Hartmut Häffner Institut für Experimentalphysik, Universität Innsbruck and
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Transcript of Hartmut Häffner Institut für Experimentalphysik, Universität Innsbruck and
Hartmut Häffner
Institut für Experimentalphysik, Universität Innsbruck andInstitut für Quantenoptik und Quanteninformation Innsbruck
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Quantum information processingwith trapped ions
1. Basic experimental techniques
2. Robust two-particle entanglement
3. Process tomography of a CNOT gate
4. Teleportation
5. Multi-particle entanglement
6. Outlook Quantum optics VI, 17.5. 2005
Quantum information offers a completely new view on quantum mechanics: we might “understand” what quantum mechanics is about.
In quantum information you can see natures strange rules at work: do “real“ bizarre Gedanken experiments!
A most fascinating topic is to look at non-local superpositions.
Why quantum information?
Pentium 4 (2002)
1 atom
1960 1970 1980 1990 2000 2010 2020
year
1910
1510
1110
710
310010
1 atom per bitnum
ber
of a
tom
s pe
r bi
t~ 2017
How many atoms per bit?How many atoms per bit?
faster = smallerfaster = smaller
ENIAC (1947)
Progress in technology …
S1/2
P1/2
D5/2
qubit
Experimental Setup
20th century
about the ENIAC:
„Where a calculator on the ENIAC is equipped with 18000 vacuum tubes and weighs 30 tons, computers in the future may have only 1000 tubes and weigh only 1 ½ tons.“
Popular Mechanics, March 1949
The fate of visionaries
qubit
qubit(quoctet)
Encoding of quantum information requires long-lived atomic states:
microwave transitions
9Be+, 25Mg+, 43Ca+, 87Sr+, 137Ba+, 111Cd+, 171Yb+
optical transitions
Ca+, Sr+, Ba+, Ra+, Yb+, Hg+ etc.
S1/2
P1/2
D5/2
S1/2
P3/2
Qubits with trapped ions
P1/2 D5/2
=1s
S1/2
40Ca+
P1/2
S1/2
D5/2
Dopplercooling Sideband
cooling
P1/2
S1/2
D5/2
Quantum statemanipulation
P1/2
S1/2
D5/2
Fluorescencedetection
Experimental procedure
1. Initialization in a pure quantum state: laser cooling,optical pumping
3. Quantum state measurement by fluorescence detection
2. Quantum state manipulation on S1/2 – D5/2 qubit transition
50 experiments / s
Repeat experiments100-200 times
One ion : Fluorescence histogram
counts per 2 ms0 20 40 60 80 100 120
0
1
2
3
4
5
6
7
8S1/2 stateD5/2 state
P1/2 D5/2
=1s
S1/2
40Ca+
Experimental procedure
1. Initialization in a pure quantum state: Laser sideband cooling
3. Quantum state measurement by fluorescence detection
2. Quantum state manipulation on S1/2 – D5/2 transition
P1/2
S1/2
D5/2
Dopplercooling Sideband
cooling
P1/2
S1/2
D5/2
Quantum statemanipulation
P1/2
S1/2
D5/2
Fluorescencedetection
50 experiments / s
Repeat experiments100-200 times
Spatially resolveddetection withCCD camera:
Multiple ions:
Addressing of individual ions
CCD
Paul trap
Fluorescencedetection
electrooptic deflector
coherentmanipulation of qubits
dichroicbeamsplitter
inter ion distance: ~ 4 µm
addressing waist: ~ 2 µm
< 0.1% intensity on neighbouring ions
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Exc
itatio
n
Deflector Voltage (V)
D-s
tate
po
pul
atio
nAddressing of individual ionsRabi oscillations
D-s
tate
po
pul
atio
nRabi oscillations
Picture atomic polarization laser phase
D-s
tate
po
pul
atio
nRabi oscillations
To prepare the state shiftthe phase of the preparation -pulsewith respect to all other pulses by .
D-s
tate
po
pul
atio
nRabi oscillations
Coherent manipulationCoherent manipulation
0 10 20 30 40 50 60 700
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (s)
D-s
tate
pop
ulat
ion
Phase switched by /2
row of qubits in a linear Paul trap forms a quantum register
External degree of freedom: ion motion
50 µm
External degree of freedom: ion motion
The common motionacts as the quantumbus.
