Quantum Complementarity ad Infinitum: Switching Higher-Order Coherence from Infinity to Zero

TL;DR

This paper demonstrates a quantum switch in multi-photon correlations using the Janus state, revealing a hierarchy of suppression where higher-order correlations can be driven to zero, showcasing profound quantum complementarity.

Contribution

It introduces a novel quantum state that acts as a switch for multi-photon correlations, enabling control over higher-order quantum coherence and non-classicality.

Findings

Higher-order correlations can be driven to zero while two-photon correlations remain finite.

The Janus state acts as a perfect quantum switch for multi-photon correlations.

Negativity in the Wigner function indicates non-classicality and quantum order.

Abstract

We report a profound manifestation of quantum complementarity in the higher-order photon statistics of the ``Janus state,'' a coherent superposition of two squeezed vacua. We find that the state acts as a perfect quantum switch for multi-photon correlations, toggled by the availability of which-path information. Erasing this information activates quantum interference that can be tuned to be maximally destructive. This reveals a remarkable hierarchy of suppression: while two-photon correlations remain finite, we prove analytically and demonstrate numerically that it is possible to drive all higher-order correlations ($g^{(k)}$ for $k \ge 3$) to zero. This transition from the extreme bunching of the constituent states ($g^{(k)} \to \infty$) to a state of profound quantum order is visualized by the emergence of negativity in the state's Wigner function, an unambiguous signature of non-classicality. This work provides a foundational demonstration of quantum complementarity in multi-photon statistics and introduces a new paradigm for engineering highly ordered, non-classical light from Gaussian resources.