Spectral single photons characterization using generalized Hong, Ou and Mandel interferometry

Abstract

We propose new methods to characterize the spectral-temporal distribution of single photons. The presented protocols take advantage of spectral filtering, frequency entanglement between two single photons the one of interest and a reference, followed by the generalized Hong, Ou and Mandel interferometer. The measurement of the coincidence probability in these different schemes reveals the chronocyclic Wigner, the pseudo-Wigner distribution and the spectrogram at the single photon level.

Quantum optics with time-frequency degrees of freedom of single photons

“…However, the mathematical equivalent of the beam-splitter in the time-frequency domain for two single photons, referred to as the "frequency beam-splitter operation" that we have presented in Ref 1,3,18 has been approximatively implemented experimentally. Such an operation takes the form e i(ωj Tk +ω k Tj ) , and act on two single photon state as:…”

“…Note that the frequency beam-splitter operation is naturally performed with a spontaneous parametric downconversion process (see Ref 3,18 ), but the process being probabilistic and can "amplify" single photon states that leads to the destruction of the single photon particle-number statistics. This is thus not a scalable method for frequency entangled single photons.…”

Time-frequency as quantum continuous variables

“…The applications of this operator are numerous [21,29] and present interesting analogies with the beam-splitter operator defined for continuous variables representation using quadratures. In the quadrature case, a balanced beam-splitter combines two modes of the electromagnetic field and performs a conditional operation that produces as an output, two modes which are the sum and the difference between two input modes.…”

“…The chronocyclic Wigner function can be measured using a modal decomposition [48] or a frequency beam-splitter operation [29], for instance. For a single photon pure state ρ = |ψ ψ| and |ψ = S(ω)dω |ω , the chronocyclic Wigner distribution can be written as…”