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Entangled photon pairs from single quantum dots

The need for photon pairs

Entangled photon pairs are a basic building block for most optical quantum communication and many studies of higher dimensional entanglement. Quantum teleportation, key distribution and the purification of entanglement have all been demonstrated using entangled photon pairs. The major source to date is spontaneous parametric down-conversion in nonlinear optical crystals. Many experiments will combine pairs from more than one source. In these experiments is often disastrous if there are two pairs coming from one source, because such an event can rarely be distinguished from a proper event with one pair from each source.

Ideally, therefore, we would like to use sources that only yield one pair at a desired time, possibly with very high efficiency. Typically, such a source must be a single quantum system so that multi-pair emissions cannot occur in the first place if re-excitation is excluded.

InAs quantum dots

While atoms, ions and molecules are certainly ideal systems they are difficult to trap one at a time and their very narrow lines only allow very low repetition rates in the production of single photons and photon pairs. In semiconductors, single quantum dots are routinely isolated, they do not escape and one and the same quantum system can basically be studied indefinitely. While there are various types of quantum dots self-assembled InAs quantum dots have proved to be particularly suited for single photon sources.

InAs quantum dots are formed when InAs is grown epitaxially on GaAs. The strain induced by the lattice mismatch results in the formation of little islands. Since the InAs islands are surrounded by GaAs, a material with a larger band-gap, electrons and holes are trapped in the InAs dots. Optical pumping creates electron-hole pairs in the surrounding and the quantum dot can capture both. States that contain an equal number of electrons and holes are often labelled X (1 e-, 1h+), XX (2e-, 2h+), etc. These neutral states can recombine to emit photons.

Benson et al. [PRL 84, 2513 (2000)] suggested that the XX-X-empty cascade could emit polarization entangled photon pairs, because there are two decay paths corresponding to the emission of photons with either vertical or horizontal polarization. However, typical quantum dots are not round and their asymmetry makes these two paths distinguishable. Therefore polarization correlation is only observed in the preferred bases and no entanglement is present [C. Santori et al, PRB 66, 045308 (2002)] .

Time-bin entanglement

Since the two photons in a cascade are emitted in fast succession we suggest than instead of polarization entanglement one use time-bin entanglement. In time-bin entanglement the degree of freedom is the time of photon detection. It has been used successfully with photon pairs from parametric down-conversion.

With quantum dots this would amount to exciting the quantum dot to the XX level twice such that the probability for emission of a photon pair is ½ for each excitation event (time-bin). If the two excitation events are indistinguishable the pair will be entangled between these two possibilities. This kind of indistinguishability has been demonstrated for two single photons from quantum dots [C. Santori et al., Nature 419, 594 (2002)] even with non-resonant pumping.

Preventing multi-pair emission

Obviously, for simple pumping mechanisms there will always be a chance to emit two photon pairs, one in the first and one in the second time slot. This is an error, ruining the entanglement. Simon and Poizat [PRL, 94,030502 (2005)] proposed to start out from a metastable (dark) state of the dot so that re-excitation via the same transition is prohibited. The good news is that in the limit of low efficiency, we can study the entanglement properties with simple non-resonant pumping since double-pair events will be a small error only.

Experiment

As a start we will employ self-assembled InAs quantum dots isolated in small mesas, cooled to about 10K in a continuous flow cryostat and pump it with pulses from a Ti:Sapphire laser at the absorption band of the InAs wetting layer, above the dot bands. The mesas will reduce the effective dot density so that pumping from a large angle is possible. This allows better suppression of tails of the pump spectrum from the collection of the photoluminescence through a high-NA microscope objective. A dichroic mirror (or grating) will separate the X and XX lines into two unbalanced interferometers after which the photons will be detected in coincidence.

The errors introduced by the finite lifetimes of the X and XX states have been studied by Simon and Poizat. For single-pair applications, such as quantum key distribution there should be no problem. For multi-pair interferometry one may have to use microcavities to speed up the emission of the XX photon in order to reduce unwanted entanglement within each cascade.