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arXiv:1807.00631 · Physica Scripta

A fermionic impurity in a dipolar quantum droplet

Matthias Wenzel, Tilman Pfau, Igor Ferrier-Barbut

Published Aug 29, 2018• 36 citations
arXivHTMLPDF

Abstract

Abstract In this article we develop the framework to describe Bose–Fermi mixtures of magnetic atoms, focusing on the interaction of bosonic self-bound dipolar quantum droplets with a small number of fermions. We find an attractive interaction potential due to the dipolar interaction with several bound states, which can be occupied by one fermion each, resulting in a very weak back-action on the bosons. We conclude, that these impurities might act as unique probes giving access to inherent properties of dipolar quantum droplets.

DOI
10.1088/1402-4896/aadd72

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Abstract In this article we develop the framework to describe Bose–Fermi mixtures of magnetic atoms, focusing on the interaction of bosonic self-bound dipolar quantum droplets with a small number of fermions. We find an attractive interaction potential due to the dipolar interaction with several bound states, which can be occupied by one fermion each, resulting in a very weak back-action on the bosons. We conclude, that these impurities might act as unique probes giving access to inherent properties of dipolar quantum droplets.
Abstract We study an impurity immersed in the mixture of Bose ultracold gases in the regime where a quantum droplet (QD) exists. The quasi-one-dimensional geometry is considered. We find an effective attractive potential, which acts by the QD onto the impurity. The bound states of the impurity in this potential are investigated. These impurity-bound states can provide potential probes for the presence of quantum fluctuation effects on the droplet properties. In the case of strong impurity–Bose–Einstein condensate coupling we study the properties of the nonlinear local modes on the impurity induced by the quantum fluctuations.
Recently created self-bound quantum droplets of binary Bose mixtures open intriguing possibilities for the study of impurity physics. We show that the properties of impurities embedded in quasi-one-dimensional droplets are determined by the interplay between back-action and quantum fluctuations. Due to such back-action, repulsive impurities may form a metastable quasi-bound state inside the droplet. In contrast, attractive impurities remain bound to the droplet, leading to the hybridization of droplet and impurity excitations, as well as to peculiar scattering resonances. Interestingly, impurity trapping may result solely from the effect of quantum fluctuations. These results may readily be probed experimentally by doping the currently available droplets of binary mixtures.
We unravel the ground state properties and emergent nonequilibrium dynamics of a mixture consisting of a few spin-polarized fermions embedded in a two-dimensional bosonic quantum droplet. For an increasingly attractive droplet-fermion interaction we find a transition from a spatially delocalized fermion configuration to a state where the fermions are highly localized and isolated. This process is accompanied by the rise of induced fermion-fermion interactions mediated by the droplet. Additionally, for increasing attractive droplet-fermion coupling, undulations in the droplet density occur in the vicinity of the fermions manifesting the back-action of the latter. Following interaction quenches from strong to weaker attractive droplet-fermion couplings reveals the spontaneous nucleation of complex excitation patterns in the fermion density such as ring- and cross-shaped structures. These stem from the enhanced interference of the fermions that remain trapped within the droplet, which emulates, to a good degree, an effective potential for the fermions. The non-negligible back-action of the droplet manifests itself in the fact that the effective potential predictions are less accurate at the level of the many-body wave function. Our results provide a paradigm for physics beyond the reduced single-component droplet model, unveiling the role of back-action in droplets and the effect of induced mediated interactions. Published by the American Physical Society 2024
These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.
Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultradilute quantum liquids. While nondipolar self-bound (without external confinement) mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. Therefore, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible, and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual nonlocal intercomponent attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultradilute liquids, which should resemble to some extent that of ^{4}He-^{3}He droplets and impurity-doped helium droplets.
Diffusion Monte Carlo calculations on the possibility of having self-bound one-dimensional droplets of SU(6) $\ifmmode\times\else\texttimes\fi{}$ SU(2) ultracold fermionic mixtures are presented. We found that, even though arrangements with attractive interactions with only two spin types are not self-bound, mixtures with at least three kinds of fermions form stable small drops. However, that stabilization decreases for very tight confinements, where a universal behavior is found for Fermi-Fermi and Fermi-Boson clusters including attractive and repulsive interactions.