• Open Access

Bound States in Boson Impurity Models

Tao Shi, Ying-Hai Wu, A. González-Tudela, and J. I. Cirac
Phys. Rev. X 6, 021027 – Published 25 May 2016

Abstract

The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work, we show the existence of an infinite number of such states for some boson impurity models. They describe free bosons coupled to an impurity and include some of the most representative models in quantum optics. We also propose a family of wave functions to describe the bound states and verify that it accurately characterizes all parameter regimes by comparing its predictions with exact numerical calculations for a one-dimensional tight-binding Hamiltonian. For that model, we also analyze the nature of the bound states by studying the scaling relations of physical quantities, such as the ground-state energy and localization length, and find a nonanalytical behavior as a function of the coupling strength. Finally, we discuss how to test our theoretical predictions in experimental platforms, such as photonic crystal structures and cold atoms in optical lattices.

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  • Received 23 December 2015

DOI:https://doi.org/10.1103/PhysRevX.6.021027

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Tao Shi, Ying-Hai Wu, A. González-Tudela, and J. I. Cirac

  • Max-Planck-Institut für Quantenoptik Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

Popular Summary

The interactions of spin impurities with bosonic reservoirs lie at the heart of very paradigmatic models in the fields of quantum optics and condensed matter physics and give rise to rich phenomena. For example, in the context of atoms coupled to photonic crystals, it has been predicted that a single atom can localize a single-photon cloud around it if its atomic frequency falls within the band gap of the material. Given recent advances in atom nanophotonics, these atom-photon bound states have experienced renewed interest in the context of quantum simulation, and they have been proposed to mediate strong and long-range interactions between atoms. Here, we study the general problem of a single spin impurity coupled to a generic bosonic bath and show that a single atom can indeed trap infinitely many bosons around it.

We construct a model consisting of a single impurity (like an atom), a multidimensional bath of free bosons, and the coupling between the impurity and the bath. Our work focuses on up to N=5 excitations, and we conduct both exact and numerical calculations. We theoretically show that the coupling of the impurity to the bath generates an effective potential to the bosons that is able to localize the bosons around it. In particular, a single atom can localize a multiphoton cloud around it within a photonic crystal. Our results highlight the existence of many different regimes with nonanalytical scaling of physical properties. Because of the generality of our model, these bound states can potentially be prepared and observed in many different platforms ranging from atoms coupled to photonic crystals to cold atoms in state-dependent optical lattices.

We expect that our findings will motivate studies of boson bound states associated with new, exotic, many-body phenomena.

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Issue

Vol. 6, Iss. 2 — April - June 2016

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