# A semiconductor source of triggered entangled photon pairs.

**ABSTRACT** Entangled photon pairs are an important resource in quantum optics, and are essential for quantum information applications such as quantum key distribution and controlled quantum logic operations. The radiative decay of biexcitons-that is, states consisting of two bound electron-hole pairs-in a quantum dot has been proposed as a source of triggered polarization-entangled photon pairs. To date, however, experiments have indicated that a splitting of the intermediate exciton energy yields only classically correlated emission. Here we demonstrate triggered photon pair emission from single quantum dots suggestive of polarization entanglement. We achieve this by tuning the splitting to zero, through either application of an in-plane magnetic field or careful control of growth conditions. Entangled photon pairs generated 'on demand' have significant fundamental advantages over other schemes, which can suffer from multiple pair emission, or require post-selection techniques or the use of photon-number discriminating detectors. Furthermore, control over the pair generation time is essential for scaling many quantum information schemes beyond a few gates. Our results suggest that a triggered entangled photon pair source could be implemented by a simple semiconductor light-emitting diode.

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**ABSTRACT:**Practical application of the generalized Bell's theorem in the so-called key distribution process in cryptography is reported. The proposed scheme is based on the Bohm's version of the Einstein-Podolsky-Rosen gedanken experiment and Bell's theorem is used to test for eavesdropping.Physical Review Letters 09/1991; 67(6):661-663. · 7.73 Impact Factor - SourceAvailable from: Hugo Zbinden
##### Article: Quantum cryptography

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**ABSTRACT:**Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Comment: 55 pages, 32 figures; to appear in Reviews of Modern PhysicsApplied Physics B 12/1998; 67(6). · 1.63 Impact Factor - SourceAvailable from: usc.edu[Show abstract] [Hide abstract]

**ABSTRACT:**Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.Nature 02/2001; 409(6816):46-52. · 42.35 Impact Factor

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A semiconductor source of triggered entangled

photon pairs

R. M. Stevenson1, R. J. Young1,2, P. Atkinson2, K. Cooper2, D. A. Ritchie2& A. J. Shields1

Entangled photon pairs are an important resource in quantum

optics1, and are essential for quantum information2applications

such as quantum key distribution3,4and controlled quantum logic

operations5. The radiative decay of biexcitons—that is, states

consisting of two bound electron–hole pairs—in a quantum dot

has been proposed as a source of triggered polarization-entangled

photonpairs6.Todate,however,experimentshaveindicatedthata

splitting of the intermediate exciton energy yields only classically

correlated emission7–9. Here we demonstrate triggered photon

pairemissionfromsinglequantumdotssuggestiveofpolarization

entanglement. We achieve this by tuning the splitting to zero,

through either application of an in-plane magnetic field or careful

control of growth conditions. Entangled photon pairs generated

‘on demand’ have significant fundamental advantages over other

schemes10–13, which can suffer from multiple pair emission, or

require post-selection techniques or the use of photon-number

discriminating detectors. Furthermore, control over the pair

generation time is essential for scaling many quantum infor-

mation schemes beyond a few gates. Our results suggest that a

triggeredentangledphotonpairsourcecouldbeimplementedbya

simple semiconductor light-emitting diode14.

The most widely used methods for generating entangled photon

pairs are nonlinear optical processes, such as parametric down

conversion10,12, which produce a probabilistic number of pairs per

excitation cycle. Existing demonstrations of entangled photons in

semiconductor systems also do not produce individual entangled

photon pairs on demand. For the nonlinear process involved in bulk

CuCl,thenumberofpairsemitted followspoissonian statistics15. For

entangled photon pairs created by the probabilistic interference of

indistinguishable photons from a single quantum dot16, post selec-

tion is required to reject the majority of photons which are not

entangled13, and even for the idealized case only 50% of the photons

are entangled. Thus the realization of a quantum dot source that

emits no more than one entangled photon pair perexcitation cycle is

fundamentally different to the demonstrations described above. It is

perhaps more closely related to generation of entangled photons in

single atoms17, of which a quantum dot may be considered the

semiconductor analogue. Another appealing feature is that after the

first photon is emitted, the proposed single quantum dot system

resides in an entangled photon-exciton state, opening up the possi-

bility of implementing quantum logic operations in the solid state as

well as photonic domains.

