Quantum limits to center-of-mass measurements

TL;DR

This paper explores the fundamental quantum limits of measuring the center-of-mass position of many-particle systems, highlighting differences between bosons and fermions, and examining quantum effects in solitons and potential for observing quantum interference.

Contribution

It introduces a quantum limit for center-of-mass measurements, analyzes the effects of quantum statistics, and studies soliton dynamics to observe quantum phenomena in macroscopic systems.

Findings

Fermions exhibit a 1/N scaling in position fluctuation due to Pauli exclusion.

Quantum wave-packet spreading causes deviations from the standard quantum limit.

Quantum diffusion impacts soliton pulse timing and enables potential interference experiments.

Abstract

We discuss the issue of measuring the mean position (center-of-mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultra-low temperatures, and discuss this limit in the context of both photons and ultra-cold atoms. In the case of fermions, we present evidence that the Pauli exclusion principle has a strongly beneficial effect, giving rise to a 1/N scaling in the position standard-deviation -- as opposed to a $1/\sqrt{N}$ scaling for bosons. The difference between the actual mean-position fluctuation and this limit is evidence for quantum wave-packet spreading in the center-of-mass. This macroscopic quantum effect cannot be readily observed for non-interacting particles, due to classical pulse broadening. For this reason, we also study the evolution of photonic and matter-wave solitons, where classical dispersion is suppressed. In the photonic case, we show that the intrinsic quantum diffusion of the mean position can contribute significantly to uncertainties in soliton pulse arrival times. We also discuss ways in which the relatively long lifetimes of attractive bosons in matter-wave solitons may be used to demonstrate quantum interference between massive objects composed of thousands of particles.