Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Entangled Photon Pairs from Semiconductor Quantum
DotsNikolay 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
Systems A and B, Hilbert space
The combined state is not entangled (seperable) if
BAH H H
1i iAB i A B i
i i
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Alice Bob
iA
iBi
1i iAB i A B i
i i
(not) Entanglement
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Entanglement
How can we tell if a general state is entangled? For two qubits, we have the Peres criterion:
is entangled iff
its partial transposition satisfies
AB
AB0AT
AB
*00,01* *00,10 01,1
00,00 00,01 00,10 00,11
01,01 01,10 01,11
10,10 10,11
11,11
0* * *00,11 01,11 10,11
ATAB
A. Peres, Phys. Rev. Lett. 77, 1413, 1996.
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Example
The state gives the density matrix
The partial transpose gives a non –positive matrix
00 11
1/ 2 0 0 1/ 2
0 0 0 0
0 0 0 0
1/ 2 0 0 1/ 2
1/ 2 0 0 0
0 0 1/ 2 0
0 1/ 2 0 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 resonanceexcitation
emission due to radiative recombination
h
S
P
P
S
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Right circular polarization
S shell 2 e-
Left circular polarization
S shell 2 h+
Entangled photon pairs from radiative cascades
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
| VVp | HHp
Suggestion: Benson Yamamoto et al PRL 2000
Bi-exiton radiative casacadeIsotropic QD Anisotropic QD
R L
L R
| |XX XXX XR L RL
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
The anisotropic e-h exchange interaction
The photon’s energy indicates the
decay path
No entanglement Classical
correlations only
H V
HV
+-
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
| | | | | |XX X HH H XX X VV VH H p G V V p G
* | |HH VV H Vp p G G
PolarizationMomentum Momentum wave functionwave function
EnvironmentEnvironment
2
2
0 0
0 0 0 0
0 0 0 0
0 0
HH HV VH VV
HH
HV
VH
VV
Reduced Density Matrix For Polarization
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Maximal Bell inequality violation:
M. Horodecki et. al., Phys. Lett. A 223,1 (1996)
Peres criterion for entanglement:
10
2
2( ) 2 1 4 2Tr B
2
2
0 0
0 0 0 0
0 0 0 0
0 0
HH HV VH VV
HH
HV
VH
VV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Two photon polarization density matrix:
2
2
0 0 0
0 0 0 0
0 0 0 0
0 0 0
HH HV VH VV
| 0
0HH VVp p
In our caseIn our case:
However, we can still make a measurement on the wave packetHowever, we can still make a measurement on the wave packet:
,
projection
P
P
P
*
2' HH VVH V
p P pG G
P
2
2*
0 0 '
0 0 0 0
0 0 0 0
' 0 0
HH HV VH VV
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 withoutwithout 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 filtering2| ( , ) |HA 2| ( , ) |VA
*
H VA A
Relative Number of photon pairs
2 2(| | | | )H V
spectral window
N A A d
Off diagonal matrix element
*1H V
spectral window
A A dN
N,γ
Δ = 27μeV
Γ = 1.6μeV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Density matrix – spectral window of 25 μeV
(closed slits)
Density matrix – spectral window of 200 μeV
(open 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
22 1+ 4 γ = 2.13 ± 0.07 > 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 ?
H V< G | G > 1No remnant ‘which path’ witness in the enviroenment of the QD!!
γ
27 eV
1.6 eV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Spectral Filtering in the presence of inhomogeneous broadening
Energy of XX photon (1)
Energy of X photon (2)
Energy conservation
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 : D1
D2correlator
IIi i (t(t22))
IIj j (t(t11))
PL
Energy
I(t) - Intensity
2 i j tij
i jt t
I t I tg
I t I t
Second order Intensity Correlation Function.Second order Intensity Correlation Function.
ji
MC
MC
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 Cross-Correlation Measurements
Decay time of 0.8 nsec Γ=1.6μeV
Time (nsec)
0 0X XX0 0X XX
number of correlated radiative cascades
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization TomographySpectral window 200 μeV
1 1 12 2 2( ) ); ;( ( )H V HD R V HLi iV
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
1.5 ns window
no subtraction of events from distinct cascades!
Peres = -0.03 ± 0.06Largest negative eigenvalue of the partially transposed matrix:
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
0.6 ns window
no subtraction of events from distinct cascades!
Peres = -0.15 ± 0.07Largest negative eigenvalue of the partially transposed matrix:
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
1.5 ns temporal window
no subtraction of events from distinct cascades!
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
0.6 ns temporal window
no subtraction of events from distinct cascades!
Technion – Israel Institute of Technology, Physics Department and Solid State Institute
Polarization TomographySpectral window 25 μeV