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

QUEST - Centre for Quantum Engineering and Space-Time ResearchQUEST - Centre for Quantum Engineering and Space-Time Research

Short History of the Lab...

20092010

2011This Talk: results 2012/13

= 150 ms

1 day

100 days

c

A

TNQ

11Instability of

frequency standard:

Qwith

3x10-15 @1s

multiple ions?

clock laser

: averaging time

NA: number of atoms

: linewidth

Motivation

Precision Spectroscopy on many ions ?

Al+/Mg+ QL-clock

single Yb+-ion?

Multi-ion clocksEntangled ion clocks

Motivation

unite

2D Paul ion traps

URF !

UDC

UDC

URF ! Axial micromotion?

Radial direction:

S0 P0

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

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

10-1810-18

GND

URF

Scalable ion clock with high control of ion motion

RF

RFextracompensationlayer

Compensated micromotion in all 3D 3D laser access Separated loading and spectroscopy segment

almost idealquadrupole trap:

Loss factor L = 1.2

Trap Prototype (Rogers 4350B)

Trap stack with OFHC Cu Foilaligned under Zeiss microscope < 20µm

Optocast 3410 Gen2: UV+heat cured

Pyka et al., Appl. Phys.B (2013)

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)

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

TemperatureSensor

First Test of the Prototype Trap with 172Yb+ !

New experiment to test and evaluate traps and Coulomb crystals

2. 172Yb+ Coulomb crystals

1 2 3

1. Shuttling of ions

• with Yb+: life time of several days observed

Measuring Micromotion in 3D - Setup

3D laser access!

Test: move ion in radial rf potential !

S/Smax = 0.01EDC = 0.9 mV/mmx ~ 50 nm

Photon-Correlation Spectroscopy

202

2

105.82

cv

2nd order Doppler shift /Time dilation:

Axial Micromotion in Rogers Trap

move ion along trap axis:

1810²

mcEkin

!

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 √

Coulomb crystals in well-controlled environment

ca. 80 ions

Linear-

Zigzag-

Helix

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

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

Ion Coulomb Crystals

Trap Potential1 D

2 D

3 D

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

Symmetry breaking in ion Coulomb crystals

Rotational symmetry Mirror symmetry

defects

1: Fishman et al., PRB 77, 064111 (2008) 2nd order phase transition1

- 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.n

asa.

gov

Examples for defects in other systems

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 crystalssuper-liquid heliumBose-Einstein condensatessuperconductors

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)

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

The Kibble-Zurek Mechanism

sizesystem

The Kibble-Zurek Mechanism

sizesystem

The Kibble-Zurek Mechanism

del Campo et al., PRL 105, 075701 (2010) Fishman et al., PRB 77, 064111 (2008)

sizesystem

test of KZM with defined , z

The Kibble-Zurek Mechanism

Prediction of KZM

Power law scaling of defect density:

test of KZM with defined , z

Inhomogeneous Systems

• harmonic trap: position dependent transition

Inhomogeneous Systems

• harmonic trap: position dependent transition

• moving transition front• compare vF with vSound

„Causality enhancement“

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 [Qax]

ln

[d]

-ln [Qax]

ln

[d]

simulation of 30 ions

„Causality enhancement“

Non adiabatic radial quenches

• confinement to 2D:t1/t2 = 1.3

• mixer nonlinearity corrections to Q,eff

• monitor radial frequencies

Radial trap frequencies

Localized kink for

Extended kink for

• same statistics, lower losses

Different types of defects

Examples of kink creation

Stability of topological defects!

Peierls-NabarroPotentials:

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

Understanding kink dynamics – short time scales

Pyka et al., arXiv:1211.7005 (2012)

• Kink losses at short time scales – simulations!

filled symbols: createdempty symbols: surviving

•Friction independent kink creation rate

→ underdamped regime!

- Kibble-Zurek

Simulations for different friction parameters

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)

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)

Kink Motion

Motion of Kinks - Simulations

quench

PN

pot

entia

l / k

B m

K

x / µm

PN

pot

entia

l / k

B m

K

x / µm

odd kink

extended kink

Motion of Kinks - Experiment

motion of localized kink

motion of extended kink

Influence of Mass Defects

Mass defects

Defect scaling with molecules YbOH+

Mass defects

Spatial distribution of kinks

two kinks – kink interaction!

Mass defects

Spatial distribution of kinks

extended kink:

odd kink:

two kinks:

Created kinks Detectable kinks

Mass defects: kink creation rate + stability

!

Deterministic Control of Kinks with Mass Defects & Electric Fields

Oscillation and stabilization by mass defects

Credit: R. Nigmatullin

Oscillation and stabilization by mass defects

Credit: R. Nigmatullin

Oscillation and stabilization by mass defects

Experiment

Electric Fields and Mass Defects

Creating a kink without a quench!E-field ramp

time

Creating Kink & Anti-Kink!

Partner et al., New J. Phys. 15, 103013 (2013)

E-field ramp

Summary

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

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)

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)

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)

411 nm23 Hz

1S0, F = 9/2

3P0

3P1

236.5 nm

230.5 nm

159 nm = 360 kHz

= 0.8 Hz

= 194 MHz1P1

~ years!

115In+

172Yb+

Two-Species System In+ / Yb+

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)

In cooperation with: E. Peik, P. O. Schmidtvisiting scientists: L. Yi, S. Ignatovich

Karsten PykaT.E.M.

The Experimentalist Team:

David MeierJonas Keller

European Network „Ion Traps for Tomorrow's Applications“DPG bilateral grant with RFBREMRP JRP„Optical Clocks with Trapped Ions“

www.quantummetrology.de

Kristijan Kuhlmann

Lin Yi

Funding:

Stepan Ignatovich(visiting scientist,

detail)

Keshav Thirumalai Heather PartnerTobias Burgermeister