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D A Ritchie^1*, R M Stevenson², R J Young²⁺, A J Hudson^1,2, D J P Ellis², A J Bennett², P Atkinson¹,
K Cooper¹, C A Nicoll¹, A J Shields<sup>2

1</sup> Cavendish Laboratory, University of Cambridge, JJ Thompson Avenue, Cambridge CB3 0HE, U.K.
²Toshiba Research Europe Limited, 208 Cambridge Science Park, Cambridge CB4 0GZ, U.K
*dar11@cam.ac.uk

        

                

Ideally this process produces a polarization entangled photon pair state which can be written in the circular (R,L), rectilinear (H,V) and diagonal (D,A) bases as

where ‘xx’ refers to the polarization of  the biexciton to exciton photon and ‘x’ to the exciton to ground state photon.

A major difficulty in using this scheme is that the degeneracy of the two exciton states is lifted by the anisotropic nature of the quantum dots causing an energy level splitting typically tens of µeV in size. This splitting is observed in the polarization sensitive photoluminescence measurements shown in figure 2. The splitting allows the decay path taken from the biexciton to the ground state to be determined, destroying entanglement and yielding only classically correlated emission e.g. [4]. We have developed several techniques to tune this splitting to less than 0.5 µeV (a) controlling the growth process and dot size [5] (b) annealing [6] and (c) using an in-plane magnetic field [7] as shown in figure 3.

InAs quantum dots grown by molecular beam epitaxy at a density of around 1 µm-2  were incorporated at the centre of a λ GaAs optical cavity situated between two GaAs/Al_0.98Ga_0.02As distributed Bragg reflectors. The planar cavity structure enhances the light collected from the sample by an order of magnitude. Apertures of 2-3µm in diameter were etched into a metal mask evaporated onto the surface of the semiconductor to isolate the emission from a single dot. The samples were cooled to 10K in a standard µ-PL system and polarization correlations were measured between the biexciton and exciton photons in the circular, rectilinear and diagonal bases. For a splitting of significant correlations were measured only in the rectilinear basis, when the splitting was reduced to zero using a magnetic field, significant correlations were measured in all three bases with a measured fidelity  of the emitted state to the ideal entangled state of 0.72±0.01 [2].

There are several factors limiting the degree of correlation; exciton spin scattering, background emission and cross-dephasing – a process which randomizes the relative phase of the split exciton states. We have developed a theoretical framework to describe the effect of these processes on the fidelity as a function of exciton energy level splitting [8]. This theory has been fitted to experimental data and suggests a cross-dephasing time greater than 2ns, significantly greater than the exciton lifetime of around 890ps.

For a finite exciton energy level splitting  , the exciton state evolves with time producing a pair photon state  where is the time between emission of the biexciton and exciton photons. We have measured the fidelity of  with the state as a function of  for several values of . These experimental results are plotted in figure 4 and show oscillations of the fidelity in good agreement with theory, the maxima having high fidelity to  and the minima high fidelity to [9].

Time-gating has been used to select photons emitted by the biexciton state for a period of 2ns and exciton photons for a period of 3ns, see figure 5. This removes early emitted photons, reducing the effect of multiple excitation and background emission with a short lifetime. Late emitted photons are removed which reduces the effect of detector dark counts. As a consequence the fidelity of  with the maximally entangled Bell state increases from a value of 79.4±1.0% to 91.2±2.4% (see figure 6), these values of fidelity both violate Bell’s inequality [10].

⁺Current address: Tyndall National Institute, Lee Maltings, Cork, Ireland.

[1] R M Stevenson et al, "A semiconductor source of triggered entangled photon pairs", Nature 439, 179 (2006).       
[2] R J Young et al, "Improved fidelity of triggered entangled photons from single quantum dots", New Journal of Physics 8, 29 (2006).
[3] O Benson et al, “Regulated and entangled photons from a single quantum dot”, Phys. Rev. Lett., 84, 2513 (2000).       
[4] R M Stevenson et al, "Quantum dots as a photon source for passive quantum key encoding", Phys. Rev. B, 66, 081302 (2002).   
[5] R J Young et al, "Inversion of exciton level splitting in quantum dots.", Phys. Rev. B 72, 113305 (2005).   
[6] D J P Ellis et al, "Control of fine-structure splitting of individual InAs quantum dots by rapid thermal annealing", Appl. Phys. Lett 90, 011907 (2007).       
[7] R M Stevenson et al, "Magnetic field induced reduction of the exciton polarization splitting in InAs quantum dots", Phys. Rev. B 73, 033306 (2006).
[8] A J Hudson et al, "Coherence of an Entangled Exciton-Photon State", Phys. Rev. Lett., 99,  266802 (2007).
[9] R M  Stevenson et al, "Evolution of entanglement between distinguishable light states", Phys. Rev. Lett., 101, 170501 (2008).
[10] R J Young et al, "Bell-Inequality Violation with a Triggered Photon-Pair Source", Phys. Rev. Lett.,102, 030406 (2009).