Asymmetric Gaussian harmonic steering in second harmonic generation

TL;DR

This paper demonstrates that intracavity second harmonic generation can produce controllable asymmetric Gaussian harmonic steering, with the asymmetry tunable via cavity loss rates, offering a simple and adjustable platform for quantum information applications.

Contribution

It introduces a novel, simple method to generate and control asymmetric Gaussian harmonic steering using intracavity second harmonic generation by tuning cavity loss rates.

Findings

Asymmetric steering depends on quadrature measurement choices.

Tuning cavity loss rates controls the symmetry of steering.

System is simpler than previous methods for asymmetric steering.

Abstract

Intracavity second harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterised, both theoretically and experimentally. We show that it can be a source of continuous variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.