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arXiv:2410.07878 · Physical Review X

Flat-Band (De)localization Emulated with a Superconducting Qubit Array

Ilan T. Rosen, Sarah E. Muschinske, Cora N. Barrett, David A. Rower, Rabindra Nath Das, David K. Kim, Bethany M. Niedzielski, Meghan Schuldt, Kyle Serniak, Mollie E. Schwartz, Jonilyn Yoder, Jeffrey A. Grover, William D. Oliver

Published Jun 16, 2025• 13 citations
arXivHTMLPDF

Abstract

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

DOI
10.1103/physrevx.15.021091

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This paper presents a concept for a quantum simulator based on a superconducting qubit coupled to a readout resonator, designed to experimentally emulate the band structure of a one-dimensional crystal. The superconducting qubit, with its intrinsic periodic potential from the Josephson effect, serves as a direct analog of an electron in a periodic lattice. The Hamiltonian of the system is analyzed in two complementary regimes: the weak-coupling regime, corresponding to nearly free electrons, and the strong-coupling regime, corresponding to electrons in the tight-binding limit. We show that the system can be continuously swept between these regimes using a flux-tunable symmetric DC-SQUID to vary the effective Josephson energy. To probe the resulting band structure, we propose an experimental method based on two-tone spectroscopy, which maps the qubit's flux-dependent transition spectrum via the dispersive shift of a coupled resonator. Numerical simulations confirm the feasibility of this approach, visualizing the transition from a broad band dispersion in the weak-coupling limit to exponentially narrow bands in the strong-coupling limit. This platform demonstrates how tunable superconducting circuits can be used as versatile quantum simulators for fundamental solid-state physics phenomena.
We study the interplay between on-site disorder and fermion pairing on the quasi-one-dimensional flat-band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat-band superconductivity is robust against disorder: The critical disorder strength Wc{W}_{c}Wc​ required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength UUU and is proportional to the superconducting weight Ds{D}_{s}Ds​ of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that Wc{W}_{c}Wc​ can be accurately determined by using an appropriate scaling function.
Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.
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