experimental control (for example, to manipulate and interrogate the system in time and space) and they can be imaged to high resolution. The behaviour of BECs, including the properties above, are captured to a high degree of accuracy by considering just the average behaviour of all the atoms: the so-called "mean-field". Over the years since 1995, a synergy of experiments and theoretical works have established a deep understanding of the quantum mean-field and how it influences the system behaviour. However, in a BEC, quantum fluctuations are small compared to the mean-field, and as such, the merits offered by BECs have not extended to the realm of quantum fluctuations.Enter the quantum liquid droplet. When two BECs co-exist, the mean-field quantum effects from each BEC can be made to cancel each other out, leaving behind the quantum fluctuations as the dominant effect within the system. This causes the system to change from a BEC gas to a liquid-like droplet. But this is far from your conventional liquid droplet: whereas, say, water is hard to compress because the electronic shells of neighbouring atoms refuse to overlap, in the quantum liquid it is because of quantum fluctuations. As such, the quantum droplet owes its existence to intrinsically quantum effects; this makes it a fascinating object to study. Moreover, it provides a platform to study quantum fluctuations, from their microscopic origins to their macroscopic manifestations.We will engineer quantum droplets, for the first time in the UK, using a mixture of caesium and ytterbium BECs; this atomic combination will enable us to exert high levels of control over the liquid. Given that this state has only recently been discovered, there is much to study and learn. We will use our experimental capabilities to push the droplets to their limits. We will map out the regimes for which they are supported, as well as the details of how they form. We will experimentally interrogate them in a range of scenarios, effectively prodding and pushing them, to understand how they respond. We will pay particular attention to effectively 2D and 1D geometries where quantum fluctuations are predicted to be greatly enhanced. Alongside our experiments, we will develop and test theoretical models to describe our observations; this will allow us to address open questions regarding the underlying physics and quantify the precise role of the quantum fluctuations. The findings of our work will be of fundamental importance in deepening our understanding of quantum fluctuations and may motivate applications of quantum droplets such as in precision spectroscopy and deposition.