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Single Photon Emitters and their use in Quantum Cryptography
Presentation by: Bram Slachter
Supervision: Dr. Ir. Caspar van der Wal
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Contents
The Ideal single photon emitter Example of their use: Quantum Cryptography in a
nutshell Experimental setups Overview of various single photon emitters:
Quantum dot single photon emitters Quantum ‘well’ single photon emitters* Molecule single photon emitters* Colour Centre single photon emitters*
Conclusion
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The ideal single photon emitter
Single photon pulses on demand Pulses have identical wavepackets Room temperature operation Easy to create Frequency tuneable
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The ideal single photon emitter: States of light
Maxwell eqs for a cube give EM modes with discrete and polarization
EM modes behave as H.O. When quantized these give traditional QM H.O. levels with energy .
For these EM modes: well defined and undefined due to number phase Heisenberg minimum uncertainty
12E n
k
Classical light (laser light, thermal light) in superposition of these states: (Super)Poissonian
E
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The ideal single photon emitter: States of light
In reality: ‘infinite’ cube -> quantization becomes continuous -> discrete goes to continuous .
Continuous mode excitation now localized in wavepackets with distribution in :
k
Wavepacket excitation still defined by number and phase but also has a distribution † †ˆ ˆ ˆ ˆ ˆ ˆ n aa n d a a
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The ideal single photon emitter
Single photon wavepackets: lowest excitation possible
†ˆ ˆ ˆ1 1 1n d a a
Consecutive wavepackets emitted -> same wavepackets
†ˆ1 0d a
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Quantum Cryptography in a Nutshell
Modern cryptography: encryption and decryption procedures depend on a secret key
This key consists of a randomly chosen string of bits which needs to be shared once in a while: key distribution problem
Mathematical solution: public key – private key insecure when quantum computer becomes available
Quantum key distribution Entangled states Non orthogonal states*
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Quantum Cryptography in a Nutshell
, 0,1
, 0,1
Sender sends a random key with each bit encoded in a random basis
Detection basis random for each bit Over a public channel the bases chosen for
each bit are compared and the ones with the right bases are kept
Randomly chosen part of the remaining key is publicly checked for errors
No errors -> safe key established
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Experimental Setups:Hanbury Brown Twist experiment
Determination multiple photon suppression:
HBT experiment
1 2(2)2
I t I tg
I
Calculation: 2 10 1 for g n
n
Two photon suppression 2 0g
Santori et al, Nature 419 pg 595 (2002)
Classical: 2 0 1g
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Experimental Setups: two photon interference Indistinguishability consecutive photons in
experiments -> wavepacket overlap Two photon interference: When two photons enter a 50-
50 beam splitter from each side they can only leave together: known as the ‘bunching’ of photons
non entangled input:
† †1 2 ˆ ˆ1 , 1 ' ' 0dt dt t t a t a t
2
3 4 3 4
12 ,0 0 ,2 1
4P P J
2
3 4
11 ,1 1 1
2P J
22 *J dt t t
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Experimental Setups: two photon interference
Santori et al, Nature 419 pg 595 (2002)
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Overview Single Photon Emitters:Quantum Dot SPE
2
2
e
C
Semiconductor quantum dot Discrete levels Charging effects
Created by MBE, Etching and E-beam
Excited with a laser:
1) Santori et al, Nature 419 pg 595 (2002)
2) Michler et al, Science 290 pg 2282 (2000)
1)
2)
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Overview Single Photon Emitters:Quantum Dot SPE
2
2
e
C
Semiconductor quantum dot Discrete levels Charging effects
Excited with a laser. Charging effects used for single photon selection
Michler et al, Science 290 pg 2282 (2000)
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Overview Single Photon Emitters:Quantum Dot SPE Wavepacket overlap by
two photon interference 0.7-0.8.
2 0 0.05 to 0.2g
Problem: Room temperature operation hard due to optical phonon emission in the bulk
Performance reasonable: lifetime limited Big advantage: electrical
excitation possible with p-i-n junction with quantum dots in intrinsic region.
Yuan et al, Science 295, pg 102 (2002)
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Overview Single Photon Emitters:Quantum Well SPE
Post structures created with MBE, E-Beam Lithography and plasma etching
Uses simultaneous Coulomb blockade for electrons and holes
Intrinsic quantum well separated by tunnel barriers from an n- and p-doped quantum well lying in a host material
Operating at 20 mK
Kim et al, Nature 397, pg 500 (1999)
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Overview Single Photon Emitters:Quantum Well SPE
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Overview Single Photon Emitters:Quantum Well SPE
Frequency controlled current Conductance quantization
Kim et al, Nature 397, pg 500 (1999)
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Overview Single Photon Emitters:Quantum Well SPE
No HBT experiment but those are probably pretty good.
Room temperature operation hard: Smaller quantum dots needed -> bigger energy spacing and
coulomb effects Higher potential barriers to suppress non radiative decay
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Overview Single Photon Emitters:Molecule SPE
Laser targeted at a single molecule: Laser light filtered Highly Fluorescent and temperature stable
molecules needed
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Overview Single Photon Emitters:Molecule SPE Molecules have been reported which work at room
temperature.
Lounis & Moerner, Nature 407, pg 491 (2000)
Reasonable two photon suppression but not always easy to process
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Overview Single Photon Emitters:Molecule SPE
Also a setup possible based on adiabatic following:
Brunel et al, Phys. Rev. Lett. 83, pg 2722 (1999)
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Overview Single Photon Emitters:Colour Centre SPE
Same 4 level principle as before Diamond nanocrystals grown from diamond powder. Nitrogen impurities naturally present By electron bombardment vacancies produced which move
next to nitrogen impurities by annealing Nitrogen-Vacancy colour centre produced Reasonable two photon suppression and room
temperature stable Can be spincoated but the difficultly of targeting the
nanocrystals remains
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Conclusion
All structures in principle capable of producing room temperature stable ‘ideal’ SPE
All structures have their drawbacks: Quantum dot/well SPE have a fight against non radiative decay Molecule/NV Colour Centre SPE less easy to process but have
already been proven to work at RT
Of all these structures NV Colour Centre looks most easiest to implement