Output photon statistics for a beam splitter with input squeezed light

Abstract

The mixing of (quadrature-) squeezed states by a lossless beam splitter is studied. Two generating functions describing the outgoing-photon distribution are calculated. With the use of these generating functions the distribution is determined explicitly for some special cases.

Generalized master equation for systems in nonideal cavities with squeezed baths

“…for even n,a n dp n =0f o ro d dn .A sh as been discussed before in the context of squeezed light irradiating a semitransparent mirror [14], the sharp distinction between even and odd n is washed out as soon as the mirror ceases to be perfect, that is, as soon as µ differs from 0. In fact, the statistics is quite sensitive to any nonideality of the mirror: already for an (intensity) reflectivity of 0.975, corresponding to µ =0.025, the distinction between even and odd n, which is characteristic of a squeezed vacuum, has disappeared almost completely.…”

“…In fact, if such a mirror with an (amplitude) reflection coefficient (1 − µ) 1/2 and a transmission coefficient −iµ 1/2 is irradiated from both sides by photons in a squeezed vacuum mode with identical frequency and squeezing parameter, the statistics of the outgoing photons is the same as that of the quasimode discussed here. The statistics of squeezed light impinging on a semitransparent mirror has been analyzed before with the use of generation functions [14]. From that analysis one derives the following distribution p n of the quasimode excitations for infinite τ :…”

“…so that one has F (+) + F (−) = F according to (14) and (27). Finally, the master equation contains two (complex) coefficient functions that are integrals over F (ζ, τ), F (±) (ζ,τ) and their derivatives.…”

Field operator transformations in quantum optics using a novel graphical method with applications to beam splitters and interferometers

“…Campos et al [25] extend this discussion with a special emphasis on the fourth-order interference applied to lossless optical systems (BS and MZI). Other authors studied more specific scenarios, for example displaced Fock states [26] or output photon statistics for input squeezed light [27].…”

“…Eqs. (27) and (28) were also obtained with merely a visual inspection of the graph depicted in Fig. 8.…”