Single Photon Emitters and their use in Quantum Cryptography

Presentation by: Bram Slachter

Supervision: Dr. Ir. Caspar van der Wal

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

The ideal single photon emitter

Single photon pulses on demand Pulses have identical wavepackets Room temperature operation Easy to create Frequency tuneable

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

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

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

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*

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

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

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

Experimental Setups: two photon interference

Santori et al, Nature 419 pg 595 (2002)

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)

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)

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)

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)

Overview Single Photon Emitters:Quantum Well SPE

Overview Single Photon Emitters:Quantum Well SPE

Frequency controlled current Conductance quantization

Kim et al, Nature 397, pg 500 (1999)

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

Overview Single Photon Emitters:Molecule SPE

Laser targeted at a single molecule: Laser light filtered Highly Fluorescent and temperature stable

molecules needed

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

Overview Single Photon Emitters:Molecule SPE

Also a setup possible based on adiabatic following:

Brunel et al, Phys. Rev. Lett. 83, pg 2722 (1999)

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

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