Generation of different Bell states within the SPDC phase-matching bandwidth

TL;DR

This paper investigates how different Bell states can be generated within the phase-matching bandwidth of SPDC, showing that entangled states vary continuously with mismatch and can be selectively filtered.

Contribution

It provides a detailed theoretical and experimental analysis of Bell state generation within SPDC bandwidth, highlighting the continuous variation and methods for selective filtering of entangled states.

Findings

Different Bell states occur at the center and slopes of the SPDC line.

Bell states can be filtered by frequency and angular selection.

Experimental results confirm theoretical predictions.

Abstract

We study the frequency-angular lineshape for a phase-matched nonlinear process producing entangled states and show that there is a continuous variety of maximally-entangled states generated for different mismatch values within the natural bandwidth. Detailed considerations are made for two specific methods of polarization entanglement preparation, based on type-II spontaneous parametric down-conversion (SPDC) and on SPDC in two subsequent type-I crystals producing orthogonally polarized photon pairs. It turns out that different Bell states are produced at the center of the SPDC line and on its slopes, corresponding to about half-maximum intensity level. These Bell states can be filtered out by either frequency selection or angular selection, or both. Our theoretical calculations are confirmed by a series of experiments, performed for the two above-mentioned schemes of producing polarization-entangled photon pairs and with two kinds of measurements: frequency-selective and angular-selective.