The Janus State: A Universal Lower Bound for Second-Order Coherence

TL;DR

The paper introduces the Janus state, a superposition of two squeezed vacua, which establishes a universal lower bound on second-order coherence, enabling the generation of strongly sub-Poissonian light from Gaussian states.

Contribution

It provides an exact analytic solution demonstrating a universal lower bound on $g^{(2)}$, revealing fundamental limits for sub-Poissonian photon statistics from Gaussian resources.

Findings

Janus state achieves $g^{(2)}$ as low as 1/2

Practical minimum $g^{(2)}$ around 0.567 at moderate squeezing

Establishes a performance limit for Gaussian-based quantum light engineering

Abstract

A single-mode squeezed vacuum is a foundational quantum state that, despite its nonclassical nature, exhibits classical-like, super-Poissonian photon statistics. This feature motivates a ``quantum-of-quantum'' inquiry: can the superposition of two such states generate the opposite behavior -- strongly sub-Poissonian light? We demonstrate that the ``Janus state,'' a coherent superposition of two squeezed vacua with opposing orientations, achieves precisely this. Our exact analytic solution reveals a universal lower bound on second-order coherence, showing that $g^{(2)}$ cannot be driven below 1/2. The mechanism is tuned interference that suppresses two-photon events. Beyond this asymptotic bound, we identify a practical minimum of $g^{(2)} \approx 0.567$ at moderate squeezing, defining an accessible ``sweet spot.'' While requiring a minimal non-Gaussian element for its creation, the Janus state establishes a definitive performance limit for engineering sub-Poissonian photon statistics from Gaussian resources, with a clear path toward quantum applications.