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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

Moving ions

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

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

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

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

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:

Trap design

Alignment of trap chips to trap axis

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

ntial /

Axial position / a.U.

500V // 0V // 35V

ntial /

Axial position / a.U.

Ion Extraction

(-2kV)

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

time of flight / µs

dark ions

nal [a

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

Factor of 4 improvement

Aperture Scans

Deflector

Aperture

Dynode Ion Detector

Verification of alignment

x-deflection voltage

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)

Dynode

Ion Detector Ion Ion lens

Translation stage

Knife edge

Eion=1.5keV

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)

ht tim

Time of flight measurements

∆𝑣

𝑣= 2.5 10−5

NV in-situ detection with Super-resolution microscope

Status:

• Singe NV identification

• Spatial resolution 100nm

• 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

-15000 -10000 -5000 0 5000 10000

ntial /

axial direction / mu

axial trap potential

-15000 -10000 -5000 0 5000 10000

ntial /

-15000 -10000 -5000 0 5000 10000

ntial /

-15000 -10000 -5000 0 5000 10000

ntial /

-15000 -10000 -5000 0 5000 10000

ntial /

Axial position [µm]

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

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

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)

• 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

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.

t = 7 ns

397 nm

Doppler cooling D5/2

t = 1 s

729 nm

Sideband cooling

Level scheme of Calcium+

2 Level Atom Harmonic trap

„Dressed“ System

„molecular

Franck Condon“

Picture

„Dressed“ System

Dn ,1Dn,

Sn ,1Sn,

„Energy

Ladder“

Picture

Laser Excitation of a single Ion

Signature: no further excitation allowed

„Dark state“ |0>

forbidden!

e,0e,1

g,1Optical Pumping into the Ground state

Sideband cooling into the Motional Ground State

t = 7 ns

397 nm

Doppler cooling D5/2

t = 1 s

729 nm

Sideband cooling

Level-Scheme of Calcium+

-1/2 ~1

Raman transition

Qubit-Manipulation

Spin dependent forces Shelving

bright

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

Only one

Laser interaction zone

280µm

Different Diabatic transport schemes Symmetric transport (back and forth) Asymmetric transport with kick

Symmetric Transport electrode 1 (size 10 screens) …………………………………………………………..……………………………………..…electrode 2

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

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

Coherent state in Fock basis:

P(n) P(n)

Theory Experiment

Controlled Displacement Kicks

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

Macroscopic Heat engine Converts thermal energy into mechanical work / motion

essential for industry

Carnot efficiency (Sadi Carnot 1823):

𝜂 =Work produced

Heat absorbed=

𝑄𝐻≤ 1 −

𝑇𝐶

𝑇𝐻= 1 −

𝛽𝐻

𝛽𝐶

heat heat Heat

Engine

mechanical

cold hot

James Watt 1783: 𝜂 ≅ 5 − 7%

Modern power plats: 𝜂 ≅ 30%

maximum

possible value

Downscaling of Heat Engines

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

(𝜔0𝑥2 𝑥2+𝜔0𝑦

2 𝑦2)𝑟04

(𝑟0 + 𝑧 tan𝛼)4+

2𝜔0𝑧

2 𝑧2

Coupling between axial and radial modes

𝐻 = ħ𝜔0𝑖 𝑎𝑖†𝑎𝑖 +

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

Equilibrium position shifted

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

isochore Cold

isochore

D (ω1,β2)

A (ω1,β1) B (ω2,β1)

C (ω2,β2)

β = 1/kT

Quantum Otto Cycle: theory

non-thermal

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

Steady state due to axial damping force (cooling laser)

Radial energy

start heat engine

Doppler cooling

Thermal ensemble

Equilibrum between

heating and cooling

detuning

Heating and cooling:

20% of axial oscillation

Phase-space analysis

radial: 0 𝜋 32𝜋

0 12𝜋 𝜋 axial:

• Ensemble average over one axial period

12𝜋

32𝜋

Phase-space analysis • transformation from thermal energy into coherent motion

DPG 2012 Johannes Roßnagel - University of Mainz 72

axial: radial:

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 −

• 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)

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

cold hot

Heat pump: working principle

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

Bath Cold

Transport single Phonons

honon impurity

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

• 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

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

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)

cosmic strings or domain walls

Thomas Kibble

(Imperial London)

Free energy landscape changes

across the critical point from a single

well to a double well potential

Spontaneous symmetry breaking

• 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)

cosmic strings or domain walls W. Zurek

(los Alamos)

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

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

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

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)

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