Quantum theory of a three-photon Kerr parametric oscillator

TL;DR

This paper explores the quantum properties of a three-photon driven Kerr oscillator, deriving solutions for its ground state, analyzing superpositions, and proposing its use as a protected Kerr-cat qutrit.

Contribution

It provides exact and approximate analytical descriptions of the ground state, revealing novel superpositions and transitions relevant for quantum information encoding.

Findings

Exact solution at spectral degeneracy

Superpositions of three macroscopically distinct states

Squeezing-to-anti-squeezing transition with detuning

Abstract

We investigate the quantum properties of a nonlinear Kerr oscillator driven by a three-photon pump. We derive both exact and approximate analytical expressions for the ground state of this interacting model. The exact solution arises at an exact spectral degeneracy, while the approximate solution describes regimes of quasi-degeneracy of the energy spectrum. In both cases, the threefold (quasi)degenerate ground-state manifold consists of quantum superpositions of three macroscopically distinct states. These states differ qualitatively from conventional three-component Schr\"odinger's cat states due to the presence of squeezing with a distinctive parametric dependence. By varying the detuning between the oscillator and the three-photon pump, we show that the squeezing can be enhanced, suppressed, or even reversed, leading to a squeezing-to-anti-squeezing transition. We analyze the generation and stabilization of these superposition states, their robustness against perturbations and analytically quantify the leakage to excited states. Our analysis elucidates how the three-photon Kerr parametric oscillator can be used to encode a Kerr-cat qutrit protected against phase-flip errors.