Classes of two-photon states defined by linear interactions and destructive two-photon quantum interference in a single mode

We describe a two-photon quantum interference effect which differs from the Hong-Ou-Mandel effect in that the destructive quantum inference occurs on a component of the state where two photons are in a single output mode while maintaining the two-photon events in the alternative mode. This effect is manifestly nonclassical but requires more sophisticated technology to observe than the Hong-Ou-Mandel effect. The theory outlined in this paper can also be used to classify two-photon states into classes which are related by the ability to transform the states within the class by using only linear optical interactions. This theory shows that there is an infinite number of these classes of two photon states when there are two or more modes which can support the photons.

Figure 1

Probability of detecting two-photon configuration events for the input state equation (28) when interacting at a beam splitter with reflectivities between 0.5 and 1 and a $\pi /2$ phase shift on transmission for both input modes. At the reflectivity found in the example of $1/(3-\sqrt{3}), P(1,1)$ and $P(2,0)$ are equal and nonzero, and $P(0,2)$ is zero. This is exactly what is expected from the starting point of the example with the state from Eq. (23).

Figure 2

The distribution for classical particle pairs when sourced from a state which is a decohered version of the state in Eq. (28). Instead of total destructive interference of the $P(0,2)$ term, a nonzero minimum value is observed.