Linear-and-quadratic reservoir engineering of non-Gaussian states

TL;DR

This paper presents a method for engineering non-Gaussian quantum states in a target mode via dissipative processes, enabling the creation of states like cubic phase and superpositions of Fock states with potential applications in quantum information.

Contribution

It introduces an analytical reservoir engineering approach for preparing non-Gaussian states, including cubic phase and Fock superpositions, in optomechanical systems.

Findings

Achieves pure non-Gaussian states regardless of initial conditions.

Identifies conditions for canonical and non-canonical transformations.

Enables stabilization of Schrödinger cat-like and Fock states.

Abstract

We study the dissipative preparation of pure non-Gaussian states of a target mode which is coupled both linearly and quadratically to an auxiliary damped mode. We show that any pure state achieved independently of the initial condition is either (i) a cubic phase state, namely a state given by the action of a non-Gaussian (cubic) unitary on a squeezed vacuum or (ii) a (squeezed and displaced) finite superposition of Fock states. Which of the two states is realized depends on whether the transformation induced by the engineered reservoir on the target mode is canonical (i) or not (ii). We discuss how to prepare these states in an optomechanical cavity driven with multiple control lasers, by tuning the relative strengths and phases of the drives. Relevant examples in (ii) include the stabilization of mechanical Schr\"odinger cat-like states or Fock-like states of any order. Our analysis is entirely analytical, it extends reservoir engineering to the non-Gaussian regime and enables the preparation of novel mechanical states with negative Wigner function.