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
QUEST - Centre for Quantum Engineering and Space-Time Research
Short History of the Lab...
2010
2009
This Talk:
results 2012/13
2011
Motivation
Instability of
frequency standard:
 
1

Q
T
1
 c
t
NA
with
Q


t: averaging time
3x10-15 @1s
NA: number of atoms
t = 150 ms
n: linewidth
clock laser
multiple ions?
100
days
1 day
Motivation
Precision Spectroscopy on many ions ?
unite
Al+/Mg+ QL-clock
Multi-ion clocks
Entangled ion clocks
single Yb+-ion
?
2D Paul ion traps
 Axial micromotion?
Radial direction:
URF !
UDC
UDC
URF !
S0  P0
Challenges
 On-axis micromotion
e.g. Al+ clock → n/n = -3×10-17 over l=3 µm observed  (1)
(1) C. W. Chou et al., PRL (2010) 070802
trap
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)
Scalable ion clock with high control of ion motion
 Compensated micromotion in all 3D
 3D laser access
 Separated loading and spectroscopy segment
RF
extra
compensation
layer
RF
almost ideal
quadrupole trap:
Loss factor L = 1.2
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)
Trap Prototype (Rogers 4350B)
200µm
2mm
lasered electrodes
Trap stack with OFHC Cu Foil
low pass filter (RC)-1 = 110 Hz x 2p
non magnetic SMD resistors+capacitors (Kester solder)
bonded gold wires d= 30µm
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
Temperature
Sensor
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
1
2
3
2. 172Yb+ Coulomb crystals
Measuring Micromotion in 3D - Setup
3D laser access!
Photon-Correlation Spectroscopy
S/Smax = 0.01
EDC = 0.9 mV/mm
x ~ 50 nm
Test: move ion in radial rf potential !
2nd order Doppler shift /
Time dilation:

v2
  2  8.5 1020

2c
Axial Micromotion in Rogers Trap
move ion along trap axis:
Time dilation shift:



Ekin
 10 18
mc²
DC Stark-shift
!
√
Sensitivity < 10-19 demonstrated
12 ions stored with time dilation shift below 10-18  √
Pyka et al., Appl. Phys.B (2013)
Coulomb crystals in well-controlled environment
Linear
Zigzag
Helix
ca. 80
ions
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
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?
Ion Coulomb Crystals
1D
2D
3D
Trap Potential
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
Higgs field
Nature Physics 7, 2 (2011) doi:10.1038/nphys1874
Symmetry breaking in ion Coulomb crystals
Rotational symmetry
Mirror symmetry
defects 
1: Fishman et al., PRB 77, 064111 (2008)
2nd order phase transition1
Examples for defects in other systems
Griffin, S. M. et al., Phys. Rev. X 2, 041022 (2012)
jpl.nasa.gov
- ferro-electric domains in solid state systems (manganites)
- early universe: appearance of domains?
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
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 sensitivity to control parameter
• well-defined critical exponents
• high control of environmental parameters
The Kibble-Zurek Mechanism

system size
The Kibble-Zurek Mechanism

system size
The Kibble-Zurek Mechanism

system size
test of KZM with defined n, z
del Campo et al., PRL 105, 075701 (2010)
Fishman et al., PRB 77, 064111 (2008)
The Kibble-Zurek Mechanism
Prediction of KZM
Power law scaling of defect density:
test of KZM with defined n, 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
„Causality enhancement“
ln[d]
ln[d]
finite size - 3 regimes
simulation of 30 ions
-ln [tQnax]
-ln [tQnax]
• 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)
Non adiabatic radial quenches
• confinement to 2D:
nt1/nt2 = 1.3
• mixer nonlinearity
corrections to tQ,eff
• monitor radial frequencies
Radial trap frequencies
Different types of defects
Localized kink for
Extended kink for
• same statistics, lower losses
Examples of kink creation
Stability of topological defects!
Peierls-Nabarro
Potentials:
Creating stable topological defects for KZM!
Shallow ramps: Odd kink
Deep ramps: extended kink
• Same statistics for d < 1
• Collision limited lifetime: ca. 1.6 s
• Spontaneous kink creation rate:
1 every 67 s
Understanding kink dynamics – short time scales
• Kink losses at short
time scales – simulations!
Simulations for different friction parameters
- Kibble-Zurek
• Friction independent
kink creation rate
→ underdamped regime!
filled symbols: created
empty symbols: surviving
Pyka et al., arXiv:1211.7005 (2012)
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)
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)
Kink Motion
Motion of Kinks - Simulations
PN potential / kB mK
odd kink
x / µm
quench
PN potential / kB mK
extended kink
x / µm
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:
two kinks:
odd kink:
Mass defects: kink creation rate + stability
Created kinks
Detectable kinks
!
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!
time
E-field ramp
Creating Kink & Anti-Kink!
E-field ramp
Partner et al., New J. Phys. 15, 103013 (2013)
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)
Two-Species System In+ / Yb+
g = 194 MHz
115In+
1P
1
159 nm
g = 360 kHz
3P
1
230.5 nm
3P
0
172Yb+
g = 0.8 Hz
236.5 nm
1S ,
0
411 nm
23 Hz
t ~ years!
F = 9/2
Spectroscopy Lasers
Keller et al., Appl. Phys. B (2013)
Stable Laser System n < 1Hz!
Ground-State Cooling of Coulomb Crystal
+ Precision Spectroscopy
+ Mode Structure of mixed crystals (In+ & Yb+)
4 x 10-16
411 nm
The Experimentalist Team:
Lin Yi
T.E.M.
Kristijan Jonas Keller Karsten Pyka Tobias Burgermeister
Kuhlmann Keshav Thirumalai Heather Partner David Meier
In cooperation with:
visiting scientists:
Funding:
E. Peik, P. O. Schmidt
L. Yi, S. Ignatovich
European Network „Ion Traps for Tomorrow's Applications“
DPG bilateral grant with RFBR
EMRP JRP„Optical Clocks with Trapped Ions“
www.quantummetrology.de
Stepan Ignatovich
(visiting scientist,
detail)