Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

S. Ulm; J. Roßnagel; G. Jacob; C. Degünther; S. T. Dawkins; U. G. Poschinger; R. Nigmatullin; A. Retzker; M. B. Plenio; F. Schmidt-Kaler; K. Singer

doi:10.1038/ncomms3290

Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

S. Ulm, J. Roßnagel, G. Jacob, C. Degünther, S. T. Dawkins, U. G. Poschinger, R. Nigmatullin, A. Retzker, M. B. Plenio, F. Schmidt-Kaler, K. Singer

Racah Institute of Physics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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 γ^β, 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.

Original language	English
Article number	2290
Journal	Nature Communications
Volume	4
DOIs	https://doi.org/10.1038/ncomms3290
State	Published - 2013

All Science Journal Classification (ASJC) codes

General Chemistry
General Biochemistry,Genetics and Molecular Biology
General Physics and Astronomy

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title = "Observation of the Kibble-Zurek scaling law for defect formation in ion crystals",

abstract = "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.",

author = "S. Ulm and J. Ro{\ss}nagel and G. Jacob and C. Deg{\"u}nther and Dawkins, \{S. T.\} and Poschinger, \{U. G.\} and R. Nigmatullin and A. Retzker and Plenio, \{M. B.\} and F. Schmidt-Kaler and K. Singer",

note = "Funding Information: 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 {\textquoteleft}Non-linear dynamics in ultra-cold trapped ion crystals{\textquoteright}. A.R. acknowledges the carrier integration grant (CIG) no. 321798. R.N. was supported by the EPSRC Doctoral Training Center for Controlled Quantum Dynamics.",

year = "2013",

doi = "10.1038/ncomms3290",

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journal = "Nature Communications",

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T1 - Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

AU - Ulm, S.

AU - Roßnagel, J.

AU - Jacob, G.

AU - Degünther, C.

AU - Dawkins, S. T.

AU - Poschinger, U. G.

AU - Nigmatullin, R.

AU - Retzker, A.

AU - Plenio, M. B.

AU - Schmidt-Kaler, F.

AU - Singer, K.

N1 - Funding Information: 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.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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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DO - 10.1038/ncomms3290

M3 - مقالة

SN - 2041-1723

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JO - Nature Communications

JF - Nature Communications

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ER -

Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

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