Characterizing Quantum Microwave Radiation and its Entanglement with Superconducting Qubits using Linear Detectors

TL;DR

This paper develops and demonstrates methods for characterizing microwave quantum fields and their entanglement with superconducting qubits, combining theoretical tools with experimental data to advance microwave quantum optics.

Contribution

It introduces joint state tomography techniques for microwave fields and qubits, accounting for finite detection efficiency, and applies these methods to experimental data.

Findings

Successfully reconstructed microwave quantum states beyond single-photon level

Demonstrated entanglement characterization between microwave fields and qubits

Developed maximum-likelihood reconstruction methods for density matrices

Abstract

Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasi-probability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.