Theory of Microwave Parametric Down Conversion and Squeezing Using Circuit QED

TL;DR

This paper presents a theoretical study of microwave parametric down conversion and squeezing in circuit QED, demonstrating how a superconducting qubit can generate highly squeezed microwave states with tunable non-linearity.

Contribution

It introduces a method to achieve microwave squeezing using a superconducting qubit in circuit QED, with tunable non-linear susceptibility and realistic parameters for high squeezing levels.

Findings

Squeezing of approximately 13dB below vacuum noise is achievable.

The non-linear susceptibility  can be tuned via gate voltage and vanishes at charge degeneracy.

Coherent coupling of cavity modes through the qubit enables the generation of squeezed states.

Abstract

We study theoretically the parametric down conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper pair box (CPB) qubit located inside a transmission line resonator. The non-linear susceptibility \chi_2 describing three-wave mixing can be tuned by dc gate voltage applied to the CPB and vanishes by symmetry at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state. Based on parameters realized in recent successful circuit QED experiments, squeezing of 95% ~ 13dB below the vacuum noise level should be readily achievable.