Oliver Benson
Humboldt-Universität zu Berlin, Nano Optics Grouphttp://nano.physik.hu-berlin.de
Thanks to: T. Aichele1, M. Scholz, S. Ramelow, V. Zwiller2 1CEA, Grenoble (F); 2Tech. Univ. Delft (NL)
Funding:
Single photons on demand:New light for quantum information
processing
SQE 2005, Beijing, Nov. 23-27
Einstein 1905 (Annalen der Physik): Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt
„Es scheint mir nun in der Tat, daß die Beobachtungen über die „schwarze Strahlung“, ..., und andere die Erzeugung bzw. Verwandlung des Lichtes betreffende Erscheinungsgruppen besser verständlich erscheinen unter der Annahme, daß die Energie des Lichtes diskontinuierlich im Raume verteilt sei. ... es besteht dieselbe aus einer endlichen Anzahl von in Raumpunkten lokalisierten Energiequanten, welche sich bewegen, ohne sich zu teilen und nur als Ganze absorbiert und erzeugt werden können.
Photoelectric Effect:Ekin=h-W
e-
SQE 2005, Beijing, Nov. 23-27
• Introduction and Overview
• Single Photon Sources based on Quantum Dots
• Multi-Photon Sources
• Multiplexed Quantum Cryptography
• Demonstration of Deutsch-Jozsa Algorithm
• Summary & Outlook
Outline
SQE 2005, Beijing, Nov. 23-27
Motivation
Prerequisites for Quantum Computing*
1. A scalable physical system with well characterized qubits
2. The ability to initialize the state of the qubits to a simple initial state
3. Long relevant decoherence times, much longer than gate operations
4. A universal set of quantum gates (single and two-qubit gates)
5. A qubit-specific measurement capability
*David DiVicenzo, Fortschr. Phys. 48, 9-11, p. 771 (2000)
Quantum information processing relies on the controlled manipulation of qubits.
+|> =
SQE 2005, Beijing, Nov. 23-27
Motivation
Why photons?
• They interact very weakly with the environment (kbT<<h in the visible).
• They are quick (v = c, “flying qubits”).
• They can be easily detected (commercial detectors with >70% efficiency).
Any problems?• They interact only very weakly with each other.
• They are difficult to store (flying qubits!).
For the moment: Photon as tools to transfer quantum information from
one place to another (quantum cryptography, teleportation)
or among different quantum systems (quantum interfaces)
Future: Proposals and first steps towards optical quantum
computing
[Knill, Laflamme, Milburn, Nature 409, 46 (2001); P. Walther, et al.,
Nature 434, 169 (2005); O'Brien, et al. Phys. Rev. Lett. 93, 080502 (2004);
Okamoto et al. quant-ph/0506263 ].
SQE 2005, Beijing, Nov. 23-27
SPS with 100% efficiency
SPS with 25% efficiency
Introduction
Single photons from attenuated light?
• Attenuation of a light pulse does not change the Poissonian photon statistics.
• Attenuted light pulses only mimick real single photon sources.
• There is always a finite probability to find more than one photon per pulse
0 1 2 30.00
0.25
0.50
0.75
1.00
Pro
bab
ilit
y
Number of photons
Weak pulse with <n> = 0.25
SQE 2005, Beijing, Nov. 23-27
1. Coherent evolution (STIRAP and cavity QED)Atoms/ions in cavities
Methods to Generate Single Photons on Demand
Pu
mp
5P 3/2
5S 1/2
ST
IRA
P
Ato
m-c
avi
tyco
upl
ing
Dec
ay
|e ,0
|g ,1
A. Kuhn et al., Phys. Rev. Lett. 89, 067901 (2002)A. Kreuter et al., Phys. Rev. Lett. 92, 203002 (2004)W. Lange et al., Nature 431, 1075 (2004)C. Maurer et al., New Journal of Physics 6, 04 (2004)P. Bertet et al., Phys. Rev. Lett. 88, 143601 (2002)B. Varcoe et al., Nature 403, 743 (2000)
SQE 2005, Beijing, Nov. 23-27
Methods to Generate Single Photons on Demand
2. Projection (down-conversion and cavity QED)• parametric down-conversion in a non-linear crystal
• Rydberg atoms
C. K. Hong et al., Phys. Rev. Lett. 59, 2044 (1987)P. Kwiat et al., Phys. Rev. Lett. 24, 4337 (1995)G. Weihs et al., Phys. Rev. Lett. 81, 5039 (1998)B. Varcoe et al. Nature 403, 743 (2000)
SQE 2005, Beijing, Nov. 23-27
Methods to Generate Single Photons on Demand
3. Spontaneous emission (single emitters)• atoms, molecules, quantum dots, defect centers
