Quantum dot single-photon source

The use of Quantum dots as single-photon sources is based on a single quantum dot placed in an optical microcavity. A pulsed laser can excite a pair of carriers in the quantum dot. Due to the discrete energy levels only one exciton can exist in the cavity at a given time. The decay of the exciton due to spontaneous emission leads to the emission of a single photon. It is a nonclassical light source that shows photon antibunching. The emission of single photons can be proven by measuring the second order intensity correlation function. The linewidth of the emitted photons can be reduced by the use of distributed Bragg reflectors (DBR’s).

Quantum-mechanical description

Figure 1: Schematic strucure of an optical microcavity with a single quantum dot placed between two layers of DBR's. This structure works as a single photon source.

Single photons are extracted out of a semiconductor by spontaneous emission of a single excitation. The challenge in making in a single photon source is to make sure that there is only one excited state in the system at a time. In order to do that, a quantum dot is placed in a microcavity (Fig. 1). A quantum dot has discrete energy levels. An excitation from its ground state to an excited state will create an exciton. The eventual decay of this exciton due to spontaneous emission will result in the emission of a single photon. DBR’s are placed in the cavity to reduce linewidth broadening. To eliminate the probability of the simultaneous emission of two photons it has to be made sure that there can only be one exciton in the cavity at one time. The Rydberg blockade prevents the excitation of two excitons at the same space. Two excitons confined in a small volume are called biexcitons. They interact with each other and thus slightly change their energy. Photons resulting from the decay of biexcitons have a different energy than photons resulting from the decay of excitons. They can be filtered out by letting the outgoing beam pass a optical filter. A pulsed laser can be used for excitation of the quantum dots. In order to have the highest probability of creating an exciton, the pump laser is tuned on resonance. This resembles a $\pi$-pulse on the Bloch sphere. However, this way the emitted photons have the same frequency as the pump laser. A polarizer is needed to distinguish between them. As the direction of polarization of the photons from the cavity is random, half of the emitted photons are blocked by this filter.

Experimental verification

A microcavity with only a single quantum dot in it is be built. The DBR’s can be grown by molecular beam epitaxy (MBE). For the mirrors two materials with different indices of refraction are grown in alternate order. Their lattice parameters should match to prevent strain. A possible combination is a combination of AlAs- and GaAs-layers. A material with smaller lattice parameter can be used to grow the quantum dot. In the first few atomic layers of growing this material, the lattice constant will match that of the DBR. A tensile strain appears. At a certain thickness, the energy of the strain becomes too big and the layer contracts to grow with its own lattice constant. At this point, quantum dots have formed naturally. The second layer of DBR’s can now be grown on top of the layer with the quantum dots. The diameter of the pillar is only a few microns. In order to prevent the optical mode from exiting the cavity the micropillar must act as a waveguide. Semiconductors usually have relatively high indices of refraction about n≅3. Therefore their extraction cone is small. On a smooth surface the micropillar works as an almost perfect waveguide. However losses increase with roughness of the walls and decreasing diameter of the micropillar.

The edges thus must be as smooth as possible to minimize losses. This can be achieved by structuring the sample with Electron beam lithography and processing the pillars with reactive ion etching.

Verification of emission of single photons

The emission of single photons can be verified by the measurement of the autocorrelation function $g^{(2)}(\tau )$. As the probability for emitting two photons at the same time is 0, $g^{(2)}(\tau )$ shows a characteristic dip around $\tau =0$. This behaviour is distinct from coherent light sources like Lasers, where $g^{(2)}(0)=1$, and from thermal light sources, where g2(tau) = 1+e^-(tau/Tauc). That is to say if g2(0) < 1, it is an experimental proof of a light source emitting nonclassical light. The value of g2(0) is a measurement for the quality of the single photon source. For an ideal single photon source, g2(0) = 0. G2(tau) can be measured by using the Hanbury Brown and Twiss effect.

See also

• Single-photon source
• Quantum Dot