The radiative decay of the biexciton state (XX) in a quantum dot

emits a pair of photons, with polarization determined by the spin of

the intermediate exciton state (X). In an ideal quantum dot with

degenerate X states, the polarization of the XX photon is predicted

to be entangled with that of the X photon, forming the state

(jHXXHX. þjVXXVX. )/p2, where H and V denote the polariza-

tion of the XX and X photons6.

In real quantum dots, the polarization of a photon can also be

determined by its energy, due to splitting of the intermediate exciton

state, shown schematically in Fig. 1. The splitting exists because of

in-plane asymmetries of structural properties of the quantum dot,

such as elongation and strain18,19, and provides ‘which path’ infor-

mation, preventing polarization entanglement of the emission. The

key to the generation of entangled photon pairs in a quantum dot is

therefore the reduction of the exciton polarization splitting to zero.

Here we describe how we were able to carefully select unsplit

quantum dots, or alternatively apply an in-plane magnetic field to

tune the splitting to zero.

By characterizing the exciton polarization splitting of a large

number of InAs/GaAs quantum dots from samples grown under

different conditions, we found the splitting to be least for relatively

LETTERS

Figure1|Polarizedphotoluminescencespectrafromsinglequantumdots.

a,Vertically(blue)andhorizontally(red)polarizedphotoluminescencefora

single quantum dot with small polarization splitting. The features

correspond to emission by the exciton (X) and biexciton (XX) state.

b, Polarization splitting, S, as a function of in-plane magnetic field for a

single dot with ‘inverted’ S at 0T. The green line shows a quadratic fit to the

data with a coefficient of 1.05meVT22. Inset shows the level diagram of the

radiative decay of the biexciton state. The competing two photon decay

pathsaredistinguishedonlybythepolarizationofthephotons,indicatedby

thearrowcolour,andthesplitting,S,oftheintermediateexcitonlevel.Error

bars span two standard deviations from the fitted line.

1Toshiba Research Europe Limited, 260 Cambridge Science Park, Cambridge CB4 0WE, UK.2Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge

CB3 0HE, UK.

Vol 439|12 January 2006|doi:10.1038/nature04446

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© 2006 Nature Publishing Group

small dots emitting at ,1.4eV, in which the electron and hole

wavefunctions are most symmetric20. Figure 1a plots polarized

photoluminescence spectra at ,10K, recorded for a typical dot

showing near-zero splitting. The biexciton photon emission energy

is1.96meVhigherthantheexcitonphotonemissionenergy,whichis

quite typical for this kind of small quantum dot21,22. The energy

difference,duetotheCoulombinteraction,allowssimplewavelength

selective separation of the two photons in the pair, which is not

possible in most schemes for entangled photon generation that

require the photons to have the same energy. No polarization

splitting can be resolved by eye between the horizontally and

vertically polarized components of the emission. The fitted central

wavelengths of all lines were used to determine the average polariza-

tion splitting for the exciton and biexciton. The resulting measured

exciton splitting was found to be 1.1 ^ 0.5meV, within the projected

homogeneous linewidth of ,1.5meV.

The samples show considerable difference in the magnitude and

signofsplittingfromdottodot,owingtovariationsindotsize,shape

and composition. However, we have found that the polarization

splitting of many dots can be tuned to zero by applying an in-plane

magnetic field. These dots are identified by the negative sign of their

splitting, using the sign convention that the splitting equals the

energy of the horizontally polarized exciton minus that of the

vertically polarized one. The tuning of the polarization splitting of

an example dot by magnetic field is shown in Fig. 1b. The splitting

varies approximately quadratically with magnetic field from

27.6 ^ 0.5meV to þ19.3 ^ 0.5meV. Most importantly, the splitting

can be tuned to approximately zero for an applied field of

2.5 ^ 0.1T. As we shall show later, this provides a way to turn on

entangled photon generation by the quantum dot.

