# Effect of incoherent pump on two-mode entanglement in optical parametric generation

## TL;DR

This paper investigates how incoherent pumping affects two-mode entanglement and purity in optical parametric generation, providing a method to analyze various incoherent pump states and their impact on quantum correlations.

## Contribution

It introduces a general approach to infer entanglement and purity under incoherent pumping using the Glauber-Sudarshan function, highlighting sensitivity to phase distribution.

## Key findings

- Entanglement is highly sensitive to the pump's phase distribution.
- Incoherent pumps like thermal and phase-averaged states reduce entanglement.
- The approach applies to various physically relevant incoherent pump states.

## Abstract

Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). The quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, superposed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entanglement and purity of the signal and the idler modes, which is of vital importance for quantum information applications and interferometry. Here we develop an approach to infer the signal-idler entanglement and purity for a general quantum incoherent pump with the given Glauber-Sudarshan function. We show that the signal-idler entanglement is extremely sensitive to the phase distribution of the pump and illustrate our findings by physically relevant examples of the incoherent pump: the noisy coherent state, slightly dephased and phase-averaged coherent states, the thermal state, and states modulated by the Kerr medium. The effect of an incoherent pump on the combined quadratures is discussed as well.