50 µm
External degree of freedom: ion motion
The common motionacts as the quantumbus.
harmonic trap
…
External degree of freedom: ion motion
harmonic trap
…
2-level-atom joint energy levels
External degree of freedom: ion motion
0,S
0,D1,D
1,S
carrier
sideband
D-s
tate
po
pul
atio
n
Coherent manipulationCoherent manipulation
0,S
0,D1,D
1,S
carrier and blue sidebandRabi oscillations
with Rabi frequencies
carrier
sideband
is the Lamb-Dicke parameter
and
Coherent manipulation
1. Basic experimental techniques
2. Robust two-particle entanglement
3. Implementation of a CNOT gate
4. Teleportation
5. Multi-particle entanglement
6. Outlook
…
… …
…
Creation of Bell states
…
… …
…
/2, BSB
Creation of Bell states
…
… …
…
/2, BSB
, carrier
Creation of Bell states
…
… …
…
/2, BSB
, BSB
, carrier
Creation of Bell states
Fluorescencedetection withCCD camera:
Coherent superposition or incoherent mixture ?
What is the relative phase of the superposition ?
SSSDDS
DD SSSDDSDD
Measurement of the density matrix:
Analysis of Bell states
A measurement yields the z-component of the Bloch vector
=> Diagonal of the density matrix
Rotation around the x- or the y-axis prior tothe measurement yields the phase informationof the qubit.
(a naïve persons point of view)
=> coherences of the density matrix
Obtaining a single qubits density matrix
Preparation and tomography of Bell states
SSSD
DSDD SSSDDSDD
SSSD
DSDD SSSDDSDD
SSSD
DSDD SSSDDSDD
Fidelity:
Entanglementof formation:
Violation of Bell inequality:
F = 0.91F = 0.91
E(exp) = 0.79
S(exp) = 2.52(6)
> 2
SSSD
DSDD SSSDDSDD
C. Roos et al., Phys. Rev. Lett. 92, 220402 (2004)
SSSD
DSDD SSSDDSDD
SSSD
DSDD SSSDDSDD
SSSD
DSDD SSSDDSDD
long lived (~ 1000 ms) short lived (1 ms)
Ene
rgy
(see e.g. Kielpinski et al.,Science 291, 1013-1015 (2001)
SSSD
DSDD SSSDDSDD
Ene
rgy
Life
time
limite
d on
ly b
y sp
onta
nteo
us d
ecay
of t
he D
leve
l
Life
time
limite
d on
ly b
y sp
onta
nteo
us d
ecay
of t
he D
leve
l
Life
time
limite
d by
lase
r fre
quen
cy s
tabi
lity
Life
time
limite
d by
lase
r fre
quen
cy s
tabi
lity
Creation of Bell statesDecoherence properties of the Bell states
Ultra-longlived Bell statesM
inim
um
fid
elity
D5/2
S1/2
Min
imu
m fi
del
ityUltra-longlived Bell states
Line possible death
Lifetime of entanglement > 20 s
control
target
1. Basic experimental techniques
2. Robust two-particle entanglement
3. Process tomography of a CNOT gate
4. Teleportation
5. Multi-particle entanglement
6. Outlook
other gate proposals include: • Cirac & Zoller • Mølmer & Sørensen, Milburn• Jonathan & Plenio & Knight• Geometric phases• Leibfried & Wineland
controlcontrol targettarget
...allows the realization of a universal quantum computer !
