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arXiv:2107.05035 · npj Quantum Information

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

Amir H. Karamlou, Jochen Braumüller, Yariv Yanay, Agustín Di Paolo, P. M. Harrington, Bharath Kannan, David K. Kim, Morten Kjærgaard, Alexander J. Melville, Sarah E. Muschinske, Bethany M. Niedzielski, Antti P. Vepsäläinen, Roni Winik, Jonilyn Yoder, Mollie E. Schwartz, Charles Tahan, Terry P. Orlando, Simon Gustavsson, William D. Oliver

Published Mar 25, 2022• 65 citations

Abstract

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 × 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.

DOI: 10.1038/s41534-022-00528-0

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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 × 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.

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We investigate localization in two models: a single particle in a two-dimensional square lattice described by the tight binding Hamiltonian, and a two-dimensional square qubit lattice. It is well-known that Anderson localization occurs under suitable conditions in which the system parameters are chosen randomly from some statistical distribution. We propose a situation in which the parameters, specifically the on-site energies, are carefully chosen in such a way that a localization-quantifying parameter is maximized. We demonstrate the optimization procedure with numerical calculations in which the engineered localization significantly exceeds the average localization caused by a random distribution of the on-site energies. We explore the relation between spatial patterns and localization efficiency. Furthermore, we use perturbation theory to gain insight into the localization mechanism and obtain an improved cost function for optimization calculations, leading to enhanced localization in both the single-particle and full Hilbert spaces. Although large-scale simulations for qubit lattices are computationally infeasible, we use small-system simulations to demonstrate that results obtained using the single-particle tight binding model can be adapted to identify optimal settings for qubit lattice systems to achieve maximum decoupling between the qubits, which can be valuable for optimizing the idle-state settings on a quantum processor.

Abstract We discuss how the observation of population localization effects in periodically driven systems can be used to quantify the presence of quantum coherence in interacting qubit arrays. Essential for our proposal is the fact that these localization effects persist beyond tight-binding Hamiltonian models. This result is of special practical relevance in those situations where direct system probing using tomographic schemes becomes infeasible beyond a very small number of qubits. As a proof of principle, we study analytically a Hamiltonian system consisting of a chain of superconducting flux qubits under the effect of a periodic driving. We provide extensive numerical support of our results in the simple case of a two-qubit chain. For this system we also study the robustness of the scheme against different types of noise and disorder. We show that localization effects underpinned by quantum coherent interactions should be observable within realistic parameter regimes in chains with a larger number of qubits.

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