Theory for the beam splitter in quantum optics: quantum entanglement of photons and their statistics, HOM effect

Abstract

The theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients R (or the transmission coefficient, where R + T = 1) and the phase shift φ. It has recently been shown that the constancy of these coefficients cannot always be satisfied for a waveguide BS, where R and φ depend in a special way on photon frequencies. Based on this, this review systematizes the concept of BS in quantum optics into "Conventional" and frequency-dependent BS, and also presents the theory of such BS. It is shown that the quantum entanglement, photon statistics at the output ports, and the Hong-Ou-Mandel (HOM) effect for such BS can be very different. Taking into account the fact that the waveguide BS is currently acquiring an important role in quantum technologies due to the possibility of its miniaturization, this review will be useful not only for theoreticians, but also for experimenters.

Nanoscale Waveguide Beam Splitter in Quantum Technologies

“…Further development of the theory of coupled waveguides showed that the previously known theory is not always applicable, not only for the HOM effect but also for a waveguide BS in general [20,21]. This is due to the fact that in old theories the coefficients R and T are always constant for waveguide BSs, and as shown in [20][21][22][23], this is not the case for the non-monochromatic photons incident on 1 and 2 BS ports. These coefficients are dependent on the frequencies of the incident photons on the ports of the BS.…”