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Topological Defect Formation and Dynamics in Ion Coulomb Crystals

Topological Defect Formation and Dynamics in Ion Coulomb Crystals. Tanja E. Mehlstäubler. K. Pyka, J. Keller , H. L. Partner, T. Burgermeister, D.M. Meier, K. Kuhlmann. Center for Qu antum E ngineering and S pace T ime Research (QUEST) Physikalisch-Technische Bundesanstalt, Braunschweig.

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Topological Defect Formation and Dynamics in Ion Coulomb Crystals

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  1. Topological Defect Formation and Dynamics in Ion Coulomb Crystals Tanja E. Mehlstäubler K. Pyka, J. Keller, H. L. Partner, T. Burgermeister, D.M. Meier, K. Kuhlmann Center for Quantum Engineering and Space Time Research (QUEST) Physikalisch-Technische Bundesanstalt, Braunschweig Ramil Nigmatullin, Alex Retzker, Martin Plenio, Adolfo del Campo, Wojciech Zurek Universität Ulm, Hebrew University Jerusalem, Los Alamos NL iQSim13 – Brighton, December 2013

  2. Short History of the Lab... 2010 2009 This Talk: results 2012/13 2011

  3. Motivation Instability of frequency standard: with t: averaging time NA: number of atoms 3x10-15 @1s t = 150 ms Dn: linewidth clocklaser multiple ions? 100 days 1 day

  4. Motivation Precision Spectroscopy on many ions ? unite Al+/Mg+ QL-clock Multi-ion clocks Entangled ion clocks ? single Yb+-ion

  5. 2D Paul ion traps • Axial micromotion? URF! UDC UDC URF ! Radial direction: S0 P0

  6. Challenges • On-axis micromotion • e.g. Al+ clock → Dn/n = -3×10-17 over Dl=3 µm observed (1) trap (1) C. W. Chou et al., PRL (2010) 070802

  7. On-axis rf trap fields FEM calculations of RF-potential GND URF Tolerance on notches Finite length effect on rf field 10-18 10-18 N. Herschbach et al., Appl. Phys. B (2012)

  8. Scalable ion clock with high control of ion motion • Compensated micromotion in all 3D • 3D laser access • Separated loading and spectroscopy segment almost ideal quadrupole trap: Loss factor L = 1.2 RF extra compensation layer RF

  9. Trap Prototype (Rogers 4350B) Trap stack with OFHC Cu Foil aligned under Zeiss microscope D< 20µm Optocast 3410 Gen2: UV+heat cured Pyka et al., Appl. Phys.B (2013)

  10. Trap Prototype (Rogers 4350B) 200µm 2mm lasered electrodes Trap stack with OFHC Cu Foil low pass filter (RC)-1 = 110 Hzx 2p non magnetic SMD resistors+capacitors (Kester solder) bonded gold wires d= 30µm Pyka et al., Appl. Phys.B (2013)

  11. High-end trap „High-accuracy optical clocks with trapped ions“ Finland (MIKES), Czech Republic (CMI), United Kingdom (NPL), Germany (PTB/QUEST) laser machined ALN ceramic wafers: • improved thermal conductivity: 160 Wm-1K-1 • mechanical stability • higher breakdown threshold Temperature Sensor

  12. First Test of the Prototype Trap with 172Yb+ ! New experiment to test and evaluate traps and Coulomb crystals • with Yb+: life time of several days observed 1. Shuttling of ions 2. 172Yb+ Coulomb crystals 1 2 3

  13. Measuring Micromotion in 3D - Setup 3D laser access!

  14. Photon-Correlation Spectroscopy DS/Smax = 0.01 DEDC = 0.9 mV/mm Dx ~ 50 nm Test: move ion in radial rf potential ! 2nd order Doppler shift / Time dilation:

  15. Axial Micromotion in Rogers Trap move ion along trap axis: Time dilation shift: ! DC Stark-shift √ Sensitivity < 10-19 demonstrated 12 ions stored with time dilation shift below 10-18 √ Pyka et al., Appl. Phys.B (2013)

  16. Coulomb crystals in well-controlled environment Linear - Zigzag - Helix ca. 80 ions

  17. Topological Defect Formation in Ion Coulomb Crystals Landa, H., Marcovitch, S., Retzker, A., Plenio, M. B., Reznik, B. “Quantum Coherence of Discrete Kink Solitons in Ion Traps”, PRL104, 043004 (2010). • Quantum information • Solitonphysics in Coulomb crystals

  18. Topological Defect Formation in Ion Coulomb Crystals Landa, H., Marcovitch, S., Retzker, A., Plenio, M. B., Reznik, B. “Quantum Coherence of Discrete Kink Solitons in Ion Traps”, PRL 104, 043004 (2010). C. Schneider, D. Porras, and T. Schaetz, Rep. Prog. Phys. 75, 024401 (2012). exp. kinks? Del Campo, A., De Chiara, G., Morigi, G., Plenio, M. B., Retzker, A. “Structural Defects in Ion Chains by Quenching the External Potential: The Inhomogeneous Kibble-Zurek Mechanism”, PRL 105, 075701 (2010). Kibble-Zurek?

