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arXiv:1510.09013 · Physical Review A

Crystallization of a dilute atomic dipolar condensate

R. N. Bisset, P. B. Blakie

Published Dec 29, 2015• 60 citations
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Abstract

We present a theory that explains the experimentally observed crystallization of a dilute dysprosium condensate into a lattice of droplets. The key ingredient of our theory is a conservative three-body interaction which stabilizes the droplets against collapse to high-density spikes. Our theory reproduces the experimental observations, and provides insight into the many-body properties of the droplet phase. Notably, we show that it is unlikely that a supersolid was obtained in experiments, however, our results suggest a strategy to realize this phase.

DOI
10.1103/physreva.92.061603

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We obtain the phase diagram for a harmonically trapped dilute dipolar condensate with a short-ranged conservative three-body interaction. We show that this system supports two distinct fluid states: a usual condensate state and a self-cohering droplet state. We develop a simple model to quantify the energetics of these states, which we verify with full numerical calculations. Based on our simple model we develop a phase diagram showing that there is a first-order phase transition between the states. Using dynamical simulations we explore the phase transition dynamics, revealing that the droplet crystal observed in previous work is an excited state that arises from heating as the system crosses the phase transition. Utilizing our phase diagram we show that it is feasible to produce a single droplet by dynamically adjusting the confining potential.
This habilitation thesis pertains to the theoretical and computational investigation of dilute dipolar Bose-Einstein condensates in the bulk, where atoms interact through both short-range and dipole-dipole interactions. Twelve papers are summarized that were published over the period from 2015 to 2024, with four based on theory-experiment collaborations, and the remaining eight papers being purely theoretical. The papers are grouped thematically into three chapters: the first focuses on quantum droplets, which are dilute liquids resulting from a balance between attractive mean-field interactions and beyond-mean-field quantum fluctuations; the second pertains to the exploration and realization of the long-sought supersolid phase of matter, which simultaneously exhibits properties of both a solid and a superuid; and the third addresses binary supersolids in two-component dipolar Bose-Einstein condensates, whose additional degrees of freedom offer the potential for novel physics and provide a pathway to realizing bulk supersolids.
Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.
We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquidlike density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.
We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate.The theory reveals a ground state phase diagram with three distinct regimes-a regular Bose-Einstein condensate and incoherent and coherent arrays of quantum droplets.The coherent droplets are connected by a background condensate, which leads-in addition to the periodic density modulation-to a robust phase coherence throughout the whole system.We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is limited only by three-body losses.Experimentally we probe and confirm the signatures of the phase diagram by observing the in situ density modulation as well as the phase coherence using matter wave interference.
We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice crystallization in a cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interaction and the same trap frequencies. The energies EEE of all three crystallizations as a function of the number NNN of atoms satisfy the universal scaling relation $E\ensuremath{\sim}{N}^{0.4}$, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed NNN, constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.