A new class of pure non-Gaussian quantum states

Non-Gaussian quantum states are essential for quantum information processing and fundamental physics, yet they are notoriously difficult to prepare and highly susceptible to decoherence. While Fock states and Schrödinger cat states are well-known, this paper explores the theoretical existence and generation of a new class of pure non-Gaussian states characterized by trigonal symmetry, extending the concept of multi-component cat states to systems with higher-order axial symmetry.

The researchers analyze a non-degenerate four-wave mixing system involving two pump modes and two signal modes. By treating the pump modes as classical fields, they derive the nonlinear evolution of the signal modes. Using a perturbative expansion of the Hamiltonian, they calculate the joint wave function of the signal modes. They then demonstrate that by performing a heralding measurement—detecting a specific photon number in one signal mode—the remaining signal mode collapses into a pure state possessing trigonal symmetry. The analytical results are validated through numerical simulations using the QuTiP framework.

The study confirms that the heralded output state is invariant under a rotation of 2π/3 in phase space, confirming its trigonal symmetry. The Fock state occupation probabilities for these states are restricted to values of n = n0 + 3k, where k is an integer. This confirms that the system effectively produces a superposition of states that maintains this discrete symmetry, offering a new pathway for engineering complex non-Gaussian states in optical systems.

Expanding the library of available non-Gaussian states is crucial for advancing quantum technologies. Trigonal states provide a novel resource for quantum interferometry and information processing. Furthermore, the methodology presented here suggests that more complex symmetries (order n > 2) could be engineered in systems with n interacting modes, opening doors to a broader class of structured quantum states.