# Quantum dynamics of the small-polaron formation in a superconducting analog simulator

## TL;DR

This paper proposes a superconducting qubit-based analog simulator to study nonequilibrium small-polaron formation, revealing detailed dynamical processes, entanglement evolution, and non-Gaussian phonon states through exact numerical methods.

## Contribution

It introduces a novel superconducting circuit scheme for simulating small-polaron dynamics and provides new insights into their formation and entanglement properties.

## Key findings

- Identification of the dynamical timescale for small-polaron formation
- Observation of near-maximal entanglement between excitation and phonons
- Detection of non-Gaussian phonon states with strong antisqueezing

## Abstract

We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to dispersionless phonons. We study its dynamics following an excitation-phonon (qubit-resonator) interaction quench using a numerically exact approach based on a Chebyshev-moment expansion of the time-evolution operator of the system. We thereby glean heretofore unavailable insights into the process of the small-polaron formation resulting from strongly momentum-dependent excitation-phonon interactions, most prominently about its inherent dynamical timescale. To further characterize this complex process, we evaluate the excitation-phonon entanglement entropy and show that initially prepared bare-excitation Bloch states here dynamically evolve into small-polaron states that are close to being maximally entangled. Finally, by computing the dynamical variances of the phonon position and momentum quadratures, we demonstrate a pronounced non-Gaussian character of the latter states, with a strong antisqueezing in both quadratures.