Stark many-body localization transitions in superconducting circuits

Abstract

Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjected to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the one-dimensional array of superconducting qubits, and the circuit where nonlocal interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly excited eigenstates, and study the nonequilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay t−ξ. The exponent ξ satisfies ξ∝|γ−γc|ν when γ<γc, and vanishes for γ≥γc, which can be employed to estimate the γc. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.

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