Hong–Ou–Mandel effect

As a Hong - Ou -Mandel effect ( often short HOM effect ) refers to the quantum mechanical interference of two photons. It is named after its discoverers CK Hong, Zhe - Yu Ou and Leonard Mandel ( 1987).

The effect occurs when two indistinguishable photons strike a respective input of a 50:50 beam splitter. Experimentally observed here is that the photons are found in pairs on one of the two outputs. The case that in both outputs per one photon is found, does not occur.

Quantum mechanical description

The HOM effect is a non-classical effect and can only be understood in the framework of quantum mechanics. The state of the system according to the interference resulting from the superposition of all possible paths that can take the photon by the beam splitter. These four options are shown in the figure. In cases 1 and 4, a photon is each transmitted during the other is reflected. In the cases 2 and 3 are each either transmitted or reflected photons. For identical particles, the processes 2 and 3 are now indistinguishable from each other (it can be only the final state can be observed, and which is equal in both cases ). In addition, the probability amplitudes of the two paths are identical except for the sign. They interfere destructively and therefore only the cases 1 and 4 can occur. The existence of the sign can be explained clearly with the help of the known from classical physics phase jump by 180 ° upon reflection at the denser medium.

Mathematical Description

In quantum mechanics, light is no longer described by the classical electric field amplitudes, but in terms of creation and annihilation operators. The coupling of the modes on the two inputs and to the output mode and the beam splitter is described by the unitary time evolution operator:

The " spin" here describes the splitting ratio of the beam splitter. For the assumed hereinafter 50:50 beam splitter is.

In the Schrödinger picture then the output state is given by multiplying the evolution operator to the input state. The input status is shown by the chain, the each describes that a photon at an input of the beam splitter is included.

The four terms in the equation correspond here exactly four possibilities for the photon shown in the picture to fly through the beam splitter. Since, by assumption, the photons are indistinguishable, and swap the operators, so that the terms proportional to and lift off and no longer appear in the final state.

Experimental observation

In order to demonstrate the Hong - Ou -Mandel effect, one observes the outputs of the beam splitter with photomultipliers and performs a coincidence measurement. The non- occurrence of temporal coincidences between detectors shows that the photons always exit the beam splitter together on the same output.