Polarization dependent twophoton correlations weremeasured as

detailed in the Methods section. Figure 2a shows the second order

cross correlation between the XX and X photon emitted by a

reference dot A, for which the exciton splitting was 49.9 ^ 0.5meV.

The polarization correlated traces shown in red are artificially time

shifted relative to the polarization anti-correlated traces shown in

blue, to aid comparison. The average total number of counts in the

peaks at zero delay is larger than the average number of counts in

the other peaks. This is due to the greater probability of detecting an

X photon in the same period that an XX photon was detected. The

degree of enhancement is dependent on the excitation efficiency,

which is the same for each pair of traces recorded simultaneously,

allowing direct comparison. The three panels represent correlations

measured in the rectilinear, diagonal and circular bases, and were

measured using a half wave plate set at 08 and 22.58, and a quarter

wave plate set at 458, placed directly after the collection lens. The top

panel shows a much higher probability of generating a pair of

photons with the same rectilinear polarization. Detection of oppo-

sitely polarized photon pairs is not fully suppressed owing to

contribution from background light and exciton dephasing, dis-

cussed later in detail. However, no polarization correlation at all is

observed in the diagonal or circular bases, demonstrated by the

middleandbottompanels.Thephotonpairsemittedbythereference

dot are therefore only classically polarization correlated as observed

previously7–9, and not entangled.

The correlation experiment was repeated for dot B, which has

approximately zero splitting. The results are shown in Fig. 2b. A

similardegreeofrectilinearpolarizationcorrelationisobservedasfor

the reference dot A, and indeed all dots measured. However, strong

diagonal polarization correlation is additionally observed, and

remarkably also strong circular polarization anti-correlation. This

is consistent with expected results for entangled photon emission

from a single quantum dot.

Awellknownpropertyofentangledphotonpairsisthatthedegree

of correlation does not depend on the absolute orientation of the

photons, but only the difference in the angle between them12. The

degree of linear correlation was measured as a function of the linear

polarization basis angle by rotating the half wave plate, which has no

effect on the difference in polarization detection angles, which was

effectively parallel. The results are shown in Fig. 2c. For the reference

dot A, the correlation fits well to sinusoidal behaviour between zero

and a maximum of 0.243 ^ 0.012, as expected for classically linearly

polarization correlated photon pairs. In stark contrast, the degree of

correlationforthedegeneratedotBisindependentoftheorientation

of the measurement basis within experimental error, as expected for

polarization entangled photon pairs. The average degree of corre-

lation is found to be 0.222 ^ 0.028, similar to the maximum of the

reference dot. Again this is what is expected for entangled photon

Figure 2 | Second order cross correlation of biexciton with exciton photons

from conventional and degenerate single quantum dots. a, b, Cross

correlationforareferencedotAwith50meVpolarization splitting(a),anda

degenerate dot B (b). Correlations measured for photons of the same

polarization are shown in red, and for orthogonal polarization in blue. The

red histograms are time shifted to allow easier comparison to the blue. The

top, middle and bottom panels represent correlations measured in the

rectilinear, diagonal and circular bases, respectively. c, The degree of linear

correlation is plotted as a function of the basis angle. Error bars span

two standard deviations. H, horizontal; V, vertical; D, diagonal;

D

0, orthodiagonal; R, right; L, left.

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pairs, in contrast to the case of classically correlated photon pairs

emitting into random bases, for which the average degree of

correlation should be less by a factor of 2.

To fully measure the two photon polarization state, a quantum

state tomography scheme was used23,24. The procedure, detailed in

the Methods section, constructs the two photon polarization density

matrix from a linear combination of cross correlation measurements

using 16 different polarization combinations.

Therealcomponentofthetwophotonpolarizationdensitymatrix

for the reference dot A is shown in Fig. 3a. The stronger elements all

lie on the diagonal, with the strongest outer elements indicating

polarizationcorrelatedemission.Theinnerdiagonalcomponentsare

due to uncorrelated photon pair emission, from background counts

and dephasing of the exciton state. The form of this density matrix is

consistent with imperfect polarization correlated photon pair emis-

sionseen previously7–9, andillustrated by theexample density matrix

of Fig. 3f. The density matrix for the degenerate dot shown in Fig. 3b

has similar diagonal elements, but now shows significant outer, off

diagonal elements. This is a feature associated with polarization

entangledphotonpairs,illustratedbythepredicteddensity matrixof

Fig. 3g.

