Process tomography of field damping and measurement of Fock state lifetimes by quantum non-demolition photon counting in a cavity

TL;DR

This paper demonstrates quantum non-demolition photon counting in a superconducting cavity to perform process tomography of field damping, revealing Fock state lifetimes and transition rates with high precision.

Contribution

It introduces a method for quantum process tomography of photon number relaxation using QND measurements, providing detailed Fock state lifetime data.

Findings

Damping rates increase linearly with photon number n.

Photon state lifetimes are accurately measured and match theoretical predictions.

Thermal effects slightly influence the damping rates.

Abstract

The relaxation of a quantum field stored in a high-$Q$ superconducting cavity is monitored by non-resonant Rydberg atoms. The field, subjected to repetitive quantum non-demolition (QND) photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the $n$ photon states ($0\leq n \leq 7$) are found to increase linearly with $n$. The results are in excellent agreement with theory including a small thermal contribution.