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Physical Review Letters

From Classical Mobility to Hopping Conductivity: Charge Hopping in an Ultracold Gas

Robin Côté

Published Dec 18, 2000• 84 citations
Publisher

Abstract

Studies of charge mobilities in an ultracold gas are reported. Calculations for the Na + Na+ system have been carried out as a function of temperature T and densities, and the conductivity of the ultracold charged gas is obtained. The total charge mobility exhibits a sharp increase as T is lowered, indicating a transition from an almost insulating to a conducting system at few microK. It is shown that the nature of the charge mobility changes with temperature: at high T, the charges are transported by massive centers (i.e., the ions), and at low T, by electrons jumping from neighboring atoms onto the positive ions (the positive holes exhibit hopping conductivity). An experiment is proposed to detect this effect.

DOI
10.1103/physrevlett.85.5316

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Studies of charge mobilities in an ultracold gas are reported. Calculations for the Na + Na+ system have been carried out as a function of temperature T and densities, and the conductivity of the ultracold charged gas is obtained. The total charge mobility exhibits a sharp increase as T is lowered, indicating a transition from an almost insulating to a conducting system at few microK. It is shown that the nature of the charge mobility changes with temperature: at high T, the charges are transported by massive centers (i.e., the ions), and at low T, by electrons jumping from neighboring atoms onto the positive ions (the positive holes exhibit hopping conductivity). An experiment is proposed to detect this effect.
Abstract For a homonuclear ion-atom system, we show that the exchange symmetry leads to special outcomes for ion transport that manifest themselves in ultracold experiments. We compute the two body charge hopping probabilities and rates, which are used to model charge hopping in the dynamics of an ultracold <?CDATA 6/7^{6/7}6/7?> 6 / 7 Li+ ion immersed within an ultracold gas of <?CDATA 6/7^{6/7}6/7?> 6 / 7 Li atoms at micro-Kelvin temperatures. We show that the charge hopping and collisional diffusion compete, giving unique results leading to charge trapping in regions of high atomic density gradient. These investigations in ion-atom systems open a new approach to probe quantum phenomena in various systems with exchange symmetry.
Studies of charge transfer and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for Na+Na+\mathrm{Na}+{\mathrm{Na}}^{+}Na+Na+ have been carried out with the best available ${}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and ${}^{2}{\ensuremath{\Sigma}}_{u}^{+}$ potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semiclassical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of a few degrees kelvin, the charge-transfer cross sections are large, and could provide an efficient way to produce cold ions.
Ultracold plasmas are a promising candidate for the creation of strongly coupled Coulomb systems. Unfortunately, the values of the coupling parameter Γe actually achieved after photoionization of the neutral atoms remain relatively small because of the considerable intrinsic heating of the electrons. A conceivable way to get around this obstacle might be to utilize a spontaneous ionization of the ultracold Rydberg gas, where the initial kinetic energies could be much less. However, the spontaneous avalanche ionization will result in a very inhomogeneous distribution (clusterization) of the ions, which can change the efficiency of the electron relaxation in the vicinity of such clusters substantially. In the present work, this hypothesis is tested by an extensive set of numerical simulations. As a result, it is found that despite a less initial kinetic energy, the subsequent relaxation of the electron velocities in the clusterized plasmas proceeds much more violently than in the case of the statistically uniform ionic distribution. The electron temperature, first, experiences a sharp initial jump (presumably, caused by the “virialization” of energies of the charged particles) and, second, exhibits a gradual subsequent increase (presumably, associated with a multi-particle recombination of the electrons at the ionic clusters). As a possible tool to reduce the anomalous temperature increase, we also considered a two-step plasma formation, involving the blockaded Rydberg states. This leads to a suppression of the clusterization due to a quasi-regular distribution of ions. In such a case, according to the numerical simulations, the subsequent evolution of the electron temperature proceeds more gently, approximately with the same rate as in the statistically uniform ionic distribution.
Quantum gases in optical lattices offer a well-controlled and defect free environment to simulate and study phenomena from condensed matter physics. In particular, questions related to conductivity and charge carrier mobility lie at the heart of the properties of many fascinating materials like superconductors, graphene and semiconductors. The latter become conductive if irradiated with photons. This effect is called photoconductivity and results from photon-induced interband transitions of electrons, leading to the creation of electron and hole excitations, which subsequently serve as free charge carriers. Photoconductivity is widely used in technological applications such as semiconductor photodiodes and photoresistors and as a powerful probe for novel materials.
Strongly correlated materials are expected to feature unconventional transport properties, such that charge, spin, and heat conduction are potentially independent probes of the dynamics. In contrast to charge transport, the measurement of spin transport in such materials is highly challenging. We observed spin conduction and diffusion in a system of ultracold fermionic atoms that realizes the half-filled Fermi-Hubbard model. For strong interactions, spin diffusion is driven by super-exchange and doublon-hole-assisted tunneling, and strongly violates the quantum limit of charge diffusion. The technique developed in this work can be extended to finite doping, which can shed light on the complex interplay between spin and charge in the Hubbard model.
We present a theoretical model of the ionization-recombination balance in the ultracold Rydberg gas-plasma mixture, which is caused by the collective processes rather than by individual interparticle interactions. We consider the electron-ion system where each electron moves for the most part of its time in the effective centrifugal potential formed by the nearest ion and sometimes jumps to the neighboring potential wells due to the perturbations from remote particles. These perturbations are described by a thermal bath with the effective "virial" temperature. Then, the electron with a sufficiently high energy, which can escape from the local potential well, should be considered as free (conducting) one; while the electron with low energy, confined within the well, as forming the Rydberg atom. As follows from our calculations, there is a sharp crossover from the insulating phase (Rydberg gas) to the conducting one (plasma) with increase in the particle density, which somewhat resembles the Mott transition in condensed-matter physics. This model should be well relevant to the steady-state ultracold plasmas obtained in the most recent experiments and represents a promising direction for further research.