Number fluctuations of cold spatially split bosonic objects

TL;DR

This paper analyzes the maximum and minimum possible number fluctuations in split bosonic systems, revealing how fragmentation affects fluctuations and comparing mean-field and many-body states.

Contribution

It introduces a theorem to determine extremal number fluctuations and applies it to various bosonic configurations, highlighting the role of fragmentation.

Findings

States that maximize particle number fluctuations are identified.

Fragmented states can have identical fluctuations to condensed states.

Number fluctuations depend on lattice sites and state fragmentation.

Abstract

We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different numbers of lattice sites and both mean-field and many-body wave functions. It is shown which states maximize the particle number fluctuations, both in lattices and double-wells. The fragmentation of the states is discussed, and it is shown that the number fluctuations of some fragmented states are identical to those of fully condensed states.