Time-resolved measurement of photon states using two-photon interference with photons from short-time reference pulses

TL;DR

This paper develops a method for time-resolved quantum state measurement of photons using two-photon interference with short-time reference pulses, enabling characterization beyond detector time resolution.

Contribution

It derives temporal measurement operators and demonstrates how to perform quantum tomography and entanglement evaluation with this approach.

Findings

Measurement operators depend on reference pulse shape

Temporal coherence can be reconstructed using superpositions of reference pulses

Energy-time entanglement can be quantified through pairwise detection time coherences

Abstract

To fully utilize the energy-time degree of freedom of photons for optical quantum information processes, it is necessary to control and characterize the quantum states of the photons at extremely short time scales. For measurements beyond the time resolution of available detectors, two-photon interference with a photon in a short time reference pulse may be a viable alternative. In this paper, we derive the temporal measurement operators for the bunching statistics of a single photon input state with a reference photon. It is shown that the effects of the pulse shape of the reference pulse can be expressed in terms of a spectral filter selecting the bandwidth within which the measurement can be treated as an ideal projection on eigenstates of time. For full quantum tomography, temporal coherence can be determined by using superpositions of reference pulses at two different times. Moreover, energy-time entanglement can be evaluated based on the two-by-two entanglement observed in the coherences between pairs of detection times.