Direct observation of temporal coherence by weak projective measurements of photon arrival time

TL;DR

This paper demonstrates a method to directly observe temporal coherence of single photons using weak projective measurements via two-photon interference, revealing non-classical time-energy correlations.

Contribution

It introduces a novel technique for measuring photon arrival time and temporal coherence through controllable weak measurements and two-photon interference.

Findings

Weak measurements of photon arrival time are feasible with controllable two-photon interference.

The method reveals complete temporal coherence of single photon wavefunctions.

Non-classical time-energy entanglement statistics can be directly observed.

Abstract

We show that a weak projective measurement of photon arrival time can be realized by controllable two photon interferences with photons from short-time reference pulses at a polarization beam splitter. The weak value of the projector on the arrival time defined by the reference pulse can be obtained from the coincidence rates conditioned by a specific output measurement. If the weak measurement is followed by a measurement of frequency, the coincidence counts reveal the complete temporal coherence of the single photon wavefunction. Significantly, the weak values of the input state can also be obtained at higher measurement strengths, so that correlations between weak measurements on separate photons can be observed and evaluated without difficulty. The method can thus be used to directly observe the non-classical statistics of time-energy entangled photons.