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arXiv:2001.08352

Polaron bubble stabilised by medium-induced three-body interactions

Pascal Naidon

Published Jan 23, 2020• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.2001.08352

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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.
A new generation of cold atom experiments trapping atomic mixtures in species-selective optical potentials opens up the intriguing possibility to create systems in which different atoms live in different spatial dimensions. Inspired by this, we investigate a mixed-dimensional Bose polaron consisting of an impurity particle moving in a two-dimensional (2D) layer immersed in a 3D Bose-Einstein condensate (BEC), using a theory that includes the mixed-dimensional vacuum scattering between the impurity and the bosons exactly. We show that similarly to the pure 3D case, this system exhibits a well-defined polaron state for attractive boson-impurity interaction that evolves smoothly into a mixed-dimensional dimer for strong attraction, as well as a well-defined polaron state for weak repulsive interaction, which becomes overdamped for strong interaction. We furthermore find that the properties of the polaron depend only weakly on the gas parameter of the BEC as long as the Bogoliubov theory remains a valid description for the BEC. This indicates that higher-order correlations between the impurity and the bosons are suppressed by the mixed-dimensional geometry in comparison to a pure 3D system, which led us to speculate that the mixed-dimensional polaron has universal properties in the unitarity limit of the impurity-boson interaction.
We investigate the fundamental problem of a small density of bosonic impurities immersed in a dilute Bose gas at zero temperature. Using a rigorous perturbative expansion, we show that the presence of the surrounding medium enhances the repulsion between dressed bosonic impurities (polarons) in the regime of weak interactions. Crucially, this differs from prevailing theories based on Landau quasiparticles, which neglect the possibility of quantum degenerate impurities and predict an exchange-induced attraction. We furthermore show that the polaron-polaron interactions are strongly modified if the medium chemical potential rather than the density is held fixed, such that the medium-induced attraction between thermal impurities becomes twice the expected Landau effective interaction. Our work provides a possible explanation for the differing signs of the polaron-polaron interactions observed in experiments across cold atomic gases and two-dimensional semiconductors, and it has important implications for theories of quasiparticles and quantum mixtures in general.
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 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 consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.