Experimentally testing quantum critical dynamics beyond the Kibble–Zurek mechanism

Abstract

We experimentally probe the distribution of kink pairs resulting from driving a one-dimensional quantum Ising chain through the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power-law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noiseinduced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond the paradigmatic Kibble-Zurek mechanism, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

“…[22,28] for item 1, and on Ref. [36] (its Supplementary Note 2 in particular) as well as on Ref. [52] for items 2 and 3, to provide pertinent physical background for our study.…”

“…The above physical picture is quite generic and the result is valid independent of the details of the system Hamiltonian. If we restrict ourselves to the quantum phase transition of the one-dimensional transverse-field Ising model, more detailed information can be extracted on the distribution of kink numbers as follows [36,52].…”

“…The Gaussian distribution Eq. (5) follows from setting to zero all cumulants κ q with q 3, a reasonable approximation as their value is much smaller than κ 1 and κ 2 ; see [36,52,60].…”

“…See also Ref. [36]. One of the important predictions of these references is that the ratio of the qth cumulant κ q (q 2) to the first cumulant κ 1 , the average, is independent of the annealing time t a [Eq.…”

“…As the dominant paradigm to describe the universal dynamics of a quantum phase transition, it has motivated a wide variety of experimental and theoretical studies [29][30][31][32]. Laboratory tests of the KZM in quantum platforms have been carried out pursuing different quantum simulation approaches, e.g., using qubits to emulate free fermion models [33][34][35][36] and via a fully digital approach using Rydberg atoms [37].…”