© 2006 Nature Publishing Group
A semiconductor source of triggered entangled
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
splitting of the intermediate exciton energy yields only classically
correlated emission7–9. Here we demonstrate triggered photon
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
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
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
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
© 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
quite typical for this kind of small quantum dot21,22. The energy
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
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
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
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.
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
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
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;
0, orthodiagonal; R, right; L, left.
NATURE|Vol 439|12 January 2006
© 2006 Nature Publishing Group
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.
for the reference dot A is shown in Fig. 3a. The stronger elements all
lie on the diagonal, with the strongest outer elements indicating
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
A similar density matrix is obtained for dot C, tuned to zero
splitting by magnetic field, as shown in Fig. 3d. This again suggests
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
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
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
strong background and entanglement were not present, we estimate
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
as those formed by interface fluctuations18. Such improvements
could lead to the realization of a semiconductor source of triggered
electrical injection of the carriers14.
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
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 () and vertically ()
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
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
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
NATURE|Vol 439|12 January 2006
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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.
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
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. (firstname.lastname@example.org).
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