$\chi^{(3)}$ non-Gaussian state generation for light using a trapped ion

TL;DR

This paper presents two efficient, deterministic methods for generating non-Gaussian states in a cavity mode using a trapped ion, crucial for quantum computation, with one method allowing arbitrary approximation and the other enabling exact state creation.

Contribution

It introduces a novel, exact method for non-Gaussian state generation with a single laser pulse, advancing quantum state engineering techniques.

Findings

Both methods are experimentally feasible.

The first method approximates $hi^{(3)}$ non-Gaussian states with quantifiable error.

The second method achieves exact state generation with a single laser pulse.

Abstract

According to the Gottesmann-Knill theorem the non-Gaussian states are necessary component for a nontrivial quantum computation. We show two efficient and deterministic methods of $\chi^{(3)}$ non-Gaussian state generation for a cavity mode using a single trapped ion. Both require ion motional state transfer to the cavity field. The methods are experimentally feasible. The first is based on the well-known protocol for an ion finite motional superposition state generation. It allows for an arbitrary good approximation of $\chi^{(3)}$ non-Gaussian states. We give criteria based on the Wigner function which quantify the error resulting from the approximation. The second and novel method enables an exact non-Gaussian state generation using one laser pulse only.