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arXiv:1111.1002 · New Journal of Physics

Multi-impurity polarons in a dilute Bose–Einstein condensate

D. H. Santamore, Eddy Timmermans

Published Oct 24, 2011• 36 citations
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Abstract

We describe the ground state of a large, dilute, neutral atom Bose–Einstein condensate (BEC) doped with N strongly coupled mutually indistinguishable, bosonic neutral atoms (referred to as 'impurity') in the polaron regime where the BEC density response to the impurity atoms remains significantly smaller than the average density of the surrounding BEC. We find that N impurity atoms with N ≠ 1 can self-localize at a lower value of the impurity–boson interaction strength than a single impurity atom. When the 'bare' short-range impurity–impurity repulsion does not play a significant role, the self-localization of multiple bosonic impurity atoms into the same single particle orbital (which we call co-self-localization) is the nucleation process of the phase separation transition. When the short-range impurity–impurity repulsion successfully competes with co-self-localization, the system may form a stable liquid of self-localized single impurity polarons.

DOI
10.1088/1367-2630/13/10/103029

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We describe the ground state of a large, dilute, neutral atom Bose–Einstein condensate (BEC) doped with N strongly coupled mutually indistinguishable, bosonic neutral atoms (referred to as 'impurity') in the polaron regime where the BEC density response to the impurity atoms remains significantly smaller than the average density of the surrounding BEC. We find that N impurity atoms with N ≠ 1 can self-localize at a lower value of the impurity–boson interaction strength than a single impurity atom. When the 'bare' short-range impurity–impurity repulsion does not play a significant role, the self-localization of multiple bosonic impurity atoms into the same single particle orbital (which we call co-self-localization) is the nucleation process of the phase separation transition. When the short-range impurity–impurity repulsion successfully competes with co-self-localization, the system may form a stable liquid of self-localized single impurity polarons.
Polarons, self-localized composite objects formed by the interaction of a single impurity particle with a host medium, are a paradigm of strong interaction many-body physics. We show that dilute gas Bose-Einstein condensates (BEC's) are the first medium known to self-localize the same impurity particles both in a Landau-Pekar polaron state akin to that of self-localized electrons in a dielectric lattice, and in a bubble state akin to that of electron bubbles in helium. We also show that the BEC-impurity system is fully characterized by just two dimensionless coupling constants, and that it can be adiabatically steered from the Landau-Pekar regime to the bubble regime in a smooth crossover trajectory.
We show that repulsive neutral-atom impurities in a dilute gas Bose-Einstein condensate (BEC) can self-localize in bubble polaron states formally analogous to electron bubbles in helium. The BEC is then the first impurity host medium known to exhibit both Landau-Pekar polaron states akin to that of self-localized electrons in a dielectric lattice and self-localized bubble polaron states. We find that the neutral BEC-impurity system is fully characterized by only two dimensionless coupling constants and that a single BEC impurity can be steered adiabatically from the Landau-Pekar to the bubble region. The adiabatic change is that of a crossover, not a transition.
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov approximation which includes the local repulsion between bosons and thereby stabilizes the Bose polaron even near and beyond the scattering resonance. We show that the Bose polaron energy remains bounded from below across the resonance and the size of the polaron dressing cloud stays finite. Our results demonstrate how the dressing cloud replaces the attractive impurity potential with an effective many-body potential that excludes binding. We find that at resonance, including the effects of boson repulsion, the polaron energy depends universally on the effective range. Moreover, while the impurity contact is strongly peaked at positive scattering length, it remains always finite. Our solution highlights how Bose polarons are self-stabilized by repulsion, providing a mechanism to understand quench dynamics and nonequilibrium time evolution at strong coupling.
Ultracold atomic gases provide a unique way for exploring many-body quantum phenomena that are inaccessible to conventional low-temperature experiments. Nearly two decades ago the Bose-Einstein condensate (BEC) - an ultracold gas of bosons in which almost all bosons occupy the same single-particle state - became experimentally feasible. Because a BEC exhibits superfluid properties, it can provide insights into the behavior of low-temperature helium liquids. We describe the case of a single distinguishable atom (an impurity) embedded in a BEC and strongly coupled to the BEC bosons. Depending on the strength of impurity-boson and boson-boson interactions, the impurity self-localizes into two fundamentally distinct regimes. The impurity atom can behave as a tightly localized 'polaron,' akin to an electron in a dielectric crystal, or as a 'bubble,' an analog to an electron bubble in superfluid helium. We obtain the ground state wavefunctions of the impurity and BEC by numerically solving the two coupled Gross-Pitaevskii equations that characterize the system. We employ the methods of imaginary time propagation and conjugate gradient descent. By appropriately varying the impurity-boson and boson-boson interaction strengths, we focus on the polaron to bubble crossover. Our results confirm analytical predictions for the polaron limit and uncover properties of the bubble regime. With these results we characterize the polaron to bubble crossover. We also summarize our findings in a phase diagram of the BEC-impurity system, which can be used as a guide in future experiments.
We study the interaction-induced localization —the so-called self-trapping— of a neutral impurity atom immersed in a homogeneous Bose-Einstein condensate (BEC). Based on a Hartree description of the BEC we show that —unlike repulsive impurities— attractive impurities have a singular ground state in 3d and shrink to a point-like state in 2d as the coupling approaches a critical value β ⋆ . Moreover, we find that the density of the BEC increases markedly in the vicinity of attractive impurities in 1d and 2d, which strongly enhances inelastic collisions between atoms in the BEC. These collisions result in a loss of BEC atoms and possibly of the localized impurity itself.