Quantum Simulation of Landau-Zener Model Dynamics Supporting the Kibble-Zurek Mechanism

Abstract

The Kibble-Zurek mechanism (KZM) captures the key physics in the non-equilibrium dynamics of second-order phase transitions, and accurately predict the density of the topological defects formed in this process. However, despite much effort, the veracity of the central prediction of KZM, i.e., the scaling of the density production and the transit rate, is still an open question. Here, we performed an experiment, based on a nine-stage optical interferometer with an overall fidelity up to 0.975±0.008, that directly supports the central prediction of KZM in quantum non-equilibrium dynamics. In addition, our work has significantly upgraded the number of stages of the optical interferometer to nine with a high fidelity, this technique can also help to push forward the linear optical quantum simulation and computation.In the early universe after the "Big Bang", cosmological phase transitions occurred with the expansion and cooling of the universe, and the symmetry of the vacuum was broken. The new vacuums were chosen locally, within space-like regions, resulting in topological defects [1,2]. The initial density of the topological defect is extremely interesting, and a rough limit of this density can be estimated by the light-cone causality; however, the exact density is not easy to determine. Zurek suggested that this cosmological mechanism can be observed in condensed matter systems in a laboratory [3][4][5]. For example, a pressure quench drives liquid 4 He from a normal phase to a superfluid phase at a finite rate, which leaves behind vortex lines.In a condensed matter system, the speed limit of the light is less useful to estimate the density of defects. However, the density of topological defects can be predicted for second order phase transitions due to the divergence of the relaxation time τ (which characterizes the time required for the order parameter to relax to its equilibrium value when the parameter has been perturbed) and the healing length (which characterizes the length over which the order parameter will return to the equilibrium value when disturbed) near the critical point. As a result of the divergence, every such transition, traversed at a finite rate, is inevitably a non-equilibrium dynamical process. The whole system can not catch up, and the symmetry will be broken with some topological defects [3][4][5]. Therefore, the Kibble-Zurek mechanism (KZM) provides a theoretical framework with which to describe the non-equilibrium dynamics of the symmetry broken in the second order transition [1][2][3][4][5].The central prediction of the KZM is that the density of the topological defects in the second order phase transition should scale with the transit rate [3][4][5]. To be more specific, consider the phase transition in liquid * smhan@ustc.edu.cn † cfli@ustc.edu.cn 4 He driven by the pressure (denoted here by t) and suppose that the critical point is located at t = 0. The entire dynamic process can be divided into three parts, the adiabatic, impulse and adiabatic regions(which are shown in Fig.1(a)), ...

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

“…However, the high degree of control and protection against noise that is required to experimentally realize the KZM in a quantum system represents a significant challenge. Experimental confirmations of the QKZM have only recently been achieved with Bose-Einstein condensates [39,40], using Rydberg atoms [41], or by directly simulating the Landau-Zener dynamics [42][43][44]. In addition, it is worth mentioning other aspects of universality arising in non-equilibrium dynamics, which have been recently identified in Refs.…”

Global Formation of Topological Defects in the Multiferroic Hexagonal Manganites

“…Early attempts were carried out on liquid crystals [3,4], superfluid 4 He and 3 He [5][6][7][8] and superconducting rings [9,10]. More recent studies have been conducted on multiferroics [11][12][13], Bose-Einstein condensates [14,15], ionic crystals [16,17], Landau-Zener setups [18], and colloidal monolayers [19]; for a review see Ref. [20].…”

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