A similar density matrix is obtained for dot C, tuned to zero

splitting by magnetic field, as shown in Fig. 3d. This again suggests

thatthephotonpairemissionhasentangledcharacter.Whenthefield

is increased to 5T, the splitting increases to 19meV, and the corre-

sponding density matrix measured is shown in Fig. 3e. As expected,

the off diagonal elements are suppressed, and the dot reverts to

emitting polarization correlated photon pairs. A similar result is

found if the field is reduced to 0T, where the splitting is 28meV as

shown in Fig. 3c. The imaginary components of the density matrices

were all found to be zero with experimental error, in agreement with

predictions.

The measurements presented above clearly suggest that dots with

small exciton splitting emit entangled photons. We now discuss the

factors limiting the degree of entanglement. In spectroscopy, our

measurements show that the background due to dark counts and

emission from layers other than the dot contributes on average 49%

of the coincidence counts; this is unusually large owing to the

proximity of the dot to the wetting layer, which is necessary to select

dotswithzerosplitting.Ifwecorrectourmeasurementsby removing

the projected number of background counts from the correlation

data, the density matrices of the degenerate and magnetically tuned

dots more closely resemble the ideal entangled case, and the largest

eigenvalues are 0.48 ^ 0.08 and 0.58 ^ 0.04, respectively. The latter,

for which the splitting is minimal, violates the 0.5 limit for classical

correlation in an unpolarized source25. The remaining deviation

from ideal behaviour is attributed to scattering between the two

intermediateexcitonspinstates7,8.Frompreviouspublicationswhere

strong background and entanglement were not present, we estimate

anexcitonscatteringtimesimilar tothe,1nsradiativelifetime.This

yields a maximum possible eigenvalue of 0.63, in rough agreement

with these measurements.

This suggests that the degree of entanglement may be increased by

resonant optical16,26or electrical6excitation in order to increase the

scattering time, or by reducing the radiative lifetime through Purcell

enhancement27,28,orbyusingdotswithlargeroscillatorstrengthsuch

as those formed by interface fluctuations18. Such improvements

could lead to the realization of a semiconductor source of triggered

entangledphotonpairsthatwouldberobustandcompact,andallow

electrical injection of the carriers14.

METHODS

Sample fabrication and characterization. Samples containing a low density

layer of InAs quantum dots (,1.6 monolayers thick) were grown by molecular

beam epitaxy. A GaAs l cavity containing the dot layer was surrounded by

AlAs/GaAs distributed Bragg reflectors, with 14 (2) repeats in the bottom (top)

mirror, to increase light collection efficiency. A metal shadow mask containing

aperturesof,2mmdiameter wasfabricatedtoisolatetheemissionofindividual

dots. Samples with a range of InAs thicknesses differing by up to ,2% were

characterized in a standard micro photoluminescence system operating at

,10K. Optical excitation was provided by ,100-ps pulses from a 635-nm

laser diode operating at 80MHz. The emission lines are inhomogeneously

broadened by charge fluctuations to ,50meV, a consequence of the non-

resonant excitation scheme29. Horizontally ([110]) and vertically ([1210])

polarized exciton and biexciton emission was fitted with lorenzian line shapes

to locate the centre energy of each transition. The exciton level splitting can be

determined both from the difference between the horizontally and vertically

polarized exciton or biexciton photons. Taking the average of these two values

removed systematic error associated with changing the polarization optics, and

the splitting S was measured with an estimated precision of ,0.5meV.

Selection of suitable dots. By measuring the splitting of 200 quantum dots, a

relationshipofdecreasingsplittingwithincreasingemissionenergy wasfound20.

Fordotsemittingat,1.4eV,thesplittingwas,0 ^ 10meV.Thusquantumdots

with splitting less than the homogeneous linewidth of ,1.5meV were selected

first by identifying dots emitting close to 1.4eV, then measuring their splitting.