• optical, electrical and STIRAP excitation
pulsed,(non-resonant)
excitation
spontaneoussingle photon
emission
relaxation
decay
QD: Kim et al., Nature 397, 500 (1999) Michler et al., Science 290, 2282 (2000) Santori et al., PRL 86, 1502 (2001) Yuan et al., Science 295, 102 (2002)
DC: Kurtsiefer et al., PRL 85, 290 (2000) Beveratos et al., PRA 64, 061802(R) (2001)
M: Brunel et al., PRL 83, 2722 (1999) Lounis & Moerner, Nature 407, 491 (2000)
SQE 2005, Beijing, Nov. 23-27
• Introduction and Overview
• Single Photon Sources based on Quantum Dots
• Multi-Photon Sources
• Multiplexed Quantum Cryptography
• Demonstration of Deutsch-Jozsa Algorithm
• Summary & Outlook
Outline
SQE 2005, Beijing, Nov. 23-27
10nm
[110]
10nm
[110] AFM
Contains ~10000 atoms
InP dots grown on GaInP
Quantum Dots
K. Georgsson et al., Appl. Phys. Lett. 67, 2981 (1995)
Transmission electron microscope images Atomic force microscope image
SQE 2005, Beijing, Nov. 23-27
Quantum Dots
Biexciton
Exciton
Ground state(empty QD)
Photoluminescence image of a set of InP quantum dots
n= 1
n= 2
n= 1
n= 2
G a InP InP G a InP
Ene
rgy
Size : O (10 nm )
Exc ito n in a Q D: Biexc ito n:
Photoluminescence of an ensemble of InAs quantum dots
exciton biexciton
SQE 2005, Beijing, Nov. 23-27
Specific advantages of single quantum dots
Quantum Dots
• Stability• Compatible with chip-technology• Wide spectral range• Electrical Pumping• High repetition rate• Strong interactions “available”
Specific disadvantages of single quantum dots
• Low temperature operation• Device production yield• Decoherence• Efficiency
TEM
AFM
SQE 2005, Beijing, Nov. 23-27
Experimental Setup
Sp
ectr
og
rap
h
Coincidence counter
Las
er( c
w o
r p
uls
ed)
Filter
Start-APD
Sto
p-
AP
D
CC
D
Michelsoninterferometer
Dichroicmirror
Hanbury Brown-Twisscorrelator
Liquid HeCryostat
(4 K)
Sample
g1 g2SPS
SQE 2005, Beijing, Nov. 23-27
Experimental Setup
SQE 2005, Beijing, Nov. 23-27
InP Quantum Dots in GaInP
Si substrate
EpoxyAl mirror (200 nm)
GaInP (400 nm)InP QDs
Si substrate
EpoxyAl mirror (200 nm)
GaInP (400 nm)InP QDs
• Emission around 690 nm (@ maximum detection efficiency of Si detectors)
• Lifetime around 2 ns
• Dot density: 108 cm-2 through 2 nm bandpass filter
• Linewidth around 100 µeV
670 675 680 685
without filtering
with 2-nm bandpass filter
Inte
nsi
ty (
a.u
.)
Wavelength (nm)
SQE 2005, Beijing, Nov. 23-27
-1 0 10
50
Nu
mb
er o
f co
inci
den
ces
(raw
dat
a, a
.u.)
Delay time (ns)-40 -20 0 20 40
0
50
100
150
Nu
mb
er o
f co
inci
den
ces
(raw
dat
a, a
.u.)
Delay time (ns)
-40 -20 0 20 400
Nu
mb
er o
fco
inci
den
ces
(arb
. un
its)
Delay time (ns)
pulsed
Intensity Correlation Measurements
V. Zwiller, et al., Appl. Phys. Lett. 82, 1509 (2003)
cw
• Central peak vanishes nearly completely
generation of only one photon per pulse
• Single photon generation observed up to 40 K
ZOOM
SQE 2005, Beijing, Nov. 23-27
Coincidence counter
-40 -20 0 20 400
Co
rrel
atio
ns
(arb
. un
its)
Delay time (ns)
Wave and Particle Aspects
Start-APD
Sto
p-
AP
D
Pulse counter(DAC)
200 250 3000
25
50
Nu
mb
er o
f co
un
ts p
er 1
0 m
s
Time after starting the measurement (s)
Taylor-experiment (1906)
Path length difference
T. Aichele, et al., AIP proc. Vol. 750, 35 (2005)V. Jacques, et al. Eur. Phys. J. D 35, 561 (2005)
SQE 2005, Beijing, Nov. 23-27
• Introduction and Overview
• Single Photon Sources based on Quantum Dots
• Multi-Photon Sources
• Multiplexed Quantum Cryptography
• Demonstration of Deutsch-Jozsa Algorithm
• Summary & Outlook
Outline
SQE 2005, Beijing, Nov. 23-27
Cascaded Emission
Young et al., PRB 72, 113305 (2005)
biexciton
exciton
ground state(empty QD)
n= 1
n= 2
n= 1
n= 2
G a InP InP G a InP
Ene
rgy
Size : O (10 nm )
Exc ito n in a Q D: Biexc ito n:exciton biexciton
-
+
+
Benson & Yamamoto, PRL 84, 2513 (2000)
SQE 2005, Beijing, Nov. 23-27
Cascaded Emission
670 675 680 685 690
250
5000
500
1000
15000
2500
5000
Wavelength / nm
ExcitonInte
nsity
/ a.
