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