Quantum Dot Single-Photon Source:
Prospects for Applications in Quantum Information Processing
A. Imamoglu
Department of Electrical and Computer Engineering, and
Department of Physics,
University of California, Santa Barbara, CA 93106
Outline
1) Quantum dots
2) Properties of quantum dot single photon sources
3) High efficiency photon counters
Co-workers
A. Kiraz, J. Urayama, B. Gayral, C. Becher, P. Michler,
C. Reese, L. Zhang, E. Hu
W.Schoenfeld, B. Gerardot, P. Petroff
Requirements for linear optics quantum computation
(LOQC)
• Linear optical elements: beam-splitters, polarizers, lenses
optical delay/memory
• Single-photon sources: indistinguishable single-photon pulses
on demand (with efficiency > 99%)
• Photon counters:
high-efficiency detectors with
single-photon discrimination
 Appears to avoid the very demanding requirement for large
(coherent) photon-photon interactions.
Single Photon Sources
A regulated sequence of optical pulses that contain one-and-only-one photon
Single atom in a cavity:
Rempe et al. PRL (2002)
Single nitrogen vacancy in diamond:
H. Weinfurter et al. PRL (2000)
P. Grangier et al. PRL (2002)
Single Molecule at room temperature:
B. Lounis and W.E. Moerner, Nature (2000)
Single InAs Quantum Dot in a microcavity:
P. Michler et al., Science 290, 2282 (2000)
C. Santori et al., PRL 86, 1502 (2001)
Z. Yuan et al., Science 295, 102 (2002)
What is the signature of a single-photon source?
• Intensity (photon) correlation function:
 gives the likelihood of a second
photon detection event at time t+,
given an initial one at time t (0).
g ( 2 ) ( ) 
: I (t ) I (t   ) :
I (t )
2
What is the signature of a single-photon source?
• Intensity (photon) correlation function:
 gives the likelihood of a second
photon detection event at time t+,
given an initial one at time t (0).
g ( 2 ) ( ) 
: I (t ) I (t   ) :
I (t )
2
• Experimental set-up for photon correlation [g(2)()] measurement:
Records the waiting-time
between the successive
photon-detection events at
the two detectors (APD).
Signature of a triggered single-photon source
• Intensity (photon) correlation function:
g ( 2 ) ( ) 
 gives the likelihood of a second
photon detection event at time t+,
given an initial one at time t (0).
: I (t ) I (t   ) :
I (t )
2
• Triggered single photon source: absence of a peak at =0 indicates
that none of the pulses contain more than 1 photon.
g(2)()
0

Quantum Dots
•
Artificial structures that confine electrons (and holes) in all 3 dimensions.
Atoms
Quantum dots (QD)
DEatom
Vatom (x)
DEQD
VQD (x)
1Å
 20 - 500 Å
 Quantized (discrete) eigenstates in both cases ( 0D density of states).
DEatom ~ 1–10 eV >> kTroom = 26 meV
DEQD ~ 1–100 meV ~ kTroom !
Unlike atoms, QDs are
sensitive to thermal
fluctuations at room temp.
Quantum Dots vs. Atoms
• Strongly trapped emitters: QDs do not have random thermal
motion.
• Easy integration in nano-cavity structures.
• Strong coupling to optical fields: QD oscillator strength
f ~ 10 – 300 (collective enhancement).
• Electrical injection of carriers (electrons and holes).
• Each QD has a different resonance (exciton) energy.
• Difficult to tune QDs into resonance with cavity modes.
Self-Assembled InAs Quantum Dots
Quantum dots appear
spontaneously due to
lattice mismatch,
during MBE growth.
2 μm
AFM of InAs QDs
Each quantum dot is different
Atom-like characteristics of Quantum Dots:
• sharp emission lines
• photon antibunching
 artificial atom for T < 77 K!
2 μm
A single InAs Quantum Dot
InAs/GaAs Single QD
phonon
emission
-
T=4K
-
p-Shell
2
P (W/cm ) s-Shell
non-resonant
laser excitation
Intensity (a.u.)
650
+
400
2X 1X
+
210
GaAs
105
1.25
exciton emission (1X)
+
InAs
GaAs
Two principal emission lines from lowest energy s shell
55
x2 in intensity
•1X
17
x5 in intensity
•2X
1.30
Energy (eV)
1.35
radiative recombination of a single e-h pair
in the s-shell (exciton)
radiative recombination when there are two e-h
pairs in the s-shell (biexciton)
Due to carrier-carrier interaction
Typically h1X = h2X + 3 meV
Photon correlation of a single-photon source
 all peaks in G(2)() have the same
intensity
 pulsed coherent light
Photon correlation of a single-photon source
Pump power well above saturation level
 all peaks in G(2)() have the same
intensity
 pulsed coherent light
 the peak at =0 disappears.
 single photon turnstile device with
at most one photon per pulse
Turnstile Device at Different Pump Powers
60 P (W/cm2)
well above saturation
40
52
0
1X Intensity
(a.u.)
