The Janus state: a universal lower bound for second-order coherence

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 a tuned interference that suppresses two-photon events. Beyond this asymptotic bound, we identify a practical minimum of g⁽²⁾≈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.