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This book introduces the theoretical description and properties of quantum fluids. The focus is on gaseous atomic Bose-Einstein condensates and, to a minor extent, superfluid helium, but the underlying concepts are relevant to other forms of quantum fluids such as polariton and photonic condensates. The book is pitched at the level of advanced undergraduates and early postgraduate students, aiming to provide the reader with the knowledge and skills to develop their own research project on quantum fluids. Indeed, the content for this book grew from introductory notes provided to our own research students. It is assumed that the reader has prior knowledge of undergraduate mathematics and/or physics; otherwise, the concepts are introduced from scratch, often with references for directed further reading.
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The past decade has seen atomic Bose-Einstein condensates emerge as a promising prototype system to explore the quantum mechanical form of turbulence, buoyed by a powerful experimental toolbox to control and manipulate the fluid, and the amenity to describe the system from first-principles. This article presents an overview of quantum turbulence in atomic condensates, from its history and fundamental motivations, its characteristics and key results to date, and finally to some promising future directions.
We study the influence of atomic interactions on quantum simulations in momentum-space lattices (MSLs), where driven atomic transitions between discrete momentum states mimic transport between sites of a synthetic lattice. Low energy atomic collisions, which are short ranged in real space, relate to nearly infinite-ranged interactions in momentum space. However, the distinguishability of the discrete momentum states coupled in MSLs gives rise to an added exchange energy between condensate atoms in different momentum orders, relating to an effectively attractive, finite-ranged interaction in momentum space. We explore the types of phenomena that can result from this interaction, including the formation of chiral self-bound states in topological MSLs. We also discuss the prospects for creating squeezed states in momentum-space double wells.
Particles of low velocity, travelling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force, are self-consistently coupled with the Gross-Pitaevskii equation. We use this model to demonstrate the existence of an effective superfluid-mediated attractive interaction between the particles; and we study numerically the collisional dynamics of particles as a function of their incident kinetic energy and the length-scale of the repulsive force. We find a transition from almost elastic to completely inelastic (sticking) collisions as the parameters are tuned. We find that aggregation and clustering result from this sticking transition in multi-particle systems.
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum, and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.
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