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arXiv:1807.09948 · Physical Review Letters

Impurity-Induced Multibody Resonances in a Bose Gas

Zhe-Yu Shi, Shuhei M. Yoshida, Meera M. Parish, Jesper Levinsen

Published Dec 11, 2018• 28 citations
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Abstract

We investigate the problem of N identical bosons that are coupled to an impurity particle with infinite mass. For noninteracting bosons, we show that a dynamical impurity-boson interaction, mediated by a closed-channel dimer, can induce an effective boson-boson repulsion which strongly modifies the bound states consisting of the impurity and N bosons. In particular, we demonstrate the existence of two universal "multibody" resonances, where all multibody bound states involving any N emerge and disappear. The first multibody resonance corresponds to infinite impurity-boson scattering length, a→+∞, while the second corresponds to the critical scattering length a^{*}>0 beyond which the trimer (N=2 bound state) ceases to exist. Crucially, we show that the existence of a^{*} ensures that the ground-state energy in the multibody bound-state region, ∞>a>a^{*}, is bounded from below, with a bound that is independent of N. Thus, even though the impurity can support multibody bound states, they become increasingly fragile beyond the dimer state. This has implications for the nature of the Bose polaron currently being studied in cold-atom experiments.

DOI
10.1103/physrevlett.121.243401

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We investigate the problem of N identical bosons that are coupled to an impurity particle with infinite mass. For noninteracting bosons, we show that a dynamical impurity-boson interaction, mediated by a closed-channel dimer, can induce an effective boson-boson repulsion which strongly modifies the bound states consisting of the impurity and N bosons. In particular, we demonstrate the existence of two universal "multibody" resonances, where all multibody bound states involving any N emerge and disappear. The first multibody resonance corresponds to infinite impurity-boson scattering length, a→+∞, while the second corresponds to the critical scattering length a^{}>0 beyond which the trimer (N=2 bound state) ceases to exist. Crucially, we show that the existence of a^{} ensures that the ground-state energy in the multibody bound-state region, ∞>a>a^{*}, is bounded from below, with a bound that is independent of N. Thus, even though the impurity can support multibody bound states, they become increasingly fragile beyond the dimer state. This has implications for the nature of the Bose polaron currently being studied in cold-atom experiments.
We consider the problem of a fixed impurity coupled to a small number NNN of noninteracting bosons. We focus on impurity-boson interactions that are mediated by a closed-channel molecule, as is the case for tuneable interatomic interactions in cold-atom experiments. We show that this two-channel model can be mapped to a boson model with effective boson-boson repulsion, which enables us to solve the three-body (N=2)(N=2)(N=2) problem analytically and determine the trimer energy for impurity-boson scattering lengths a>0a>0a>0. By analyzing the atom-dimer scattering amplitude, we find a critical scattering length a∗{a}^{*}a∗ at which the atom-dimer scattering length diverges and the trimer merges into the dimer continuum. We furthermore calculate the tetramer energy exactly for a>0a>0a>0 and show that the tetramer also merges with the continuum at a∗{a}^{*}a∗. Indeed, since the critical point a∗{a}^{*}a∗ formally resembles the unitary point 1/a=01/a=01/a=0, we find that all higher-body bound states (involving the impurity and N>1N>1N>1 bosons) emerge and disappear at both of these points. We show that the behavior at these ``multibody resonances'' is universal, since it occurs for any model with an effective three-body repulsion involving the impurity. Thus we see that the fixed-impurity problem is strongly affected by a three-body parameter even in the absence of the Efimov effect.
Small weakly bound droplets determine a number of properties of ultracold Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and atom-dimer thresholds lead to enhanced losses from bosonic clouds. Generalizations to four- and higher-body systems have also been considered. Moreover, Efimov trimers have been predicted to play a role in the Bose polaron with large boson-impurity scattering length. Motivated by these considerations, the present work provides a detailed theoretical analysis of weakly bound NNN-body clusters consisting of $N\ensuremath{-}1$ identical bosons (denoted by ``B'') of mass mmm that interact with a single distinguishable impurity particle (denoted by ``X'') of mass MMM. The system properties are analyzed as a function of the mass ratio $\ensuremath{\kappa}$ (values from $\ensuremath{\kappa}=1$ to 50 are considered), where $\ensuremath{\kappa}$ is equal to m/Mm/Mm/M, and the two-body sss-wave scattering length aBX{a}_{\text{BX}}aBX​ between the bosons and the impurity. To reach the universal Efimov regime in which the size of the BBX trimer as well as those of larger clusters is much larger than the length scales of the underlying interaction model, three different approaches are considered: resonance states are determined in the absence of BB and BBX interactions, bound states are determined in the presence of repulsive three-body boson-boson-impurity interactions, and bound states are determined in the presence of repulsive two-body boson-boson interactions. The universal regime, in which the details of the underlying interaction model become irrelevant, is identified.
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.
We investigate the problem of an infinitely heavy impurity interacting with a dilute Bose gas at zero temperature. When the impurity-boson interactions are short-ranged, we show that boson-boson interactions induce a quantum blockade effect, where a single boson can effectively block or screen the impurity potential. Since this behavior depends on the quantum granular nature of the Bose gas, it cannot be captured within a standard classical-field description. Using a combination of exact quantum Monte Carlo methods and a truncated basis approach, we show how the quantum correlations between bosons lead to universal few-body bound states and a logarithmically slow dependence of the polaron ground-state energy on the boson-boson scattering length. Moreover, we expose the link between the polaron energy and the spatial structure of the quantum correlations, spanning the infrared to ultraviolet physics.
We address the Bose polaron problem of a mobile impurity interacting strongly with a host Bose-Einstein condensate through a Feshbach resonance. On the repulsive side at strong couplings, theoretical approaches predict two distinct polaron branches corresponding to attractive and repulsive polarons, but it remains unclear how the two are related. This is partly due to the challenges resulting from a competition of strongly attractive (destabilizing) impurity-boson interactions with weakly repulsive (stabilizing) boson-boson interactions, whose interplay is difficult to describe with contemporary theoretical methods. Here, we develop a powerful variational framework that combines Gaussian correlations among impurity-boson scattering states, including up to an infinite number of bosonic excitations, with exact non-Gaussian correlations among bosons occupying an impurity-boson bound state. This variational scheme enables a full treatment of strong nonlinearities arising in the Feshbach molecule on the repulsive side of the resonance. Within this framework, we demonstrate that the interplay of impurity-induced instability and stabilization by repulsive boson-boson interactions results in a discrete set of metastable many-body bound states at intermediate energies between the attractive and repulsive polaron branches. These states exhibit strong quantum statistical characteristics in the form of non-Gaussian quantum correlations, requiring nonperturbative beyond mean-field treatments for their characterization. Furthermore, these many-body bound states have sizable molecular spectral weights, accessible via molecular spectroscopy techniques. This work provides a unified theory of attractive and repulsive Bose polarons on the repulsive side of the Feshbach resonance.
Abstract We study the ground state properties and non-equilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurity–impurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastrophe of Bose polarons. We find that for an increasing postquench repulsion the impurities reside in a superposition of two distinct two-body configurations while at strong repulsions their corresponding two-body correlation patterns show a spatially delocalized behavior evincing the involvement of higher excited states. For attractive interspecies couplings, the impurities exhibit a tendency to localize at the origin and remarkably for strong attractions they experience a mutual attraction on the two-body level that is imprinted as a density hump on the bosonic bath.