Technion – Israel Institute of Technology, Physics Department and Solid State Institute 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
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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