Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble-Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γβ, where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.
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We acknowledge helpful discussions with John Goold. The Mainz team acknowledges support by the Volkswagen-Stiftung, the DFG-Forschergruppe (FOR 1493) and the EU-project DIAMANT (FP7-ICT). M.B.P. acknowledges support provided by the EU STREP Project PICC (FP7-ICT), the Alexander von Humboldt Professorship and the GIF project ‘Non-linear dynamics in ultra-cold trapped ion crystals’. A.R. acknowledges the carrier integration grant (CIG) no. 321798. R.N. was supported by the EPSRC Doctoral Training Center for Controlled Quantum Dynamics.