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Kilian Singer
Quantum information processing with ions and towards scalable quantum information processing with solid state systems
http://www.quantenbit.de
Collaborations: P. Zahariev, P. Ivanov, N. Vitanov F. Schmidt-Kaler, U. Poschinger, A. Walther, S. Dawkins Implantation: F.Jelezko, B. Naydenov (Ulm), J. Wrachtrup (Stutt.), J. Meijer, S. Pezzagna (Bochum), S. Hell(Göttingen)
Moving ions
• out of the trap for ion implantation connecting solid state quantum systems
• within the trap for quantum information processing
• with heat for the realization of a heat engine
• to investigate the Kibble-Zurek mechanism
Cold
Hot
Work
Moving ions
• out of the trap for ion implantation connecting solid state quantum systems
• within the trap for quantum information processing
• with heat for the realization of a heat engine
• to investigate the Kibble-Zurek mechanism
Cold
Hot
Work
Motivation: Scalable Quantum Computing with Nitrogen vacancy colour centers
[NV] color center
Wavelength 637 nm
Line width 24 MHz
Dipole moment 1×10-29 Cm
ms = +/-1
ms = 0
3E
3A
optical excitation 637nm
2.88GHz 0.3nm
J. Meijer et al., Appl. Phys. B 82, 321 (2006).
Coupling through Dipolar Magnetic Interaction of the Electron Spins
10nm
2 NV interacting:
100kHz @ 10nm
P. Neumann, et al.,Nature Physics 6, 249 (2010)
Future Visions for 2nd vw funding period
Motivation: Scalable Quantum Computing with Nitrogen vacancy colour centers
Universität Stuttgart, RUBION, Bochum
T=1.6 K 10 µm
1 NV
2 NV
3 NV
2 MeV: spot size 300nm
MV tandem accelerator
(Bochum)
kV nano-beam setup
(Bochum)
kV single laser
cooled ions
(Mainz)
300nm higher resolution 1nm
Ion Implantation
Kooperation: F.Jelezko, B. Naydenov (Ulm),J. Wrachtrup (Stutt.), J. Meijer, S. Pezzagna (Bochum),S. Hell, D. Wildanger (Göttingen)
+ Top-down method
+ Singly charged ions
+ Independent of doping atom
+ Low energies (<1keV)
+ Nm resolution (expected)
- 3 Hz throughput
Segmented Paul Trap as Perfect Point Source for Laser Cooled Ions
AFM tip
Segmented ion trap
Electrostatic
einzel-lens
Substrate
Translation stage
9nm
Trap design
KS, U. Poschinger, M. Murphy, P. Ivanov, F. Ziesel, T. Calarco, F. Schmidt-Kaler, Rev. Mod. Phys. 82, 2609 (2010)
Trap modelling with Fast Multipole Method:
9nm
Trap design
Alignment of trap chips to trap axis
9nm
Trap design
Filter board
Trap Design
• Fs-laser cut alumina (125µm thickness)
• 11 electrodes
• 1 mm distance between chips
• 1 MHz (ax.)/2 MHz (rad.)
Motivation: Transport out of Trap for Deterministic High Resolution Ion Implantation
35V // 0V // 35V
Pote
ntial /
a.U
.
Axial position / a.U.
.
500V // 0V // 35V
Pote
ntial /
a.U
.
Axial position / a.U.
Dia
mond
Ion Extraction
(-2kV)
Amp
Phase switch
Helical resonator
01.08.2013 17
Automatic Extraction of Ions
12,2 12,4 12,6 12,8 13,0 15,0 15,2 15,4 15,6
0,00
0,05
E
M d
ete
cto
r sig
na
l / a
.u.
time of flight / µs
dark ions
EM
dete
cto
r sig
nal [a
.U.]
