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arXiv:1409.6279 · Physical Review A

Mobile impurities and orthogonality catastrophe in two-dimensional vortex lattices

M. A. Caracanhas, Rodrigo G. Pereira

Published Jan 12, 2015• 4 citations
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Abstract

We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice in a Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low-energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight, and effective impurity mass. The divergence of the effective mass in the low-energy limit gives rise to a power-law singularity in the impurity spectral function and provides an example of an emergent orthogonality catastrophe in a bosonic system.

DOI
10.1103/physreva.91.013608

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We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice in a Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low-energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight, and effective impurity mass. The divergence of the effective mass in the low-energy limit gives rise to a power-law singularity in the impurity spectral function and provides an example of an emergent orthogonality catastrophe in a bosonic system.
We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight and effective impurity mass. The divergence of the effective mass in the low energy limit gives rise to an orthogonality catastrophe which is manifested as a power law singularity in the impurity spectral function.
The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory.Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures.In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas.We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice.As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length.Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping.In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2 and 3 BEC cloud.The resulting impurity-bath interaction leads to the formation of a polaron (particle "dressed" by the phonon excitations of the BEC), which is characterized by its spectral function.We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron.These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons.In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation.In spite of qualitatively similar results obtained for the 2 and 3 bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2 BEC bath would be a better candidate to observe stable quasi-particle properties.
Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching, the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as $D(T)\ensuremath{\propto}{ln}^{2}T$. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emergent orthogonality catastrophe. In this case we map the problem onto a set of one-dimensional channels and use conformal field theory techniques to obtain $D(T)\ensuremath{\propto}{T}^{\ensuremath{\nu}}$ with an interaction-dependent exponent $\ensuremath{\nu}$. The different regimes can be detected in the nonequilibrium expansion dynamics of an initially confined impurity.
We analyze the properties of impurities immersed in a vortex lattice formed by ultracold bosons in the mean field quantum Hall regime. In addition to the effects of a periodic lattice potential, the impurity is dressed by collective modes with parabolic dispersion (Tkachenko modes). We derive the effective polaron model, which contains a marginal impurity-phonon interaction. The polaron spectral function exhibits a Lorentzian broadening for arbitrarily small wave vectors even at zero temperature, in contrast with the result for optical or acoustic phonons. The anomalous damping of Tkachenko polarons could be detected experimentally using momentum-resolved spectroscopy.
We consider the problem of finding the bound-state spectrum of an impurity immersed in a weakly interacting two-dimensional Bose-Einstein condensate supporting a single vortex. We obtain approximate expressions for the energy levels and show that, due to the finite size of the condensate, the impurity can access only a finite number of physical bound states. By virtue of the topological quantization of the vorticity and of the emergence of the Tkachenko lattice, this system is promising as a robust and scalable platform for the realization of qubits. Moreover, it provides a potentially new paradigm for polaron physics in Bose-Einstein condensates and a glimpse towards the study of quantum turbulence in low-dimensionality systems.
Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.