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arXiv:1307.0144 · Physical Review Letters

Tkachenko Polarons in Vortex Lattices

M. A. Caracanhas, Vanderlei Salvador Bagnato, Rodrigo G. Pereira

Published Sep 10, 2013• 10 citations
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Abstract

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.

DOI
10.1103/physrevlett.111.115304

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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 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.
We investigate the effects of a nearly uniform Bose-Einstein condensate (BEC) on the properties of immersed trapped impurity atoms. Using a weak-coupling expansion in the BEC-impurity interaction strength, we derive a model describing polarons, i.e., impurities dressed by a coherent state of Bogoliubov phonons, and apply it to ultracold bosonic atoms in an optical lattice. We show that, with increasing BEC temperature, the transport properties of the impurities change from coherent to diffusive. Furthermore, stable polaron clusters are formed via a phonon-mediated off-site attraction.
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.
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.
We consider a polaronic model in which impurity fermions interact with background bosons in a dipolar condensate. The polaron in this model emerges as an impurity dressed with a cloud of phonons of the dipolar condensate, which, due to the competition between the attractive and repulsive parts of the dipole-dipole interaction, obey an anisotropic dispersion spectrum. We study how this anisotropy affects the \ifmmode \check{C}\else \v{C}\fi{}erenkov-like emission of Bogoliubov phonon modes, which can be directly verified by experiments in which a dipolar Bose-Einstein condensate moves against an obstacle. We also study the spectral function of impurity fermions, which is directly accessible to the momentum-resolved rf spectroscopy in cold atoms.
A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground-state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion, at both zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground-state properties, such as the effective polaron mass, which show a continuous behavior as the coupling is increased, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more open in the density of states at low energy, while the high-energy part of the spectrum is broad and can be qualitatively explained by a strong coupling adiabatic approximation. As a consequence, narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such an effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum always has a multipeaked structure.