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

2. QUEST - Centre for Quantum Engineering and Space-Time Research Short History of the Lab... 2009 2010 2011 This Talk: results 2012/13

3.  = 150 ms 1 day 100 days Instability of frequency standard: with 3x10 -15 @1s multiple ions? clock laser  : averaging time N A : number of atoms  : linewidth Motivation

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

5. 2D Paul ion traps U RF ! U DC U RF !  Axial micromotion? Radial direction: S0  P0S0  P0

6. Challenges  On-axis micromotion e.g. Al + clock →  = -3×10 -17 over  l=3 µm observed  (1) (1) C. W. Chou et al., PRL (2010) 070802 trap

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

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

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

10. Trap Prototype (Rogers 4350B) Trap stack with OFHC Cu Foil lasered electrodes 200µm 2mm non magnetic SMD resistors+capacitors (Kester solder) bonded gold wires d= 30µm low pass filter (RC) -1 = 110 Hz x 2  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 -1 K -1  mechanical stability  higher breakdown threshold Temperature Sensor

12. First Test of the Prototype Trap with 172 Yb + ! New experiment to test and evaluate traps and Coulomb crystals 2. 172 Yb + Coulomb crystals 123 1. Shuttling of ions with Yb + : life time of several days observed

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

14. Test: move ion in radial rf potential !  S/S max = 0.01  E DC = 0.9 mV/mm  x ~ 50 nm Photon-Correlation Spectroscopy 2 nd order Doppler shift / Time dilation:

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

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

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”, PRL 104, 043004 (2010). Quantum information Soliton physics in Coulomb crystals

18. 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). 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? exp. kinks? Topological Defect Formation in Ion Coulomb Crystals

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

20. Symmetry breaking phase transitions What happens when a system changes from one equilibrium condition to another? Examples for phase transitions: - water freezes to ice - ferro-magnetism  para-magnetism - metal  superconductor - early universe Nature Physics 7, 2 (2011) doi:10.1038/nphys1874 Higgs field

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

22. - ferro-electric domains in solid state systems (manganites) - early universe: appearance of domains? Griffin, S. M. et al., Phys. Rev. X 2, 041022 (2012) jpl.nasa.gov 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.

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 liquid crystals super-liquid helium Bose-Einstein condensates superconductors 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)

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

25. The Kibble-Zurek Mechanism

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

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

29. Inhomogeneous Systems harmonic trap: position dependent transition

30. Inhomogeneous Systems harmonic trap: position dependent transition moving transition front compare v F with v Sound „Causality enhancement“

31. Inhomogeneous Systems finite size - 3 regimes homogeneous KZM inhomogeneous KZM max. 1 defect  doubled: 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) -ln [  Q ax ] ln[d] -ln [  Q ax ] ln[d] simulation of 30 ions „Causality enhancement“

32. Non adiabatic radial quenches confinement to 2D:  t1 / t2 = 1.3 mixer nonlinearity  corrections to  Q,eff monitor radial frequencies Radial trap frequencies

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

34. Examples of kink creation

35. Stability of topological defects! Peierls-Nabarro Potentials:

36. Creating stable topological defects for KZM! Same statistics for d < 1 Collision limited lifetime: ca. 1.6 s Spontaneous kink creation rate: 1 every 67 s Shallow ramps: Odd kink Deep ramps: extended kink

37. Understanding kink dynamics – short time scales Pyka et al., arXiv:1211.7005 (2012) Kink losses at short time scales – simulations! filled symbols: created empty symbols: surviving Friction independent kink creation rate → underdamped regime! - Kibble-Zurek Simulations for different friction parameters

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

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

40. Kink Motion

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

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

43. Influence of Mass Defects

44. Mass defects Defect scaling with molecules YbOH +

45. Mass defects Spatial distribution of kinks two kinks – kink interaction!

46. Mass defects Spatial distribution of kinks extended kink: odd kink: two kinks:

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

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

51. Oscillation and stabilization by mass defects Experiment

52. Electric Fields and Mass Defects Creating a kink without a quench! E-field ramp time

53. Creating Kink & Anti-Kink! Partner et al., New J. Phys. 15, 103013 (2013) E-field ramp

54. Summary created stable types of kinks by adiabatic quenches demonstrated different stability and motional properties deterministic creation and control of kinks via mass defects

55. Outlook Soliton physics with laser cooled ions defects behave like quasi-particles Entanglement generation using kink solitons: Landa et al., arXiv:1308.2943(2013) Trapping of 2D & 3D kinks: Mielenz et al., PRL (2013) Long coherence times of localized internal modes: Landa et al., PRL (2010)

56. Outlook Soliton physics with laser cooled ions defects behave like quasi-particles Entanglement generation using kink solitons: Landa et al., arXiv:1308.2943(2013) Trapping of 2D & 3D kinks: Mielenz et al., PRL (2013) Long coherence times of localized internal modes: Landa et al., PRL (2010)

57. Outlook Soliton physics with laser cooled ions defects behave like quasi-particles investigation of heat transport  optical frequency standard quantum thermodynamics Bermudez, A., Bruderer, M. & Plenio, M. B. PRL (2013)

58. 411 nm 23 Hz 1 S 0, F = 9/2 3P03P0 3P13P1 236.5 nm 230.5 nm 159 nm  = 360 kHz  = 0.8 Hz  = 194 MHz 1P11P1  ~ years! 115 In + 172 Yb + Two-Species System In + / Yb +

59. Stable Laser System  < 1Hz! Ground-State Cooling of Coulomb Crystal + Precision Spectroscopy + Mode Structure of mixed crystals (In + & Yb + ) Spectroscopy Lasers 411 nm 4 x 10 -16 Keller et al., Appl. Phys. B (2013)

60. In cooperation with:E. Peik, P. O. Schmidt visiting scientists:L. Yi, S. Ignatovich Karsten PykaT.E.M. The Experimentalist Team: David Meier Jonas Keller European Network „Ion Traps for Tomorrow's Applications“ DPG bilateral grant with RFBR EMRP JRP„Optical Clocks with Trapped Ions“ www.quantummetrology.de Kristijan Kuhlmann Lin Yi Funding: Stepan Ignatovich (visiting scientist, detail) Keshav ThirumalaiHeather Partner Tobias Burgermeister