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Sci Rep. 2016 Mar 8;6:22667. doi: 10.1038/srep22667.

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

Gong M1,2, Wen X3, Sun G4,5, Zhang DW6, Lan D1, Zhou Y4, Fan Y4, Liu Y1, Tan X1, Yu H1,5, Yu Y1,5, Zhu SL1,5, Han S2, Wu P4,5.

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National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China.
Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA.
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China.
Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China.


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 speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.

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