Engineering cubic quantum nondemolition Hamiltonian with mesoscopic optical parametric interactions

TL;DR

This paper proposes a scheme to realize a cubic quantum nondemolition Hamiltonian using optical parametric interactions in a nonlinear medium, enabling the engineering of non-Gaussian quantum states with high tolerance to detection inefficiencies.

Contribution

It introduces a novel method to generate a cubic QND Hamiltonian using mesoscopic optical parametric interactions, enhancing nonlinear coupling and robustness against losses.

Findings

Effective cubic QND Hamiltonian achieved with squeezed fields in a nonlinear medium.

Scheme shows high tolerance to detection inefficiencies with phase-sensitive amplification.

Feasibility indicated for near-future pulsed nonlinear nanophotonics experiments.

Abstract

We propose a scheme to realize cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second harmonic fields propagating in a $\chi^{(2)}$ nonlinear medium effectively evolve under a cubic QND Hamiltonian. We highlight the versatility offered by such Hamiltonian for engineering non-Gaussian quantum states, such as Schr\"odinger cat states and cubic phase states. We show that our scheme can be highly tolerant against overall detection inefficiency with an auxiliary high-gain phase-sensitive optical amplifier. Our proposal involves parametric interactions in a mesoscopic photon-number regime, significantly enhancing the effective nonlinear coupling from the nat\"ive single-photon coupling rate while providing powerful means to fight photon propagation loss. Experimental numbers suggest that our scheme might be feasible in the near future, particularly with pulsed nonlinear nanophotonics.