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arXiv:2012.12156 · Journal of Physics B Atomic Molecular and Optical Physics

Bosonic impurity in a one-dimensional quantum droplet in the Bose–Bose mixture

F. Kh. Abdullaev, R. M. Galimzyanov

Published May 26, 2020• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6455/ab9659

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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 explore the ground-state properties of a single impurity immersed in a one-dimensional quantum droplet medium formed by a two-component Bose mixture. Relying on ab initio simulations, we demonstrate that tuning the impurity-droplet interactions allows to controllably reshape the droplets' density profiles and associated correlation patterns. For attractive impurity-medium couplings, the impurity becomes localized within the droplet, which exhibits a density hump at the vicinity of the impurity, while repulsive interactions facilitate phase separation. Comparing our many-body results with the appropriate extended Gross-Pitaevskii description, we find adequate agreement for the droplet density profiles, with the effective field approach systematically overestimating impurity localization. Following a release of the external trap, we unveil that the sign and magnitude of the interactions between the impurity and the droplet hosts dictate the response of the three-component setting, which experiences expansion unless strongly attractive intercomponent couplings are present. These results corroborate the role and presence of correlations in impurity-droplet mixtures and inspire future investigations on impurity physics for probing droplet configurations.
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 theoretically investigate the temperature effect in a Bose–Bose mixture with attractive inter-species interactions, in the regime where a self-bound ultradilute quantum droplet forms due to the subtle balance between the attractive mean-field force and the repulsive force provided by Lee–Huang–Yang quantum fluctuations. We find that in contrast to quantum fluctuations, thermal fluctuations destabilize the droplet state and completely destroy it above a threshold temperature. We show that the threshold temperature is determined by the intra-species interaction energy. For a three-dimensional Bose–Bose mixture, the threshold temperature is less than one-tenth of the Bose–Einstein condensation temperature under the typical experimental conditions. With increasing temperature, the droplet’s equilibrium density gradually decreases and can be reduced by several tens of percent upon reaching the threshold temperature. We also consider a one-dimensional quantum droplet and find a similar destabilization effect due to thermal fluctuations. The threshold temperature in one dimension is roughly set by the binding energy of the inter-species dimer. The pronounced thermal instability of a self-bound quantum droplet predicted in our work could be examined in future experiments, by measuring the temperature dependence of its central density and observing its sudden disappearance at the threshold temperature.
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in details. Precisely, we are interested in investigating the possibility of droplet formation in a quasi one dimensional geometry. The recent observation have concluded that the droplets are stabilized by the competition between effective mean-filed and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self bound droplet formations.
Two-dimensional quantum gases provide a distinctive setting in which enhanced thermal fluctuations, finite-size effects, and two-body bound-state formation are intrinsically intertwined. In this work, we study a single attractive impurity immersed in a finite, weakly interacting two-dimensional Bose gas, where finite size stabilizes a nonzero condensate fraction by introducing an infrared momentum scale, thereby enabling a Bogoliubov description of the bath. Using a hybrid approach that combines finite-temperature many-body scattering theory with input from path-integral Monte Carlo, we analyze the impurity quasiparticle energy across the condensate and normal regimes. The infrared scale generates a phonon-activation temperature below which the impurity energy remains nearly temperature independent. Once the resolved phonon modes become thermally populated, their contribution competes with condensate depletion, producing a nonmonotonic temperature dependence of the polaron energy. These results suggest that attractive Bose polarons may serve as sensitive probes of finite-size thermal fluctuations, phonon dressing, and bound-state physics in low-dimensional Bose gases.