u.
Biexciton
Triexciton
40 60 800
25
50
300
400
500
200
400
600
t / ns
Exciton
Triexciton
Cor
rela
tions
/ a.
u.
Biexciton
Spectra and anti-bunching in photon cascades:
SQE 2005, Beijing, Nov. 23-27
Cascaded Emission
Coincidence counter
Start-APD
Sto
p-
AP
D
biexc.
exc.biexciton
triexciton
-40 -20 0 20 400
50
100
Co
inci
den
ces
(a.u
.)
Delay time (ns)
exciton
biexciton
Correlation measurements reveal dynamics of multiphoton cascades
J. Persson et al., Phys. Rev. B 69, 233314 (2004) D. V. Regelmann, et al. Phys. Rev. Lett. 87, 257401 (2001)E. Moreau et al., Phys. Rev. Lett. 87, 163601 (2001)A. Kiraz et al. Phys. Rev. B 65, 161303 (2002)
-20 -10 0 10 20800
1000
1200
1400
Co
inci
den
ces,
a.u
.
Delay time (ns)
SQE 2005, Beijing, Nov. 23-27
Single Photon Multiplexing
Separating spectral lines using a Michelson interferometer
One quantum emitter acts as two independent single photon sources.D e lay=
1 /2 R ep .R a te
Delaying the two photons by half the excitation repetition time doubles the photon rate.
-40 -20 0 20 400
10
20
30
406.6 ns
Co
inci
den
ces
(a. u
.)
Delay time (ns)
SQE 2005, Beijing, Nov. 23-27
• Introduction and Overview
• Single Photon Sources based on Quantum Dots
• Multi-Photon Sources
• Multiplexed Quantum Cryptography
• Demonstration of Deutsch-Jozsa Algorithm
• Summary & Outlook
Outline
SQE 2005, Beijing, Nov. 23-27
Quantum Cryptography:the BB84 Protocol
Alice Bob
Quantum channel
Classical public channel:
1 0
1 0
Eve Eve cannot copy the photon(no cloning theorem)
Bennett, Brassard, Proc. IEEE Int. Conf. on Computers, Systems & Signal Processing (1984), First realization with QDs: Waks et al., Nature 420, 762 (2002)
SQE 2005, Beijing, Nov. 23-27
BB84 Protocol
• Alice sends randomly polarized photons (0, 45, 90 or 135°) to Bob.
• Bob randomily measures in the straight or diagonal base.
• Bob keeps his results secret.
• Bob publically tells his measurement bases (not the results!). Alice publically tells him if he chose the right base.
• Alice and Bob keep only the results with the common bases.
• They both have now a common and random key: 1 1 0 0 1 ...
SQE 2005, Beijing, Nov. 23-27
M i c h e l s o nD e l a yF r o mS i n g l e P h o t o nS o u r c e A L I C E E O M Q u a n t u m C h a n n e lw 1
w 2 M i c h e l s o n B O BD e t e c t i o nE O M A n a l y z e r
E O MF r o mS i n g l e P h o t o nS o u r c e A L I C E E O M
Q u a n t u m C h a n n e lw 1
w 2 M U X D E M U XM i c h e l s o n M i c h e l s o nM i c h e l s o n D e t e c t i o n
B O B
E O ME O M D e t e c t i o n
A n a l y z e r
M iche lson
D e lay
F romS ing le P ho ton
S ource
ALIC E
E O M
Q uantum C hannelw 1
w 2
M iche lson
BO B
D etectionE O M
A na lyzer
E O MF rom
S ing le P ho tonS ource
ALIC EE O M
Q uantum C hannelw 1
w 2 M U X D E M U X
M iche lson M iche lsonM iche lson
D etection
BO B
E O M
E O M D etection
A na lyzer
Multiplexed Quantum Cryptography
SQE 2005, Beijing, Nov. 23-27
Multiplexed Quantum CryptographyBB84 Protocol
EO M EO M AP D
From sing lephoton source
Alice Bob
Polarizer Analyzer
Alice´s original data Encoded image Bob´s decoded image
Transmission to Bob: 30 successfull counts/s at a laser modulation of 20 kHz
Similarity between Alice´s and Bob´s keys: 95%
T. Aichele, G. Reinaudi, O. Benson, Phys. Rev. B, 70, 235329 (2004)
SQE 2005, Beijing, Nov. 23-27
• Introduction and Overview
• Single Photon Sources based on Quantum Dots
• Multi-Photon Sources
• Multiplexed Quantum Cryptography
• Demonstration of Deutsch-Jozsa Algorithm
• Summary & Outlook
Outline
SQE 2005, Beijing, Nov. 23-27
Deutsch-Jozsa-Problem
0
1
0
1
1
0
0
0
1
1
f01 f10 f00 f11
Counterfeighterproblem
Mathematical problem:constant or balanced function?
