Quantum transport and localization in 1d and 2d tight-binding lattices

TL;DR

This paper experimentally investigates quantum transport and localization in 1D and 2D tight-binding lattices using a controllable superconducting qubit array, confirming theoretical models and enabling future exploration of complex quantum systems.

Contribution

It demonstrates high-fidelity control and measurement of a 3x3 qubit lattice to study quantum transport and localization phenomena, aligning experimental results with theoretical predictions.

Findings

Quantitative agreement with numerical simulations

Observation of localization in Anderson and Wannier-Stark regimes

Control of disorder and gradients in a superconducting qubit array

Abstract

Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of each lattice site in a highly coherent quantum system. Here, we experimentally study quantum transport in one-dimensional and two-dimensional tight-binding lattices, emulated by a fully controllable $3 \times 3$ array of superconducting qubits. We probe the propagation of entanglement throughout the lattice and extract the degree of localization in the Anderson and Wannier-Stark regimes in the presence of site-tunable disorder strengths and gradients. Our results are in quantitative agreement with numerical simulations and match theoretical predictions based on the tight-binding model. The demonstrated level of experimental control and accuracy in extracting the system observables of interest will enable the exploration of larger, interacting lattices where numerical simulations become intractable.