Vacuum Measurements and Quantum State Reconstruction of Phonons

TL;DR

This paper demonstrates a highly efficient vacuum measurement scheme to reconstruct the quantum state of phonons in a trapped ion, verifying quantum dynamics and interference effects predicted by theory.

Contribution

It introduces a novel vacuum measurement approach for quantum state reconstruction of phonons and applies it to observe Jaynes-Cummings dynamics and quantum interference.

Findings

Measured the $Q$-function of vibrational motion in a Yb ion

Reconstructed the Wigner function showing quantum interference

Observed the bifurcation and revival of the coherent state

Abstract

A quantum state is fully characterized by its density matrix or equivalently by its quasiprobabilities in phase space. A scheme to identify the quasiprobabilities of a quantum state is an important tool in the recent development of quantum technologies. Based on our highly efficient vacuum measurement scheme, we measure the quasiprobability $Q$-function of the vibrational motion for a \Yb ion {\it resonantly} interacting with its internal energy states. This interaction model is known as the Jaynes-Cummings model which is one of the fundamental models in quantum electrodynamics. We apply the capability of the vacuum measurement to study the Jaynes-Cummings dynamics, where the Gaussian peak of the initial coherent state is known to bifurcate and rotate around the origin of phase space. They merge at the so-called revival time at the other side of phase space. The measured $Q$-function agrees with the theoretical prediction. Moreover, we reconstruct the Wigner function by deconvoluting the $Q$-function and observe the quantum interference in the Wigner function at half of the revival time, where the vibrational state becomes nearly disentangled from the internal energy states and forms a superposition of two composite states. The scheme can be applied to other physical setups including cavity or circuit-QED and optomechanical systems.