Symmetry Breaking and Topological Defect Formation in Ion ...
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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