Quantum walk and Anderson localization of rotational excitations in disordered ensembles of polar molecules

T Xu,R V Krems

doi:10.1088/1367-2630/17/6/065014

Abstract

We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.

Highlights

Scattering of electrons by impurities in disordered crystals leads to Anderson localization [1, 2], which determines the conductor - insulator transitions in metals [3], quasi-crystals [4] and granular metal films [5], and is associated with many interesting phenomena, such as the quantized phases of the integer Hall effect [2, 6]
In order to elucidate the dynamics of quantum walk in higher dimensions and the implications of Figure 6, we present in Figure 7 the time dependence of the distribution widths L computed for a rotational excitation in 2D and 3D lattices of varying size with varying concentrations of vacant sites
We study the dynamics of quantum walk of rotational excitations in finite disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices

Summary

Introduction

Scattering of electrons by impurities in disordered crystals leads to Anderson localization [1, 2], which determines the conductor - insulator transitions in metals [3], quasi-crystals [4] and granular metal films [5], and is associated with many interesting phenomena, such as the quantized phases of the integer Hall effect [2, 6]. Disordered-induced localization has been studied with microwaves in a tubular waveguide [8, 9], optical photons in opaque media [10, 11] and ultracold atoms in optical lattices [12,13,14,15]. Despite these studies, there are still many open questions about Anderson localization. Important and widely debated are the effects of inter-particle interactions [17] and dissipative forces [18] on localization in far-from-equilibrium systems or the role of long-range tunnelling amplitudes [19,20,21] allowing particles to transition between distant lattice sites

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