Symmetry Breaking and Topological Defect Formation in Ion

Symmetry Breaking and Topological
Defect Formation in Ion Coulomb Crystals
Tanja E. Mehlstäubler
J. Keller, K. Pyka, 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
ECRYS 2014, Cargese, 12. August 2014
PTB – national metrology institute
Braunschweig
~ 2000 employees
Founded 1887:
by Werner von Siemens
and Hermann von Helmholtz
Time & Frequency Metrology
Single ion as atomic reference
Trap Depth ~ 104 K
νsec
single Yb+-ion
3D-Paul trap
Yb+ ion clock: ∆ν/ν = 4 x 10-18
Nobel Prize 2012: Dave Wineland (NIST)
“for groundbreaking experimental methods, that allow to
manipulate and measure single quantum systems.”
(1)
priv. comm. E. Peik
~10 nm
Multi-ion clocks
Now needed: „experimental methods, that allow to manipulate
and measure many-body quantum systems.”
?
single Yb+-ion
Coulomb crystal of Yb+-ions
Quantum Metrology ↔ Quantum Simulation & Information
Scalable Ion Trap Prototype
low micromotion
non-magnetic
UHV proof
3D laser access
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
Trap stack with OFHC Cu Foil
Experimental Setup
• Single-ion resolution
• 3D laser access!
Coulomb crystals in well-controlled environment
172Yb+
Coulomb crystals
ca. 80
ions
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
1D
2D
3D
Trap Potential
Example: linear to zigzag transition
Eigenmodes across phase transition
Fishman et al., PRB 77, 064111 (2008)
Phonon Spectrum
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
Higgs field
Nature Physics 7, 2 (2011) doi:10.1038/nphys1874
Symmetry breaking in ion Coulomb crystals
Rotational symmetry
νt(t)
Mirror symmetry
defects ?
U
U
Ψ
Ψ
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!
The Kibble-Zurek Mechanism
ξ
system size
test of KZM with defined ν, 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 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).
The Kibble-Zurek Mechanism
Prediction:
Log [Probability]
ion traps
- Log [Duration of Ramp]
Experiment: non adiabatic radial quenches
Radial trap frequencies
exp. details in
Pyka et al.,
Nat. Comm 4,
2291 (2013)
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!
Simulations for different friction parameters
- Kibble-Zurek
filled symbols: created
empty symbols: surviving
Friction independent
kink creation rate
→ underdamped regime! ν = ½; z = 1
Scaling of defect density with quench time
excluded by simulations
• Theory(1):
8/3 º 2.67
• Experiment:
2.7 ± 0.3
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
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
Spatial distribution of kinks
two kinks – kink interaction!
Mass defects
The Peierls-Nabarro Potential:
Radial (ponderomotive) trapping potential:
extended kink:
two kinks:
odd kink:
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
Kink = higher charge density
credit: R. Nigmatullin
Oscillation and stabilization by mass defects
II: Electric Fields and Mass Defects
creating kink & anti-kink without a quench
time
E-field ramp
II: E-field Creating Kink & Anti-Kink
E-field ramp
time
Partner et al., New J. Phys. 15, 103013 (2013)
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 Freiburg
Mielenz 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 Freiburg
Mielenz 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)
Coulomb crystal with impurities (In+ / Yb+)
γ = 194 MHz
115In+
1P
1
159 nm
γ = 360 kHz
3P
1
230.5 nm
3P
0
172Yb+
γ = 0.8 Hz
Crystal modes
236.5 nm
1S ,
0
411 nm
F = 9/2
Spectroscopy of internal DOFs / spin of ions
• Sideband spectroscopy + Ground state preparation
• Coherent laser-atom interaction:
Jaynes-Cummings Hamiltonian:
Spectroscopy of internal DOFs / spin of ions
5 x 10-16
→ Keep length between cavity mirrors
constant to < 0.05 fm !
Spectroscopy of internal DOFs / spin of ions
• Sideband spectroscopy + Ground state preparation
• Coherent laser-atom interaction:
First observed Rabi-flops:
T ~ 50 µK
T ~ 1 mK
Bermudez, A., Bruderer, M. & Plenio, M. B. PRL (2013)
The experimentalist team:
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

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