Entangled Photon Pairs from
Semiconductor Quantum Dots
Nikolay Akopian, Eilon Poem and David Gershoni
The Solid State Institute and the Physics Department, Technion, Haifa 32000,
Israel
Netanel Lindner, Yoav Berlatzky and Joseph Avron
The Physics Department, Technion, Haifa 32000, Israel
Brian Gerardot and Pierre Petroff
Materials Department, UCSB, CA 93106, USA
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Outline






Motivation: deterministic sources for entangled photons.
Entanglement.
Radiative cascades in semiconductor quantum
dots.
Entanglement by spectral projection.
Why does it work in spite of inhomogeneous
broadening.
Conclusion: semiconductor quantum dots are
practical sources for entangled photons on demand.
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Motivation



Entanglement is an essential resource of quantum
information processing.
Entangled photons are particularly attractive due to
their non interacting nature, and the ease with which
they can be manipulated.
Quantum computing, quantum communication require
“Event ready” entangled photon pairs. Therefore,
deterministic sources of entangled photons are
needed.
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Entanglement
H  H AHB

Systems A and B, Hilbert space

The combined state is not entangled (seperable) if
 AB  
i
i
i
i  A   B
i  1
i
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
(not) Entanglement
Alice
Bob
i
A
i
B
i
 AB  
i
i
i
i  A   B
i  1
i
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Entanglement


How can we tell if a general state  AB is entangled?
For two qubits, we have the Peres criterion:
 AB is entangled iff
TA
its partial transposition satisfies  AB
0
A. Peres, Phys. Rev. Lett. 77, 1413, 1996.

TA
AB
 00,00
 *
00,01

 *
 00,10
 *
 00,11
00,01 00,10
01,01 01,10
*
01,1
10,10
0
*
*
01,11 10,11
00,11 

01,11

10,11 

11,11 
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Example

The state   00  11
1/ 2
 0
 
 0
1/ 2


gives the density matrix
0
0
0
0
0 1/ 2 
0 0 

0 0 
0 1/ 2 
The partial transpose gives a non –positive matrix
0
0 
1/ 2 0
 0
0 1/ 2 0 

 
0 
 0 1/ 2 0
 0
0
0 1/ 2 

Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Strain induced Self assembled Quantum Dots
3D confinement of charge carriers
with discrete spectrum of spin
degenerate energy levels.
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Single semiconductor quantum dot
Off resonance
excitation
P
S
emission due to
radiative recombination
h
S
P
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Entangled photon pairs from radiative
cascades
Right circular
polarization
S shell 2 e-
Left circular
polarization
S shell 2 h+
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Bi-exiton radiative casacade
Isotropic QD
R
Anisotropic QD
L
| pHH  | pVV 
L
R
 | RX LXX   | LX RXX 
Suggestion: Benson Yamamoto et al PRL 2000
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
The anisotropic e-h exchange interaction
H
The photon’s energy
indicates the decay
path
V
-
+
H
V

No entanglement
Classical
correlations only
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
   | H XX H X | pHH | GH   | VXXVX | pVV | GV 
Polarization
Momentum
wave function
HH
HV VH


 0
 
0

 

2
0 0
0 0
0 0
0 0
Environment
VV
 

0 
0 

2
 
HH
HV
VH
Reduced Density Matrix
For Polarization
   *  pHH | pVV  GH | GV 
VV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
HH
HV VH


 0
 
0

 

2
0 0
0 0
0 0
0 0
VV
 

0 
0 

2
 
Peres criterion for entanglement:
HH
HV
1
  0
2
VH
VV
Maximal Bell inequality violation:
M. Horodecki et. al., Phys. Lett. A 223,1 (1996)
Tr ( B )  2 1  4 
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
2
2
Two photon polarization density matrix:
HH
HH HV
HVVH
VH VV
VV
In our case:
 pHH | pVV  0
  0
 2 2

  00

 00

 0 *
  '
00 0 ' 

00 00  
00 00  

22
00 00   

00
00
00
However, we can still make a measurement on the wave packet:
P

,
P
P  projection
 '
 * pHH P pVV
P 
2
GH GV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
The experimental setup
Nika
Akopian
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization sensitive photoluminescence
  27  eV



Spectral
diffusion!!
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization density matrix
without spectral projection
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Spectral projection – Elimination of the ‘which
path’ Information.
Photons
from both
decay paths
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Spectral filtering
| AV (, ) |2
| AH (, ) |2
Δ = 27μeV
Γ = 1.6μeV
N,γ
*
AH AV
Relative Number of
photon pairs
N
Off diagonal matrix element

(| AH |  | AV | )d 
2
2
spectral  window
1
*

AH AV d

N spectral window
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Density matrix – spectral window of 200
25 μeV
μeV
(closed
(open slits)
slits)
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Density matrix – spectral window of 25 μeV
(closed slits)
γ = 0.18 ± 0.05
2 1 + 4 γ = 2.13 ± 0.07 > 2
2
Bell inequality violation
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Is there any ‘which path’ information left in the degrees
of freedom of the QD’s environment ?
  1.6 eV
  27  eV
γ
No remnant ‘which path’ witness in the
enviroenment of the QD!!
< G H | G V > 1
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Spectral Filtering in the presence of inhomogeneous
broadening
Energy of X
photon (2)
Energy
conservation
Energy of XX
photon (1)
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Spectral Filtering in the presence of inhomogeneous broadening
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Conclusions:

First demonstration of entangled photon pairs from the
radiative cascade in SCQDs.
No other “which path” information in the environment.
Deterministic entangled photon pair devices based on
SCQD are thus possible provided   is increased
such that no spectral filtering is needed.
Akopian et al, Phys. Rev. Lett. 96, 130501 (2006)

Lindner et al, quant-ph/0601200 .



Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Intensity Cross--Correlation Function :
j
D1
MC
i
PL
Energy
Second order Intensity Correlation Function.
gij   
 2
Ii  t  I j  t   
Ii  t 
t
I j t 
t
Ij (t1)
MC
D2
Ii (t2)
t
correlator
I(t) - Intensity
conditional probability of detecting photon from line j at time
(t+) after photon from line i had been detected at time (t)
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization Sensitive Intensity CrossCorrelation Measurements
X 0  XX 0 X 0  XX 0
number of correlated
radiative cascades
Decay time of 0.8 nsec
Γ=1.6μeV
Time (nsec)
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization Tomography
D
1
2
( H  V ); R 
1
2
Spectral window 200 μeV
( H  iV ); L 
1
2
( H  iV )
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
no subtraction of events from distinct cascades!
1.5 ns window
Largest negative eigenvalue of
the partially transposed matrix:
Peres = -0.03 ± 0.06
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
no subtraction of events from distinct cascades!
0.6 ns window
Largest negative eigenvalue of
the partially transposed matrix:
Peres = -0.15 ± 0.07
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
no subtraction of events from distinct cascades!
1.5 ns
temporal
window
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
no subtraction of events from distinct cascades!
0.6 ns
temporal
window
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization Tomography
Spectral window 25 μeV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute