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arXiv:1601.05869 · Physical Review A

Properties of a dipolar condensate with three-body interactions

P. B. Blakie

Published Mar 23, 2016• 62 citations
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Abstract

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.

DOI
10.1103/physreva.93.033644

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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.
We consider the ground state properties of a trapped dipolar condensate under the influence of quantum fluctuations. We show that this system can undergo a phase transition from a low density condensate state to a high density droplet state, which is stabilized by quantum fluctuations. The energetically favored state depends on the geometry of the confining potential, the number of atoms, and the two-body interactions. We develop a simple variational ansatz and validate it against full numerical solutions. We produce a phase diagram for the system and present results relevant to current experiments with dysprosium and erbium condensates.
We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
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.
Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an sss-wave scattering length a<0a<0a<0 and a three-body scattering hypervolume D>0D>0D>0. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.
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 show that the ground state of a dipolar Bose gas in a cylindrically symmetric harmonic trap has a rich phase diagram, including droplet crystal states in which a set of droplets arrange into a lattice pattern that breaks the rotational symmetry. An analytic model for small droplet crystals is developed and used to obtain a zero temperature phase diagram that is numerically validated. We show that in certain regimes a coherent low-density halo surrounds the droplet crystal, giving rise to a novel phase with localized and extended features.