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arXiv:1304.7704

Single impurities in a Bose-Einstein condensate can make two polaron flavors

Alina Blinova, M. G. Boshier, Eddy Timmermans

Published Apr 29, 2013• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.1304.7704

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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.
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.
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 investigate the properties of a dilute gas of impurities embedded in an ultracold gas of bosons that forms a Bose–Einstein condensate (BEC). This work focuses mainly on the equation of state (EoS) of the impurity gas at zero temperature and the induced interaction between impurities mediated by the host bath. We use perturbative field-theory approaches, such as Hugenholtz–Pines formalism, in the weakly interacting regime. In turn, for strong interactions, we aim at non-perturbative techniques such as quantum–Monte Carlo (QMC) methods. Our findings agree with experimental observations for an ultra dilute gas of impurities, modeled in the framework of the single impurity problem; however, as the density of impurities increases, systematic deviations are displayed with respect to the one-body Bose polaron problem.
Mixing two kinds of particles that repel each other usually results in either a homogeneous mixture when the repulsion is weak, or a complete phase separation of the two kinds when their repulsion is too strong. It is shown however that there is an intermediate regime where the two kinds can coexist in their ground state as a bubble immersed in a gas of one kind. Such a situation is obtained by adding heavy repulsive impurities into a Bose-Einstein condensate. Above a certain strength of the mutual repulsion, a stable bubble of impurities and bosons can be formed, resulting from the equilibrium between the interactions induced by the bosons inside the bubble and the outside pressure from the surrounding bosons. At some particular strength, the effective interactions between the impurities consist of only three-body interactions. Finally, above a critical strength, the bosons are ejected from the bubble and the impurities collapse into a pure bubble of impurities. This phenomenon could be observed with an imbalanced mixture of ultra-cold atoms of different masses. Moreover, it appears possible to reach a regime where the impurities form a dense bubble of strongly-interacting particles.