Full Schmidt characterization of spatiotemporally entangled states produced from spontaneous parametric down-conversion

TL;DR

This paper performs the first full Schmidt decomposition of spatiotemporally entangled states from SPDC, revealing detailed mode structures and spectra, and demonstrating their potential for advanced quantum imaging and spectroscopy.

Contribution

We developed a method leveraging rotational symmetry to efficiently perform the full Schmidt decomposition of complex SPDC states, revealing their detailed mode structure and spectral properties.

Findings

Schmidt modes exhibit vortex phase profiles with orbital angular momentum.

Schmidt spectrum narrows with increasing pump strength in high-gain regimes.

Decomposition spans over 10^4 modes, revealing detailed entanglement structure.

Abstract

The full Schmidt decomposition of spatiotemporally entangled states generated from spontaneous parametric down-conversion (SPDC) has not been carried out until now due to the immense computational complexity arising from the large dimensionalities of the states. In this Letter, we utilize the rotational symmetry of the states to reduce the complexity by at least four orders of magnitude and carry out the decomposition to reveal the precise forms of the spatiotemporal Schmidt modes and the Schmidt spectrum spanning over 10^4 modes. We show that the Schmidt modes have a phase profile with a transverse spatial vortex structure that endows them with orbital angular momentum at all frequencies. In the high-gain regime, these Schmidt modes broaden and the Schmidt spectrum narrows with increasing pump strength. Our work can spur novel applications at the intersection of quantum imaging and spectroscopy that utilize entangled states produced from SPDC.