Symmetry Breaking and Topological

Defect Formation in Ion Coulomb Crystals

Center for Quantum Engineering and Space Time Research (QUEST)

Physikalisch-Technische Bundesanstalt, Braunschweig

Tanja E. Mehlstäubler

ECRYS 2014, Cargese, 12. August 2014

Ramil Nigmatullin, Alex Retzker, Martin Plenio,

Adolfo del Campo, Wojciech ZurekUniversität Ulm, Hebrew University Jerusalem, Los Alamos NL

J. Keller, K. Pyka, H. L. Partner, T. Burgermeister, D.M. Meier, K. Kuhlmann

~ 2000 employees

PTB – national metrology institute

Braunschweig

Founded 1887:by Werner von Siemensand Hermann von Helmholtz

3D-Paul trap

single Yb+-ion

Time & Frequency Metrology

Nobel Prize 2012: Dave Wineland (NIST)“for groundbreaking experimental methods, that allow tomanipulate and measure single quantum systems.”

νsec

~10 nm

Trap Depth ~ 104 K

Yb+ ion clock: ∆ν/ν = 4 x 10-18

Single ion as atomic reference

(1) priv. comm. E. Peik

single Yb+-ion

Multi-ion clocks

Coulomb crystal of Yb+-ions

Now needed: „experimental methods, that allow to manipulate and measure many-body quantum systems.”

?

Quantum Metrology ↔ Quantum Simulation & Information

Scalable Ion Trap Prototype

Trap stack with OFHC Cu Foil

Low pass filters

N. Herschbach et al., Appl. Phys. B 107, 891 (2012)Pyka et al., Appl. Phys. B (2013), DOI: 10.1007/s00340-013-5580-5

� low micromotion

� non-magnetic

� UHV proof

� 3D laser access

Experimental Setup

• Single-ion resolution• 3D laser access!

Coulomb crystals in well-controlled environment

ca. 80 ions

172Yb+ Coulomb crystals

Phases of Coulomb Crystals (172Yb+)

Coulomb crystals:

Ekin < Epot

With simple Doppler laser cooling:

T = 1 mK

Symmetry Breaking and

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).

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).

Ion Coulomb Crystals

Trap Potential1 D

2 D

3 D

Fishman et al., PRB 77, 064111 (2008)

Example: linear to zigzag transition

Phonon SpectrumEigenmodes across phase transition

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 Ø para-magnetism- metal Ø 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

νt(t)

Ψ

U

Ψ

U

- 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 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)

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!

universal theory applicable to all

2nd order phase transitions

The Kibble-Zurek Mechanism

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

sizesystem

ξ

test of KZM with defined ν, z

The Kibble-Zurek Mechanism

Prediction of KZM

Power law scaling of defect density:

test of KZM with defined ν, z

Harmonic Ion Traps – Inhomogeneous Case

Inhomogeneous and finite system!

Harmonic Ion Traps – Inhomogeneous Case

• Ions in harmonic potential:phase transition spreads out from center!

• Phase front faster than speed of sound!

Del Campo, A., De Chiara, G., Morigi, G., Plenio, M. B., Retzker, A.,PRL 105, 075701 (2010).

Prediction:

Log

[Pro

babi

lity]

- Log [Duration of Ramp]

ion traps

The Kibble-Zurek Mechanism

Experiment: non adiabatic radial quenches

exp. details in

Pyka et al.,

Nat. Comm 4,

2291 (2013)

Radial trap frequencies

Examples of kink creation

Demonstration of stable defects in Coulomb crystals!

Localized (Odd) Defect

Extended Defect

Collision limited lifetime: ca. 1.6 s

νt1/νt2 = 1.3

Understanding kink dynamics – short time scales

• Kink losses at short

time scales – simulations!

filled symbols: created

empty symbols: surviving

Friction independent

kink creation rate

→ underdamped regime! ν = ½; z = 1

- Kibble-Zurek

Simulations for different friction parameters

Scaling of defect density with quench time

• Theory(1):

8/3 º 2.67

• Experiment:

2.7 ± 0.3

excluded by simulations

Pyka et al., Nat. Com. 4, 2291 (2013) BS

Ulm et al., Nat. Com. 4, 2290 (2013) Mainz

G. Nikoghosyan et al., „Universality in the

dynamics of second-order phase transitions”,

arXiv:1311.1543 (2013)

(1) del Campo et al., PRL 105, 075701 (2010)

Kink Dynamics

Stability of topological defects

Peierls-Nabarro

Potentials:

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

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

Spatial distribution of kinks

two kinks – kink interaction!

Mass defects

extended kink:

odd kink:

two kinks:

The Peierls-Nabarro Potential:

Radial (ponderomotive) trapping potential:

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

Deterministic Control of Kinks

with Mass Defects & Electric Fields

Combine Kink Oscillation

& Mass Defect

Thermally activated Oscillation of Kink

credit: R. Nigmatullin

Kink = higher charge density

Oscillation and stabilization by mass defects

II: Electric Fields and Mass Defects

creating kink & anti-kink without a quench

E-field ramptime

II: E-field Creating Kink & Anti-Kink

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

E-field ramp

time

Outlook

- Applications

Outlook – quantum information

• Soliton physics with laser cooled ions

defects behave like quasi-particles

Long coherence times of localized internal modes:Landa et al., PRL (2010)

Trapping of 2D & 3D kinks:Tobias Schätz, Uni FreiburgMielenz et al., PRL (2013)

Outlook – quantum information

• Soliton physics with laser cooled ions

defects behave like quasi-particles

Long coherence times of localized internal modes:Landa et al., PRL (2010)

Trapping of 2D & 3D kinks:Tobias Schätz, Uni FreiburgMielenz et al., PRL (2013)

Outlook – quantum information

• 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 – Friction / Frenkel-Kontorova

• tribology with ion Coulomb crystals

• observing Aubry transition

Peyrard and Aubry, J. Phys. C 16, 1593 (1983)Pruttivarasin et al., N. J. Phys. 13, 075012 (2011)Benassi et al., Nat. Commun. 2, 236 (2011)

Outlook – heat transport

• investigation of heat transport

Ø optical frequency standard

• quantum thermodynamics

Bermudez, A., Bruderer, M. & Plenio, M. B. PRL (2013)

1S0, F = 9/2

3P0

3P1

236.5 nm

230.5 nm

159 nm γ = 360 kHz

γ = 0.8 Hz

γ = 194 MHz1P1

115In+

172Yb+

Coulomb crystal with impurities (In+ / Yb+)

Crystal modes

411 nm

• Sideband spectroscopy + Ground state preparation

• Coherent laser-atom interaction:

Spectroscopy of internal DOFs / spin of ions

Jaynes-Cummings Hamiltonian:

Spectroscopy of internal DOFs / spin of ions

5 x 10-16

→ Keep length between cavity mirrorsconstant to < 0.05 fm !

• Sideband spectroscopy + Ground state preparation

• Coherent laser-atom interaction:

Bermudez, A., Bruderer, M. & Plenio, M. B. PRL (2013)

First observed Rabi-flops:

Spectroscopy of internal DOFs / spin of ions

T ~ 1 mK

T ~ 50 µK

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

Funding:

Keshav Thirumalai Heather Partner

Tobias Burgermeister