Two-Mode Janus States: non-Gaussian generalizations of thermofield double

TL;DR

The paper introduces the Two-Mode Janus State, a non-Gaussian quantum state generalizing the thermofield double, with tunable non-Gaussianity and potential applications in relativistic quantum physics.

Contribution

It develops an analytical framework for the TMJS, including squeezing polynomials and a Janus phase for controlling non-Gaussian features, and proposes a physical realization via superposed DCE trajectories.

Findings

Non-Gaussianity is controllable via Janus phase.

States exhibit strong Wigner negativity in certain regimes.

Potential applications in relativistic quantum information and detector modeling.

Abstract

We introduce the Two-Mode Janus State (TMJS), a non-Gaussian quantum state defined as a coherent superposition of two distinct Two-Mode Squeezed States (TMSS). This construction serves as a direct, non-Gaussian generalization of the canonical thermofield double (TFD) state, which is itself a single, Gaussian TMSS. We develop a complete analytical framework for the TMJS's arbitrary $k$-th order photon statistics, identifying a new family of "squeezing polynomials" that govern all diagonal and off-diagonal moments. Our central result is that the state's non-Gaussianity is dynamically steerable via an external "Janus phase." This phase acts as a switch, allowing the higher-order coherences ($g^{(k)}$) to be tuned from perfectly thermal (matching the TFD marginal) to deeply sub-Poissonian, a regime marked by strong Wigner negativity. We further establish a physical realization for the TMJS, proposing its generation via coherently superposed Dynamical Casimir Effect (DCE) trajectories, distinguishing it from the static, observer-dependent Unruh effect. The TMJS provides a versatile, interference-enhanced platform for engineering Unruh-DeWitt detector responses and probing non-Gaussian physics in relativistic settings.