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Dipolar Droplets in Quantum Ferrofluids

Periodic Reporting for period 1 - DDQF (Dipolar Droplets in Quantum Ferrofluids)

Reporting period: 2018-10-01 to 2020-09-30

Cooled to a few billionths of a degree above absolute zero, Bose-Einstein condensates (BECs) are some of the cleanest, most flexible, many-body quantum systems available. They have been used to answer fundamental questions for a large variety of physical phenomena with remarkable clarity, as well as the discovery of new physics. The field is currently in the midst of a revolution, thanks to the development of key technologies such as the ability to create BECs of rare-earth elements, producing highly-magnetic quantum ferrofluids. Recently, in a dramatic turn of events, an experiment by the Pfau group revealed the discovery of an unforeseen phase of matter: self-bound dipolar droplets. These were formed by the stabilisation of a collapsing quantum ferrofluid, with around 1000 atoms per droplet. They were subsequently demonstrated to be stabilised by quantum fluctuations.

Our project studied the exciting new physics resulting from dipolar interactions and quantum fluctuations, with a particular emphasis on the three most intriguing and timely topics: supersolidty, roton excitations, and quantum droplets. The three main objectives were:

To realise the long-sought supersolid

A seemingly-paradoxical phase of matter, the supersolid was predicted more than 50 years ago to simultaneously exhibit global superfluidity and crystalline order. However a genuine supersolid has remained elusive until now. We developed the theoretical tools required to guide and confirm the experimental realisation of the supersolid, and finally achieved this in an exciting collaboration with the Modugno experimental group, resulting in a joint publication in Physical Review Letters. We realised supersolidity by triggering a roton instability of a dipolar BEC, causing the initially smooth density to break up into overlapping superfluid droplets.

To deepen our understanding of the novel dipolar roton

The concept of the roton originally arose in the middle of last century from studies of liquid helium, for which the excitation energy was found to exhibit a local minimum at finite momentum. Much later, in 2003, it was predicted that analogous rotons should exist for weakly interacting dipolar BECs, but this proved highly elusive until very recent experiments led the Ferlaino group confirmed their existence. The presence of roton excitations is expected to radically modify the physics of Bose-Einstein condensates. We developed a novel, practical method to experimentally probe the roton-maxon spectrum by using a weak perturbing lattice. If the lattice is suddenly removed then the ensuing time-dependent density oscillations will reveal telltale signatures of the roton excitations. We believe that our method will also be applicable more broadly for non-dipolar quantum gases.

More recently, we developed novel numerical methods, describing important quantum effects in two-component dipolar BECs. Using these methods we predicted that, remarkably, self-bound droplets can be constructed from ultra-dilute liquids that strongly repel one another, but which are bound together via long-range magnetic interactions to form a droplet molecule. This work was recently accepted in the journal Physical Review Letters. We expect our work to also open many doors to study roton physics, the creation of bulk supersolid phases, and the study of quantum impurities in ideal settings.

To develop theoretical methods to study dipolar droplets beyond the local-density approximation.

An important part of this project has been to fundamentally improve the theoretical description of ultra-dilute quantum droplets and supersolids. This is important not only for quantitative descriptions, but also for a qualitative one in many situations, such as for small droplets or low dimensions. During this project we developed numerous theoretical descriptions, including theories that go beyond the local-density approximation, and this continues today as ongoing collaboration between Professor Santos and Assistant Professor Bisset.
Summary of work performed, results and outcomes:

In order to realise the long-sought supersolid phase, Bisset developed novel finite temperature theory and computational codes, leading to the joint theory-experiment collaboration: Phys. Rev. Lett. 122, 130405 (2019). Bisset also used his computational codes for another collaboration resulting in a publication studying vortex dynamics and instability in self-bound dipolar droplets: Phys. Rev. A 98, 063620 (2018).

To shed light on the newly confirmed roton-maxon spectrucm, we developed a novel theoretical description of two-component dipolar BECs. Importantly, this theory includes a consistent theoretical description of the quantum fluctuations for such systems. This work was recently accepted in the journal Physical Review Letters. We also developed a novel method for studying rotonic dispersion relations in dipolar Bose-Einstein condensates, based on the application of a weak perturbation, resulting in the publication: Phys. Rev. A 100, 013620 (2019).

We developed theoretical descriptions, based on the Hugenholtz Pines approach, that allow us to study quantum fluctuations without making the local density approximation. We expect this to be important in certain regimes, such as for small droplets and for BECs deep in the roton regime. This work forms the basis of an ongoing collaboration.

The Individual Fellowship has been instrumental for the development of Assistant Professor Bisset's research career, and for this he is extremely grateful. He was recently shortlisted for five permanent or tenure-track positions, and subsequently offered two of these. Regarding dissemination, all published papers are also freely available on the open access preprint server The knowledge exchange between Bisset and the University of Hannover has very much been a two-way process, facilitated by regular seminars, scientific discussions, as well as direct and ongoing collaborations. Bisset has worked to broadly disseminate the results of the Individual Fellowship by attending international conferences and visiting six Universities. The results of the action have been spread widely in the international media to both specialists and nonspecialists.
One of the most prominent achievements of the action was to provide direct theoretical support that led to the experimental creation and verification of the long-sought supersolid phase. This was enabled by our development of novel theoretical descriptions of the finite-temperature effects in dipolar Bose-Einstein condensates. Our simulations accurately modeled the dynamics of the roton instability, demonstrating that quantum fluctuations can stabilise the ensuing density modulations, forming a crystal of linked droplets with a globally interconnected superfluid.

We also developed theoretical methods to accurately describe for the first time important quantum effects in two-component dipolar BECs. In addition to predicting a novel phase of matter - a self-bound droplet molecule where two quantum gases are strongly immiscible while simultaneously binding one other via long-range magnetic interactions - we believe our results will open numerous doors for studies of quantum fluctuations, impurity physics, and for realising bulk supersolids.
Simulations showing the formation of the novel supersolid phase.
Phase diagram predicting the parameter region for the self-bound droplet molecule.