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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. - PowerPoint PPT Presentation
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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