  19. Ion Coulomb Crystals 1 D Trap Potential 2 D 3 D

  20. Symmetry breaking phase transitions What happens when a system changes from one equilibrium condition to another? • Examplesforphasetransitions: • - waterfreezestoice • - ferro-magnetism para-magnetism • - metalsuperconductor • - earlyuniverse Higgs field Nature Physics 7, 2 (2011) doi:10.1038/nphys1874

  21. Symmetry breaking in ion Coulomb crystals Rotational symmetry Mirror symmetry  defects 2nd order phase transition1 1: Fishman et al., PRB 77, 064111 (2008)

  22. Examples for defects in other systems Regions with different orientation of the electric charges in yttrium manganite (white and black areas correspond to a positiver and negative charge distribution, respectively). The star-shaped intersections where bright and dark regions meet are the defects corresponding to the cosmic strings. - ferro-electricdomains in solid statesystems (manganites) - earlyuniverse: appearanceofdomains? jpl.nasa.gov Griffin, S. M. et al.,Phys. Rev. X2, 041022 (2012)

  23. The Kibble-Zurek Mechanism 1976: Tom Kibble postulates the appearance of domains in the early Universe 1985: Wojciech Zurek proposes to test cosmology in super-liquid helium universal theory applicable to all 2nd order phase transitions Chuang et al., Science (1991) Ruutu et al., Nature (1996) Sadler et al., Nature (2006) Weiler et al., Nature (2008) Griffin et al.,Phys. Rev. X(2012) liquid crystals super-liquid helium Bose-Einstein condensates superconductors

  24. The Kibble-Zurek Mechanism 1976: Tom Kibble postulates the appearance of domains in the early Universe 1985: Wojciech Zurek proposes to test cosmology in super-liquid helium universal theory applicable to all 2nd order phase transitions → test in laser-cooled ion Coulomb crystals! • high sensitivitytocontrolparameter • well-definedcriticalexponents• high controlof environmental parameters

  25. The Kibble-Zurek Mechanism

  26. The Kibble-Zurek Mechanism

  27. The Kibble-Zurek Mechanism test of KZM with defined n, z del Campo et al., PRL 105, 075701 (2010) Fishman et al., PRB 77, 064111 (2008)

  28. The Kibble-Zurek Mechanism Prediction of KZM Power law scaling of defect density: test of KZM with defined n, z

  29. Inhomogeneous Systems • harmonictrap: • positiondependenttransition

  30. Inhomogeneous Systems • harmonictrap: • positiondependenttransition • movingtransition front • comparevFwithvSound „Causality enhancement“

  31. Inhomogeneous Systems finite size - 3 regimes „Causality enhancement“ ln[d] ln[d] • homogeneous KZM • inhomogeneous KZM • max. 1 defect  doubled: simulationof 30 ions -ln [tQnax] -ln [tQnax] Saito et al., Phys. Rev. A 76, 043613 (2007) Dziarmaga et al., Phys. Rev. Lett. 101, 115701 (2008) Monaco et al., Phys. Rev. B 80, 180501(R) (2009)

  32. Non adiabatic radial quenches • confinementto 2D: • nt1/nt2 = 1.3 • mixernonlinearity •  correctionstotQ,eff • monitor radial frequencies Radial trap frequencies

  33. Different types of defects Localized kink for Extended kink for • same statistics, lower losses

  34. Examples of kink creation

  35. Stabilityoftopologicaldefects! Peierls-Nabarro Potentials:

  36. Creatingstabletopologicaldefectsfor KZM! Shallow ramps: Odd kink Deep ramps: extended kink • Same statisticsfor d < 1 • Collision limited lifetime: ca. 1.6 s • Spontaneouskinkcreation rate: • 1 every 67 s

  37. Understanding kinkdynamics – short time scales • Kink lossesatshort • time scales – simulations! Simulations for different friction parameters - Kibble-Zurek filled symbols: created empty symbols: surviving • Frictionindependent • kinkcreation rate • → underdampedregime! Pyka et al., arXiv:1211.7005 (2012)

  38. Test of Kibble-Zurek Scaling light grey: simulations • Theory: • 8/3  2.67 • Simulations: • 2.63 ± 0.13 • Experiment: • 2.7 ± 0.3 Pyka et al., Nat. Commun. 4, 2291 (2013)

  39. Test of Kibble-Zurek Scaling light grey: simulations • Theory: • 8/3  2.67 • Simulations: • 2.63 ± 0.13 • Experiment: • 2.7 ± 0.3 Pyka et al., Nat. Commun. 4, 2291 (2013) Ulm et al., Nat. Commun. 4, 2290 (2013)

  40. Kink Motion

  41. Motion of Kinks - Simulations odd kink PN potential / kB mK x / µm quench extended kink PN potential / kB mK x / µm

  42. Motion of Kinks - Experiment motion of localized kink motion of extended kink

  43. Influence of Mass Defects

  44. Massdefects Defect scaling with molecules YbOH+

  45. Massdefects Spatial distribution of kinks two kinks – kink interaction!

  46. Massdefects Spatial distribution of kinks extended kink: two kinks: odd kink:

  47. Mass defects: kink creation rate + stability Created kinks Detectable kinks !

  48. Deterministic Control of Kinks with Mass Defects & Electric Fields

  49. Oscillation and stabilization by mass defects Credit: R. Nigmatullin

  50. Oscillation and stabilization by mass defects Credit: R. Nigmatullin

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