control
target
Cirac-Zoller two-ion controlled-NOT operation
ion 1
motion
ion 2
control qubit
target qubit
SWAP
Cirac-Zoller two-ion controlled-NOT operation
ion 1
motion
ion 2
control qubit
target qubit
Cirac-Zoller two-ion controlled-NOT operation
ion 1
motion
ion 2
SWAP-1
control qubit
target qubit
Cirac - Zoller two-ion controlled-NOT operation
F. Schmidt-Kaler et al., Nature 422, 408 (2003)
ion 1
motion
ion 2
SWAP-1SWAP
Ion 1Ion 1
Ion 2Ion 2
pulse sequence:pulse sequence:
Cirac - Zoller two-ion controlled-NOT operation
control qubitcontrol qubit
target qubittarget qubit
laser frequencypulse lengthoptical phase
Phase gate
Phase gate
Composite 2π-rotation:
Example:
CNOT
Mapping between product and Bell basis
Product states Bell states
Ion 1
Ion 2
CNOT
Mapping between Product and Bell basis
Experimental fidelity of Cirac-Zoller CNOT operation
input
output
F. Schmidt-Kaler et al.,Nature 422, 408 (2003)
Gate tomography
characterizes gate operation completely
Process tomography, theory
ideal CNOT gate operation
Process tomography, experiment
real CNOT gate operation
1. Basic experimental techniques
2. Robust two-particle entanglement
3. Process tomography of a CNOT gate
4. Teleportation
5. Multi-particle entanglement
6. Outlook
Alice
Bob
Bell state
unknowninput state
recoverinput state
rotation
classical communication
measurementin Bell basis
Phys. Rev. Lett. 70, 1895 (1993)
Teleportation protocol
Ion 3
Ion 2
Ion 1
Bell
state
initialize #1, #2, #3
classical communication
conditional rotations
CNOT -- Bell basis
Alice
Bob
Selectiveread out
Implementation of the teleportation protocol
recovered on ion #3
Protecting qubits from readout
detect quantum state of ion #1 only
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
ion #1 ion #2 ion #3
Protecting qubits from readout
detect quantum state of ion #1 onlysuperpositions of ions #2, #3 protected
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
D5/2
S1/2
ion #1 ion #2 ion #3
D D‘ DD‘
Ion 3
Ion 2
Ion 1
conditional rotations using electronic logic, triggered by PM signal
conditional rotations using electronic logic, triggered by PM signalP
U
U
P
C C C
B
B B B B C
CU P
B
C
C P
spin echo sequencespin echo sequence
full sequence:26 pulses + 2 measurements
full sequence:26 pulses + 2 measurements
B
C
blue sideband pulsesblue sideband pulses
carrier pulsescarrier pulses
P
C
B
B
Teleportation protocol, details
Input test states Output statesInitial Final
TPU U-1
Ion #1 Ion #3
Teleportation procedure, analysisTeleportation procedure, analysis
Similar results also from Boulder!
Fidelity: 0.83
Classicalthreshold
Quantum teleportation on demand
Teleportation on demand
no post-selection
it works for all Bell states
only 10 m
Deterministicteleportation
Process tomography of teleportation
represent input/output states with Bloch spheres:
input sphere
output sphere
Process tomography of the teleportation
1. Basic experimental techniques
2. Robust two-particle entanglement
3. Process tomography of a CNOT gate
4. Teleportation
5. Multi-particle entanglement
6. Outlook
Density matrix of W – state
experimental result theoretical expectation
DDDDDS
DSDDSS
SDDSDS
SSDSSS
Fidelity: 85 %
DDDDDS
DSDDSS
SDDSDS
SSDSSS
Bell statesurvives !
Photon-version: M. Eibl et al., Phys. Rev. Lett. 92, 077901 (2004).
projection of the center ion
Quantum mechanics at work
1. Basic experimental techniques
2. Robust wo-particle entanglement
3. Process tomography of a CNOT gate
4. Teleportation
5. Multi-particle entanglement
6. Outlook
- optimization of Cirac-Zoller gateachieve 3 - 5 CNOT gate operations
- error correction protocols with three and five qubits
- qubit manipulation in DFS
- implementation with 43Ca+
- test of segmented traps
Summary
- Robust entanglement (more than 20 s)
- Multi-particle entanglement
- Process tomography of a CNOT
- Process tomography of a
teleportation algorithm
The Innsbruck ion trap group
F. Schmidt-KalerA. Wilson P. Bushev
C. Becher
D. Rotter
G. Lancaster
C. Russo
M. Riebe
T. Körber
T. Deuschle
M. Chwalla
C. Roos M. Bacher
V. SteixnerA. KreuterR. Bhat
R. Blatt
J. Benhelm
W. Hänsel
F. Splatt
H. Häffner
http://heart-c704.uibk.ac.at
Ph.D. positions
available !!!
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