Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system

TL;DR

This paper demonstrates the simulation of the Kibble-Zurek mechanism in the Ising model using a superconducting qubit system, revealing the connection between KZM and Landau-Zener transitions through time-resolved quantum dynamics.

Contribution

It establishes the equivalence between KZM and LZT in a superconducting qubit system and develops a nano-second resolution approach to study their dynamics.

Findings

Observation of the boundary between adiabatic and impulse regions.

Detection of the freeze-out phenomenon in the impulse region.

Verification of the square root scaling law of excited state population.

Abstract

The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching rate. Our results supply the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.