(2)
G ()
20
onset of saturation
40
20
0
20
0 50 100 150
Power (W/cm2)
14
well below saturation
 Lower pumping power has
the same effect as loss in the
optical path
4
0
-10
0
10 20 30 40 50 60 70 80
Delay Time  (ns)
Microdisk Cavities
GaAs
GaAs
GaAs
GaAs
AlGaAs
AlGaAs
GaAs
substrate
GaAs
substrate
No roughness on the sidewall up to 1nm !
Q>18000 for 4.5mm diameter microdisk
Q=11000 for 2mm diameter microdisk
Photoluminescence from a high-QD
density sample
Q>18000
Fundamental whispering
gallery modes cover a ring
with width ~ l/2n on the
microdisk
A single quantum dot embedded in a microdisk
Intensity (a.u.)
Larger width of the peaks due
to longer lifetime of the
quantum dot
P=20W/cm2
T=4K
1X
Q = 6500
2X
Pump power well above saturation level
WGM
1.315
1.320
1.325
Energy (eV)
1.330
Tuning the exciton into resonance with a cavity mode
Energy (meV)
1323
WGM
1X
1322
Cavity coupling can provide better collection
1321
1320
1319
T=44K
1318
0
10
20
30
40
50
60
WGM Intensity (a.u.)
Temperature (K)
800
600
400
200
0
-1.5
-1.0
-0.5
WGM
E
0.0
1X
-E
0.5
(meV)
1.0
•Small peak appears at =0
•Peaks in G(2)() are narrower:
Purcell effect ?
Quantum dot lifetime measurement
1
T=50K
1.9nsec
Intensity (a.u.)
Intensity (a.u.)
1
0.1
T=4K
1.7nsec
0
2
4
6
8
10
Time (ns)
12
14
16
18
T=4K
1.75nsec
0.1
T=48K
1.75nsec
T=31K
850psec (resonance)
0
2
4
6
8
10
12
14
16
18
Time (ns)
 Time-correlated single-photon counting experiments show no temperature
dependence for exciton lifetime.
 First direct measurement of Purcell effect (FP  2) for a single quantum dot.
20
Purcell Effect: cavity-induced decay
• When an emitter is placed inside a high-Q, low volume cavity, there are two
channels for radiative decay:
i) spontaneous emission into vacuum modes (Gspon)
ii) irreversible emission into the cavity mode (g2/ Gcav) – scales as Q/Veff
 Purcell effect: g2/ Gcav > Gspon
Purcell effect in a single photon source
i) Fast emission  reduced jitter in photon emission time.
ii) Emission predominantly into a single cavity mode  high collection efficiency.
iii) Reduced sensitivity to dephasing  Transform limited (indistinguishable) photons in
the good-cavity limit: g2 > Gcav gdep
 Purcell effect is essential for applications in linear optics quantum computation.
Linear optics quantum computation (LOQC)
•
Key step is two-photon interference on a beam-splitter:
E1
E3
|yout>  |20>  |02>
 g34(2)(=0) = 0
|yin>  |11>
E2
E4
No coincidence detection for
indistinguishable photons
 Requires that the two incident photons have the same spatio-temporal profile:
single photon pulses have to be transform-limited . For LOQC we need (?)
g34(2)(=0) < 0.01
[ Santori et al. observed g34(2)(=0) = 0.3 using resonant excitation]
Can we use QD single-photon source in LOQC?
• High single-photon collection efficiency (h ~ 44%) has been
demonstrated using the Purcell effect (Gerard et al., Pelton et al.):
 FP ~ 10 gives h  90% and photon emission time sp ~ 100 psec.
• Even under resonant p-shell excitation, we have jitter in photon emission
time ~ 10 psec:
phonon
 Coincidence count-rate in two-photon
interference will be ~ 10%, since
information about the single-photon
pulse can be obtained from the
emitted phonon(s).
emission
resonant laser
excitation
 The requirements for high collection efficiency and complete
indistinguishability are incompatible (even in the good-cavity limit)!
Photon counting using stored light
• It is possible to map the quantum state of a propagating light pulse
onto metastable collective excitations of an atomic gas, using
electromagnetically induced transparency (EIT).
 # of incoming photons = # of atoms in the (hyperfine) excited state.
• State-selective fluorescence measurements (developed for trapped
ions) can achieve efficiencies > 99% in measuring the number of
atoms/ions in a given state – without requiring high efficiency photon
detection.
 By combining these two techniques, we could realize a photon counter
with efficiency > 99%.
Storing light using electromagnetically induced
transparency (EIT)
i) coupling laser on
EIT medium
coupling laser
signal pulse
ii) coupling laser on; signal
pulse inside the medium
signal pulse
F=2, mF=2
signal pulse
F=1, mF=1
iii) coupling laser off
# of atoms in state |F=2,mF=2>
= # of initial signal photons
Stored signal pulse (dark
polariton)
Measuring photon number using EIT
F=3, mF=3
detection laser
scattered
photons
EIT medium
F=2, mF=2
stored singal pulse
(dark polariton)
detection laser
F=1, mF=1