Deterministic Extraction of Ions
Ca 40 +
88(3) % detected
independent
of ion or molecule species
Dark ions ( CaO ) +
W. Schnitzler, N. M. Linke, R. Fickler, J. Meijer, F. Schmidt-Kaler, K. Singer, PRL 102, 070501 (2009)
Velocity Distribution
Velocity (m/s)
= 7 . 10
v
v -5
Factor of 4 improvement
Aperture Scans
Deflector
Aperture
300µ
m
Dynode Ion Detector
Verification of alignment
x-deflection voltage
y-d
eflection v
oltage
95% efficiency
Lens design
Determinstic single ion delivery with 5nm resolution
13 µm before lens
(7x improved)
Electr. deflector
Blade Position (nm)
Hitra
te
Dynode
Ion Detector Ion Ion lens
Translation stage
Knife edge
Eion=1.5keV
2 keV
5.1 ± 2.7nm
Ion lens
(1000x improved)
Results:
Setup:
Agreement with simulations Spot Size @ 2mK
Nitrogen loading with ion gun
• Loading rate typically 1 Nitrogen per 10s
• Extraction 1 per minute
• N2+ (Mass from flight time: 28.4 ± 0.5 AMU)
• Tests of loading Pr+ are in progress
• Narrow velocity distribution
Trigger-delay (s) Trigger-delay (s)
Flig
ht tim
e (
s)
Flig
ht tim
e (
s) N2
+ Ca+
Time of flight measurements
∆𝑣
𝑣= 2.5 10−5
NV in-situ detection with Super-resolution microscope
1µm
Status:
• Singe NV identification
• Spatial resolution 100nm
Plan:
• In-situ annealing of NV
• Improving resolution to 10nm
• Integration of MW double-resonance
spectoscopy
S. Pezzagna, B. Naydenov, F. Jelezko, J. Wrachtrup and J. Meijer, New J. Phys. 12 065017
(2010)
NV Yield versus implantation energy
NV Yield
Handling Dark Ions: Separation of ion chains in the trap
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15000 -10000 -5000 0 5000 10000
ele
ctr
ic p
ote
ntial /
V
axial direction / mu
axial trap potential
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15000 -10000 -5000 0 5000 10000
ele
ctr
ic p
ote
ntial /
V
axial direction / mu
axial trap potential
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15000 -10000 -5000 0 5000 10000
ele
ctr
ic p
ote
ntial /
V
axial direction / mu
axial trap potential
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15000 -10000 -5000 0 5000 10000
ele
ctr
ic p
ote
ntial /
V
axial direction / mu
axial trap potential
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15000 -10000 -5000 0 5000 10000
ele
ctr
ic p
ote
ntial /
V
axial direction / mu
axial trap potential
Axial position [µm]
Axi
al t
rap
pin
g p
ote
nti
al[V
]
Handling Dark Ions: Feedback position control
desired position
real position
Voltage control Trap
CCD Image & Real time position determination
Handling Dark Ions: Separation of ion chains in the trap
Vo
ltag
e /
V
Time / s
J. Eble, S. Ulm, P. Zahariev, F. Schmidt-Kaler, KS,
Journal of the Optical Society of America B 27, A99 (2010).
After separation any motional excitation of the dark ion has to be minimized !
Moving ions
• out of the trap for ion implantation connecting solid state quantum systems
• within the trap for quantum information processing
• with heat for the realization of a heat engine
• to investigate the Kibble-Zurek mechanism
Cold
Hot
Work
Scalable Quantum Information with Segmented Ion Traps
J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried,
and D. J. Wineland,
“Complete Methods Set for Scalable Ion Trap Quantum
Information Processing”,
Science 325, 1227 (2009).
D. Kielpinski, C. Monroe and D. J. Wineland,
“Architecture for a large-scale ion-trap
quantum computer”
Nature 417, 709 (2002).
Ion Transport in Segmented Traps electrode 1 (size 10 screens) …………………………………………………………..……………………………………..…electrode 2
Size of wavefunction:
a single pixel on a HD screen (2000x1000)
Fast Diabatic Transport in Segmented Microtrap
• A. Walther, F. Ziesel, M. Hettrich , S. Dawkins,
KS, F. Schmidt-Kaler,U.G. Poschinger, PRL 109, 080501 (2012).