SQE 2005, Beijing, Nov. 23-27
U
x,
1
0
y x,y0 1
H
H
y
x
x,x,y2
y f(x)
x
f
H
y3
21 x
Quantum circuit: Four possible functions f(x):
f00 f11 f01 f10
f(0) 0 1 0 1
f(1) 0 1 1 0
constant balanced
|<1|x>|2 0 0 1 1
• possibility to decide, if f(x) is balanced or constant using only one evaluation of f(x)!
• any classical apparatus would need at least two evaluations of f(x)!
Deutsch-Jozsa-Algorithm
SQE 2005, Beijing, Nov. 23-27
qubit |x>: spatial modes of the photon
qubit |y>: polarization of the photon
• photon state behind polarizer
|y>=( |0> - |1> )/21/2
= Hadamard gate for |y>
• BS1 and BS2 representHadamard gates for |x>
Implementation of Uf by /2 plates flipped in the beam.
f00 f11 f01 f10
/2 at
{|x>= |0>}
out in out In
/2 at
{|x>= |1>}
out in In out
Realization with Linear Optics
Polarisator
x1
=x
BS1= 0
0
21 xBS2
Uf
1
Polarizer
E. Brainis et al., Phys. Rev. Lett. 90, 157902 (2003)M. Michler et al., Phys. Rev. Lett. 84, 5457 (2000)S. Takeuchi, Phys. Rev. A 62 , 032301 (2000) N. J. Cerf et al., Phys. Rev. A 57,1477 (1998)
Singlephoton
SQE 2005, Beijing, Nov. 23-27
• distinguishability of balanced from constant function in a single quantum computation with a probability of 85%M. Scholz, S. Ramelow, T. Aichele, O. Benson, submitted
• well controllable single photonic qubit • feasibility of upscaling and use in LOQC
D. Fattal, E. Diamanti, K. Inoue, Y. Yamamoto, PRL 92, 037904 (2004)
Deutsch-Jozsa-Algorithm: Experimental Results
SQE 2005, Beijing, Nov. 23-27
from source
BS
PBS
PBS
phasenoise
BS
Hb -Vb
Ha -Va
Hb -Va
Ha -Vb
Hb -Vb
Ha -Va
/2
Demonstration of Algorithms and Influence of Decoherence
• Scholz, et al., submitted • M. Mohseni, et al., PRL 91,
187903 (2003)• M. Bourennane, et al. PRL 92,
107901(2004)
Single photon sources based on single quantum dots can be used to demonstrate and test influence of noise and decoherence on qubits in quantum algorithms.
E.g.: Encoding of qubits in states that are insensitive to a certain class of (phase) noise
SQE 2005, Beijing, Nov. 23-27
• Introduction and Overview
• Single Photon Sources based on Quantum Dots
• Multi-Photon Sources
• Multiplexed Quantum Cryptography
• Demonstration of Deutsch-Jozsa Algorithm
• Summary & Outlook
Outline
SQE 2005, Beijing, Nov. 23-27
Optical quantum computing
based on single photons and
linear optics requires triggered
indistinguishable photons
[Knill, Laflamme, Milburn, Nature
409, 46 (2001)].
Realization of indistinguishable
photons and entangled photon
pairs in recent experiments by
Yamamoto
[Santori, et al., Nature 419, 594
(2002)]:
Quantum Computing with Single Photons
SQE 2005, Beijing, Nov. 23-27
Demonstration of multiplexed quantum cryptography and realization of a quantum computing algorithm
Single photon sources based on quantum dots are a reliable tool for quantum information processing
Efficient LOQC based on qdot sources according to KLM [E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2000)] can be envisioned
Realization of indistinguishable photons (ancillas)Entangled photon pairs on demandImplementations in controlled experiment
Next stepsReliable sources of multiple ancilla states Formation of entanglement using cascaded emissionStorage of single photons from single quantum dots
Summary and Outlook