1. 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)
2. 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
3. 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
4. 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
2.88GHz0.3nm
J. Meijer et al., Appl. Phys. B 82, 321 (2006).
5. Coupling through Dipolar Magnetic
Interaction of the Electron Spins
10nm
2 NV interacting:
100kHz @ 10nm
P. Neumann, et al.,Nature Physics 6, 249 (2010)
7. 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
8. 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)
9.
10. + 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
11. 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:
15. Motivation: Transport out of Trap for
Deterministic High Resolution Ion Implantation
35V // 0V // 35V
Potential/a.U.
Axial position / a.U.
500V // 0V // 35V
Potential/a.U.
Axial position / a.U.
Diamond
18. 12,2 12,4 12,6 12,8 13,0 15,0 15,2 15,4 15,6
0,00
0,05
EMdetectorsignal/a.u.
time of flight / µs
dark ions
EMdetectorsignal[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)
25. 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)
Flighttime(s)
Flighttime(s)
N2
+
Ca+
Time of flight measurements
∆𝑣
𝑣
= 2.5 10−5
26. 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
27. S. Pezzagna, B. Naydenov, F. Jelezko, J. Wrachtrup and J. Meijer, New J. Phys. 12 065017
(2010)
NV Yield versus implantation energy
NV Yield
28. 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
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
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
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
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
axial direction / mu
axial trap potential
Axial position [µm]
Axialtrappingpotential[V]
29. Handling Dark Ions:
Feedback position control
desired
position
real
position
Voltage control
Trap
CCD Image & Real time position determination
30. Handling Dark Ions:
Separation of ion chains in the trap
Voltage/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 !
31. 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
32. 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).
33. Ion Transport in Segmented Traps elect
Size of wavefunction:
a single pixel on a HD screen (2000x1000)
34. 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)
35. 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
37. 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
38. 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.
39. P1/2
S1/2
t = 7 ns
397 nm
Doppler cooling
D5/2
t = 1 s
729 nm
Sideband cooling
Energy
Level scheme of Calcium+
40. 2 Level Atom Harmonic trap
„Dressed“ System
„molecular
Franck Condon“
Picture
„Dressed“ System
Sn ,1
Dn ,1
Dn,
Dn ,1
Sn ,1
Sn,
„Energy
Ladder“
Picture
S
D
D
S
Laser Excitation of a single Ion
41. Signature: no further excitation allowed
„Dark state“ |0>
forbidden!
g,0
e,0
e,1
g,2
g,1
Optical Pumping into the Ground state
e,2
Sideband cooling into
the Motional Ground State
42. P1/2
S1/2
t = 7 ns
397 nm
Doppler cooling
D5/2
t = 1 s
729 nm
Sideband cooling
Energie
Level-Scheme of Calcium+
+1/2
-1/2
~10MHz
@6G
~10-100
GHz
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).
43. Different Diabatic transport schemes
Symmetric transport (back and forth) Asymmetric transport with kick
distance
time
distance
time
Seg 1
Seg 2
Only one
Laser interaction zone
280µm
44. Different Diabatic transport schemes
Symmetric transport (back and forth) Asymmetric transport with kick
distance
time
distance
time
Seg 1
Seg 2
48. 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: 𝜂2
𝑛 ≪ 1,
well within Lamb-Dicke
regime
→ allows gates after
transport
𝑓𝑡𝑟𝑎𝑝 = 1.4 𝑀𝐻𝑧
50. 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
53. Transport of Spin Motion Entanglement
Transport
p/2 bsb p/2 bsbp 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).
54. 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).
55. 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
56. Macroscopic Heat engine
Converts thermal energy into mechanical work / motion
essential for industry
Carnot efficiency (Sadi Carnot 1823):
𝜂 =
Work produced
Heat absorbed
=
𝑊
𝑄 𝐻
≤ 1 −
𝑇𝐶
𝑇 𝐻
= 1 −
𝛽 𝐻
𝛽 𝐶
heat heat
Heat
Engine
mechanical
work
coldhot
James Watt 1783: 𝜂 ≅ 5 − 7%
Modern power plats: 𝜂 ≅ 30%
maximum
possible value
57. 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
58. 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)
59. 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
60. Realization: tapered Paul trap
angle between rf-rods
𝜔 𝑥,𝑦 𝜔 𝑥,𝑦(𝑧)
Pseudo potential:
𝑉𝑝 𝑟, 𝑧 =
𝑚
2
(𝜔0𝑥
2
𝑥2+𝜔0𝑦
2
𝑦2)𝑟0
4
(𝑟0 + 𝑧 tan 𝛼)4
+
𝑚
2
𝜔0𝑧
2
𝑧2
Coupling between axial and radial modes
𝐻 = ħ𝜔0𝑖 𝑎𝑖
†
𝑎𝑖 +
1
2
− 𝐶 ∙ 𝑧 (𝜔0𝑥
2
𝑥2 + 𝜔0𝑦
2
𝑦2) 𝐶 =
2𝑚 tan 𝜃
𝑟0
𝑖∈ 𝑥,𝑦,𝑧
Difference to
linear Paul trap
61. 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
68. 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)
69. 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)
70. Radial energy
start heat engine
Doppler cooling
Thermal ensemble
time
Equilibrum between
heating and cooling
detuning
Heating and cooling:
20% of axial oscillation
work
72. Phase-space analysis
• transformation from thermal energy into coherent motion
DPG 2012 Johannes Roßnagel - University of Mainz 72
axial:radial:
x
x v
v
73. 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
74. Efficiency at maximum power
Classical Carnot limit
adiabatic
Curzon-Ahlborn
𝜼 𝑪𝑨 = 𝟏 − 𝜷 𝟐/𝜷 𝟏
O. Abah, J. Roßnagel, G. Jacob et al., Phys. Rev. Lett. 109, 203006 (2012)
efficiencyη
sudden switch
𝛽2 𝛽1 = 𝑇1/𝑇2
Engine can run at maximum power 𝜔2 𝜔1 = 𝛽1 𝛽2
75. Single ion refrigerator• Reverse the thermodynamic
cycle to convert mechanical
work into heat flow
• Carnot efficiency for heat
pump:
𝜀 𝐶 =
1
𝜂 𝐶
=
𝑇𝑐
𝑇ℎ − 𝑇𝑐
heat
R
mechanical
work
cold hot
heat
78. 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
79. 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
#phonon
1 n
# ion
#phonon impurity
1 n
G.D. Lin, L.M. Duan, NJP 13 (2011)
Ivanov, Vitanov, Singer, Schmidt-Kaler, arXiv (2010)
Bermudez, Bruderer, Plenio, arXiv (2013)
80. 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:
86. 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
87. Observation of the Kibble Zurek scaling law
for defect formation in ion crystals
88. 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).
89. 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
90. 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).
91. 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).
92. • 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
93. Defect formation in ion crystals
Linear
Zig-zag
Zag-zig
Defect
Defect
Double defect
94. 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
95. 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
98. 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
99. 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
100. 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)