• Ryan Bowler, J. Gaebler, Y. Lin, T. R. Tan, D. Hanneke, J. D. Jost, J. P.
Home, D. Leibfried, and D. J. Wineland,
PRL 109, 080502 (2012)
• Blakestad et al., PRL 102, 153002 (2009)
Fast Diabatic Transport in Segmented Microtrap
• fs-laser cut Alumina
• 3-layered sandwich design
• evaporated gold as electrode material
• 31 individual DC segments
• typical trap frequencies:
1.4 MHz (ax.)/3 MHz (rad.)
• possible total transport distance: ~ 5mm
Fast Diabatic Transport in Segmented Microtrap
FPGA
DAC 1
Output → filters → trap segments
Prerequisites: Precision arbitrary waveform source for ion transport
• Virtex 5FXT FPGA
• 64 Mbyte DDR RAM
• 400 MHz Power PC CPU
• 10ns timing
• GB Ethernet
• 64 IO
Prerequisites: Precision arbitrary waveform source for ion transport
• serial 16 bit DACs (TI DAC8814)
• 2.5 MSamples/s/electrode
• Resolution: 0.3 mV
• 12 channels per analog card
• expandable to 4 analog cards Optimized signal routing, to minimize digital cross talk.
P1/2
S1/2
t = 7 ns
397 nm
Doppler cooling D5/2
t = 1 s
729 nm
Sideband cooling
Energ
y
Level scheme of Calcium+
2 Level Atom Harmonic trap
„Dressed“ System
„molecular
Franck Condon“
Picture
„Dressed“ System
Sn ,1
Dn ,1Dn,
Dn ,1
Sn ,1Sn,
„Energy
Ladder“
Picture
S
D
D
S
Laser Excitation of a single Ion
Signature: no further excitation allowed
„Dark state“ |0>
forbidden!
g,0
e,0e,1
g,2
g,1Optical Pumping into the Ground state
e,2
Sideband cooling into the Motional Ground State
P1/2
S1/2
t = 7 ns
397 nm
Doppler cooling D5/2
t = 1 s
729 nm
Sideband cooling
Energ
ie
Level-Scheme of Calcium+
+1/2
-1/2 ~1
0 M
Hz
@ 6
G
~1
0-1
00
GH
z
Raman transition
Qubit-Manipulation
Spin dependent forces Shelving
bright
dark
U. G. Poschinger, et. al, KS, F. Schmidt-Kaler, Journal of Physics B 42,
154013 (2009).
Different Diabatic transport schemes Symmetric transport (back and forth) Asymmetric transport with kick
dis
tan
ce
time
dis
tan
ce
time
Seg 1
Seg 2
Only one
Laser interaction zone
280µm
Different Diabatic transport schemes Symmetric transport (back and forth) Asymmetric transport with kick
dis
tan
ce
time
dis
tan
ce
time
Seg 1
Seg 2
Symmetric Transport electrode 1 (size 10 screens) …………………………………………………………..……………………………………..…electrode 2
Size of wavefunction:
a single pixel on a HD Screen (2000x1000)
Transport Backtransport
Energy measurement
Efficient Energy Measurement
Results of symmetric transport
Pseudo energy
Phonon fit to Rabi oscillations
• Trap periodicity
visible
• Coherent control of
oscillation amplitude
over 4 orders of
magnitude
• < 0.1 phonons
minimal energy
transfer
Dwell time is scanned:
Transport details (each direction):
• 20 sample points
• 8 µs → ~ 11 motion cycles
• 220 µm → to next segment, ~23000
times the size of ion wavepacket
• Speed: >2000 wavepackets/cycle
• ~100 km/h
Note: 𝜂2𝑛 ≪ 1,
well within Lamb-Dicke
regime
→ allows gates after
transport
𝑓𝑡𝑟𝑎𝑝 = 1.4 𝑀𝐻𝑧
Assymmetric Transport electrode 1 (size 10 screens) …………………………………………………………..……………………………………..…electrode 2
Size of wavefunction:
a single pixel on a HD Screen (2000x1000)
Transport with decelleration kick
3.85 V
-3.68 V
• Control via kick voltage or wait time
• demonstration of fast, controlled one-way
transport
• 0.2 phonons minimal energy transfer
Controlled Displacement Kicks
Kick
Coherent state in Fock basis:
P(n) P(n)
Theory Experiment
Controlled Displacement Kicks
Kick
Displaced Fock state in Fock basis:
P(n) P(n)
Theory Experiment
Transport of Spin Motion Entanglement
Transport
p/2 bsb p/2 bsb p bsb
• Very sensitive measurement of trap frequency variations during transport
• No effect of magnetic field gradients due to compensation with Ramsey spectroscopy on
carrier transition
(A. Walther, U. Poschinger, F. Ziesel, M. Hettrich, A. Wiens, J. Welzel, and F. Schmidt-Kaler,
Phys. Rev. A 83, 062329 (2011).
s=390 Hz
Carrier Ramsey Ramsey on blue sideband
Transport of a motional superposition state
without transport
with transport
A. Walther, F. Ziesel, M. Hettrich , S. Dawkins, KS, F. Schmidt-Kaler, U.G. Poschinger, Physical Review Letters 109, 080501 (2012).
Moving Ions
• out of the trap for ion implantation connecting solid state quantum systems
• within the trap for quantum information processing
• with heat for the realization of a heat engine
• to investigate the Kibble-Zurek mechanism
Cold
Hot
Work
Macroscopic Heat engine Converts thermal energy into mechanical work / motion
essential for industry
Carnot efficiency (Sadi Carnot 1823):
𝜂 =Work produced
Heat absorbed=
𝑊
𝑄𝐻≤ 1 −
𝑇𝐶
𝑇𝐻= 1 −
𝛽𝐻
𝛽𝐶
heat heat Heat
Engine
mechanical
work
cold hot
James Watt 1783: 𝜂 ≅ 5 − 7%
Modern power plats: 𝜂 ≅ 30%
maximum
possible value
Downscaling of Heat Engines
Size
Car Engine
mini heat engine
m mm µm nm
Steeneken et al., Nature Phys. 7, 354 (2011)
Blickle et al., Nature Phys 8, 143 (2012)
piezoresistive heat engine
colloidal heat engine
single particle
thermodynamics
? single trapped ion
in a Paul Trap
Quantum regime excessible
Fundamental limit
Single Ion heat engine
Proposal: • Heat engine with one single ion trapped in a Paul trap as working
substance.
– Excellent preparation and control
– Allow for reservoir engineering • detuned lasers Doppler interaction
• electronic noise
• …
• Potential to reach quantum regime
– Quantum heat engines: studied theoretically for >50 years
– No one has been realized yet
Scovil,Schulz-Dubois, PRL (1959)
Hot bath Cold bath
Abah, Rossnagel, Jacob, Deffner, Lutz, Schmidt-Kaler, Singer, Phys. Rev. Lett. 109, 203006 (2012)
Realization: Idea • Converting thermal energy into motion
– Thermal state of ion expands when heated
– Driving the engine in the radial states of motion (linear paul trap) – Converting thermal ernergy of the radial mode into
motion – Storing motional energy in axial mode
heating
Realization: tapered Paul trap angle between rf-rods
𝜔𝑥,𝑦 𝜔𝑥,𝑦(𝑧)
Pseudo potential:
𝑉𝑝 𝑟, 𝑧 =𝑚
2
(𝜔0𝑥2 𝑥2+𝜔0𝑦
2 𝑦2)𝑟04
(𝑟0 + 𝑧 tan𝛼)4+
𝑚
2𝜔0𝑧
2 𝑧2
Coupling between axial and radial modes
𝐻 = ħ𝜔0𝑖 𝑎𝑖†𝑎𝑖 +
1
2− 𝐶 ∙ 𝑧 (𝜔0𝑥
2 𝑥 2 + 𝜔0𝑦2 𝑦 2) 𝐶 =
2𝑚 tan𝜃
𝑟0 𝑖∈ 𝑥,𝑦,𝑧
Difference to
linear Paul trap
The trapped ion as engine gas Doppler heating/cooling in radial direction induces axial displacement
To reach reach large axial amplitudes of movement
• strong radial confinement
• weak axial confinement
Pseudopotential
heating
r z
F
Equilibrium position shifted
A
B C
D
Working cycle
heating
moving
cooling
moving
Driving resonantly
with axial trap freq.
Equivalence to macroscopic Heat Engine
heating
moving
cooling
moving
ignition
expansion
compression
themalizing
Equivalence to macroscopic Heat Engine
Converting thermal energy into motion
=
Heat engine
Classical thermodynamics:
Large ensemble of particles
Quantum Otto Cycle: principle
Isentropic expansion
Isentropic compression
Hot
isochore Cold
isochore
𝑊3
𝑄4
𝑊1
𝑄2
D (ω1,β2)
A (ω1,β1) B (ω2,β1)
C (ω2,β2)
1
2
3
4
β = 1/kT
Quantum Otto Cycle: theory
non-thermal
non-thermal
unitary
unitary
Quantum Otto cycle: efficiency Exact quantum expression:
Adiabaticity Parameter Qi* (Husimi 1953)
– Depends on driving
Adiabatic process: 𝑄∗
1,2 = 1 approximates our process
Sudden switch (extreme): 𝑄∗1,2 = (𝜔1
2 + 𝜔22)/(2𝜔1𝜔2)
Monte Carlo Simulation simulating thermal state of a single ion
High temperture limit - classical trajectories:
• Ensemble of classical realizations
• Thermal probability distribution through Monte-Carlo simulation of laser interaction
Realistic trap geometries:
Finite size method to calculate potentials
including micromotion and realistic dynamics
Probability for spontanous scattering
Momenteum Transfer of Photons
R. Casdorff, R. Blatt, Appl. Phys. B 45, 175 (1988)
K. Singer et al., Rev. Mod. Phys. (2010)
Excitation of the heat engine • Resonant driving of heating and cooling cycles
• Sum over large ensembles of realizations
Thermal states in
radial modes
Coherent
excitation of axial
modes
Steady state due to axial damping force (cooling laser)
Radial energy
start heat engine
Doppler cooling
Thermal ensemble
time
Equilibrum between
heating and cooling
detuning
Heating and cooling:
20% of axial oscillation
work
Phase-space analysis
radial: 0 𝜋 32𝜋
0 12𝜋 𝜋 axial:
• Ensemble average over one axial period
12𝜋
32𝜋
x
x
p
p
α
Phase-space analysis • transformation from thermal energy into coherent motion
DPG 2012 Johannes Roßnagel - University of Mainz 72
axial: radial:
x x v
v
Efficiency at maximum power • Two essential characteristics of HE:
power output and efficiency at maximum power
Power 𝑃 =Work done per cycle
Duration of cycle= −
𝑊1 + 𝑊3
𝑡cycle
Maximization of P for given heat baths and ω1
maximum condition for ω2
𝜔2 𝜔1 = 𝛽1 𝛽2
Adiabatic process (Q*=1):
• High temperture (classical) limit:
𝜂 = 1 −𝛽2
𝛽1= 1 −
𝑇1
𝑇2
• Low temperture limit (for cold bath):
𝜂 = 1 −𝛽2
𝛽1= 1 −
ħ𝜔1
2 𝑘𝑇2
Curzon-Ahlborn Efficiency (1975)
𝜔2 = 2𝜔1 ħ𝛽2
Quantum Efficiency
Efficiency at maximum power
Classical Carnot limit
adiabatic Curzon-Ahlborn
𝜼𝑪𝑨 = 𝟏 − 𝜷𝟐/𝜷𝟏
O. Abah, J. Roßnagel, G. Jacob et al., Phys. Rev. Lett. 109, 203006 (2012)
effic
iency η
sudden switch
𝛽2 𝛽1 = 𝑇1/𝑇2
Engine can run at maximum power 𝜔2 𝜔1 = 𝛽1 𝛽2
Single ion refrigerator • Reverse the thermodynamic
cycle to convert mechanical work into heat flow
• Carnot efficiency for heat pump:
𝜀𝐶 =1
𝜂𝐶=
𝑇𝑐𝑇ℎ − 𝑇𝑐
heat R
mechanical
work
cold hot
heat
Heat pump: working principle
Heat pump: working principle
heat
transport
Single Ion Refrigerator
• Smallest possible refrigerator
• Driving three ion Egyptian mode
• Middle ion transfers heat between two oscillatory reservoirs
• Coupling to all kind of micro-oscillators possible
Heat Transport
Transport oscillation Transport thermal energy
heat transport of radial modes along the crystal
Steady state
Between two heat baths
Hot
Bath Cold
Bath
Transport single Phonons
# ion
# p
honon
1 n
# ion
# p
honon impurity
1 n
G.D. Lin, L.M. Duan, NJP 13 (2011)
Ivanov, Vitanov, Singer, Schmidt-Kaler, arXiv (2010)
Bermudez, Bruderer, Plenio, arXiv (2013)
Squeezed thermal bath
Cooling to ground state
• Heat baths: increasing
and decresing single
phonons
• kT 1/2 ħω
Driving quantum
states
• Storing energy not in
coherent states but in
non-classical states
• Amplifing cat state,
squeezed ground
state…
Non-classical
thermodynamics
• Driving engine by
non-classical
baths
• Squeezed baths
increases
efficiency
• Spin bath,
magnetic gradient
along the trap axis
O. Abah, E. Lutz, arXiv:1303.6558(2013)
Non-classical heat baths:
Squeezed heat engine
squeezing
Phase space:
Thermal state
effective
distribution
becomes larger…
…Impact on axial
movement stronger
Non-thermal heat baths • Introducing squeezed hot reservoir bath:
• Hot bath heats and squeezes thermal state
• 𝐻∗ = 𝐻 + ∆𝐻 𝑛 ∗ = 𝑛 + ∆𝑛 higher effective temperature
squeezin
g
Non-thermal heat baths
Increasing efficiency • Repeat same calculations as before…
𝜂∗ = 1 −𝛽2
𝛽1 1+2 sinh2 𝑟
Limit for large squeezing (𝑟 ≫ 0):
𝜂∗ = 1 −𝛽2
𝛽12 exp (−2𝑟)
Limit for low squeezing (𝑟 → 0):
𝜂∗ = 1 −𝛽2
𝛽1(1 − 2𝑟2)
increases efficiency exponentially
Carnot-limit
𝛽2 𝛽1 = 0.3
𝛽2 𝛽1 = 0.6
𝛽2 𝛽1 = 0.9
Efficiency above Carnot Limit is possible!
Experimental realization
Holding and
compensation
electrodes
RF-electrodes
Anti-symmetric
supply on all of the
four rods
Mount and endcaps
Gold coated ceramics
Distance ion – endcaps: 4mm
Distance ion – electrodes: 1.5mm
RF driving: 800Vpp at 60MHz
Axial trap frequency: 35kHz
Radial trap frequency: 6MHz
Moving Ions
• out of the trap for ion implantation connecting solid state quantum systems
• within the trap for quantum information processing
• with heat for the realization of a heat engine
• to investigate the Kibble-Zurek mechanism
Cold
Hot
Work
Observation of the Kibble Zurek scaling law
for defect formation in ion crystals
1976 (Kibble)
symmetry breaking at a second order
phase transitions such that topological
defects form, this may explain formation of
cosmic strings or domain walls
Thomas Kibble
(Imperial London)
Universal principles of defect formation
T. W. B. Kibble, Journal of Physics A 9, 1387 (1976). T. W. B. Kibble, Physics Reports 67, 183 (1980).
1976 (Kibble)
symmetry breaking at a second order
phase transitions such that topological
defects form, this may explain formation of
cosmic strings or domain walls
Thomas Kibble
(Imperial London)
Universal principles of defect formation
Free energy landscape changes
across the critical point from a single
well to a double well potential
Spontaneous symmetry breaking
Universal principles of defect formation
• System response time, thus information transfer,
diverges when approaching critical point
• At some moment, the system becomes non-
adiabatic and freezes
Freezout
timescale
Linear quench
Diverging slow
response
Relative Temperature:
Relaxation time:
W. H. Zurek, Physics Reports 276, 177 (1996).
1976 (Kibble)
symmetry breaking at a second order
phase transitions such that topological
defects form, this may explain formation of
cosmic strings or domain walls W. Zurek
(los Alamos)
Universal principles of defect formation
1985 (Zurek)
Sudden quench though the critical point leads to
defect formation, experiments in solid state phys.
may test theory of universal scaling
• Experiments with rapid cooling of liquid
crystals observe structures
• Experiments for vortex formation in liquid 3He
• Experiments with vortexes in superconductors
2010 (Morigi, Retzger, Plenio et al)
Proposal for KZ study in trapped ions crystals
W. H. Zurek, Nature 317, 505 (1985).
• Landau Ginzburg theory of phase transition for ion trap situation
• Universal scaling found
• Prediction of for the inhomogenious case
Proposal for KZ physics with ion crystals
Defect formation in ion crystals
Linear
Zig-zag
Zag-zig
Defect
Defect
Double defect
Experimental setup and parameters
Trap with 11 segments
Controlled by FPGA and
arbitray waveform gen.
/2p = 1.4MHz (rad.)
/2p = 160 – 250kHz (ax.)
Laser cooling /
CCD observation
Smooth axial compression over critical point
• Exponential soft start and stop
• Low excitation of axial breathing mode
• Slope at critical point variable for variable quench times
• Acurate frequency determination
Molecular dynamics simulations
Molecular dynamics simulations Simulation of
ion trajectories
Tiny axial
excitation
No position flips
Experimental test of the =8/3 power law scaling
= 2.68 ± 0.06 for anisotropy at
critical point of 1.03
= 2.62 ± 0.15 for anisotropy at
critical point of 1.05
fits prediction for the
inhomogenious Kibble Zurek case
with 8/3 = 2.67
Saturation of
defect density
Offset kink
formation
S. Ulm, et. al., KS, accepted at Nat. Com. (2013) 1302.5343. also Pyka et al., arXiv:1211.7005
Summary/Outlook Paul-trap successfully established as first
deterministic source of single ions Verification of nm resolution and generation of NV
Scalable diabatic transport of a ground state
cooled ion Splitting of Ion chains with combined gate
operations Numerical simulation and prototype Using squeezed states to increase efficiency Realization of the Kibble-Zurek mechanism Tranisition between inhomogeneous and
homogeneous KZM by shaping the potentials
Cold
Hot
Work
www.quantenbit.de
Ion Light Interface
(FSK) Rydberg Ions (FSK) Zig-Zag Ion Crystals
(KS/FSK) Quantum Sim (RG)
Ion Implantation (KS)
QI with Ions (UGP/FSK)
www.quantenbit.de
PhD,
Postdoc
positions!
A. Bautista, S. Dawkins, C. Degüther, T. Feldker, R. Gerritsma,
M. Hettrich, G. Jacob, H. Kaufmann, A. Kesser, N. Kurz, U.G. Poschinger, J. Roßnagel, T. Ruster, F. Schmidt-Kaler, K. Singer, S. Ulm, A. Walther, C. Warschburger, J. Welzel,
S. Wolf, F. Ziesel
Single Ion Heat Engine (KS)