Nondestructive Probing of Means, Variances, and Correlations of Ultracold-Atomic-System Densities via Qubit Impurities

TL;DR

This paper demonstrates how impurity atoms acting as qubits can noninvasively measure moments and correlations of ultracold atomic densities, providing a new method for probing quantum many-body systems.

Contribution

It introduces a technique using qubit dephasing to extract density moments and correlations in ultracold gases, expanding the tools for quantum system measurement.

Findings

Impurity qubits can measure density means, variances, and correlations.

Dephasing functions resemble characteristic functions in probability theory.

Short-time derivatives of dephasing reveal moments of the system operator.

Abstract

We show how impurity atoms can measure moments of ultracold atomic gas densities, using the example of bosons in a one-dimensional lattice. This builds on a body of work regarding the probing of systems by measuring the dephasing of an immersed qubit. We show this dephasing is captured by a function resembling characteristic functions of probability theory, of which the derivatives at short times reveal moments of the system operator to which the qubit couples. For a qubit formed by an impurity atom, in a system of ultracold atoms, this operator can be the density of the system at the location of the impurity, and thus, means, variances, and correlations of the atomic densities are accessible.