For dots emitting .1.4eV, the splitting was inverted, and the lowest energy

exciton line is horizontally polarized. For these dots, the configuration of the

exchange energies and g-factors allows reduction of the splitting with an applied

in-plane magnetic field, driven by partial mixing of optically active and inactive

exciton states30. Thus dots suitable for tuning to zero splitting are conveniently

identified by their emission energy. The proportion of dots that have, or can be

tuned to, zero splitting is ,30%, which could be improved by better growth

control. The proportion of suitably isolated single dots could be improved by

fabrication of smaller microstructures.

Photon pair counting. Quantum dots were optically excited, with the power

adjustedtogiveoptimumphotonpairdetectionratetobackgroundratio.Atthis

power, the biexciton intensity is around half that of the exciton. A 50/50 beam

splitter divided the emission into two spectrometers, set to transmit at the XX

andX photonenergies respectively, with ,0.5meV bandwidth. Polarizingbeam

splitters were placed after the spectrometers, and three single photon detectors

Figure 3 | Density matrices for the biexciton–exciton two-photon cascade

from conventional and degenerate quantum dots. a–e, Real parts of

measured density matrices corresponding to reference dot A with

polarization splitting, S ¼ 50meV (a), dot B with S < 0meVat 0T (b), and

dot C, with S tuned by the magnetic field to be 28meV (c), 0meV (d) and

19meV(e).The imaginarycomponentsare notshown,andwerezerowithin

experimental error. Density matrices b and d feature strong outer off

diagonal elements associated with entangled photon pair states, which are

not present in the reference case (a). f, g, Density matrices representing the

predicted state for ideal classically correlated (f) and entangled (g)

photon pairs, including 50% contribution from uncorrelated background

light.

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were used to measure the vertically polarized XX photons, and horizontally and

vertically polarized X photons. The time between detection of XX photons and

X photons was measured by a time interval analyser.

Photons can be counted over a number of hours by compensating for

fluctuations in excitation and detection efficiency over time. This is achieved

by determining the degree of correlation from the ratio of the two correlations

measured simultaneously, each normalized by the number of pairs detected in

different laser cycles.

Theapproachisvalidforunpolarizedsources,andunpolarizingtransmission

of the light collection system up to the wave plates. Our system satisfies these

requirements, as the emission was unpolarized within error, and the trans-

mission was only weakly polarizing. For the results of Fig. 2, a single half or

quarter wave plate was inserted directly after the collection lens to select the

measurement basis for the exciton and biexciton photons simultaneously, and

the transmission was zero within experimental error. For the measurements of

Fig. 3, a quarter wave and half wave plate was used before each spectrometer to

select the polarization detection basis for the exciton and biexciton indepen-

dently, and the transmission was only ,10% polarizing. The total number of

coincident pairs detected over the course of an experiment is typically up to

1,000, which dictates the measurement errors.

Quantum tomography analysis. The probability that a photon pair is detected

with a selected polarization combination was determined experimentally from

pairs of two photon correlations measured simultaneously. 16 such measure-

ments were used to construct each two photon density matrix, using the

polarization combinations and methods of ref. 24. The density matrix fully

describes the two-photon quantum state, and thus can be used to test for

entanglement. The test we chose is that of the largest eigenvalue, which is a

generaltestthatmakesnoassumptionaboutthenatureoftheentangledstate,in

contrast to a Bell inequality, for which violation is maximal when the entangled

state corresponds to that for which the polarization measurement bases were

chosen. For an unpolarized classical source, the probability that a photon pair

exists in any given polarization state cannot exceed 0.5, therefore an eigenvalue

.0.5 signifies the presence of entanglement.

Received 28 July; accepted 16 November 2005.

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Acknowledgements We acknowledge continued support from M. Pepper. This

work was partially funded by the EU projects RAMBOQ, QAP and SANDiE, and

by the EPSRC through the IRC for Quantum Information Processing.

Author Information Reprints and permissions information is available at

npg.nature.com/reprintsandpermissions. The authors declare no competing

financial interests. Correspondence and requests for materials should be

addressed to R.M.S. (mark.stevenson@crl.toshiba.co.uk).

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