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 subjecting 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 1D array of superconducting qubits, and the circuit where non-local interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly-excited eigenstates, and obtain the lower bound of the critical linear potential ${\gamma }_c$, using the finite-size scaling collapse. Moreover, we study the non-equilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay $t^{-\xi }$. The exponent $\xi$ satisfies $\xi \propto |\gamma -{\gamma }_c{|}^{\nu }$ when $\gamma <{\gamma }_c$, and vanishes for $\gamma \ge {\gamma }_c$, which can be employed to estimate the ${\gamma }_c$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.

9+7 pages, 10+7 figures, 2 tables

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Spectral signatures of many-body localization with interacting photons
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Recent progress in many-body localization
• Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Many-body localization due to random interactions
• Stark many-body localization: Evidence for Hilbert-space shattering
• Many-body localization of bosons in optical lattice: Dynamics in disorder-free potentials
• Many-body localization in tilted and harmonic potentials
• Many-body localization in presence of cavity mediated long-range interactions
• Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential

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• Many-body localization in a quantum gas with long-range interactions and linear external potential
• Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
• Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping