On the observation of nonclassical excitations in Bose-Einstein condensates

TL;DR

This paper reviews the application of quantum optics nonclassicality criteria to matter-wave excitations in Bose-Einstein condensates, analyzing theoretical calculations and experimental challenges in observing nonclassical effects.

Contribution

It provides a detailed comparison of nonclassicality criteria between quantum optics and matter waves, and calculates observables for BECs under various conditions to assess nonclassicality.

Findings

Nonclassical effects have not yet been conclusively observed in relevant experiments.

Additional noncommuting observables may be necessary to detect nonclassicality.

Theoretical calculations show the importance of measurement choices in identifying nonclassical states.

Abstract

In the recent experimental and theoretical literature well-established nonclassicality criteria from the field of quantum optics have been directly applied to the case of excitations in matter-waves. Among these are violations of Cauchy-Schwarz inequalities, Glauber-Sudarshan P-nonclassicality, sub-Poissonian number-difference squeezing (also known as the two-mode variance) and the criterion of nonseparability. We review the strong connection of these criteria and their meaning in quantum optics, and point out differences in the interpretation between light and matter waves. We then calculate observables for a homogenous Bose-Einstein condensate undergoing an arbitrary modulation in the interaction parameter at finite initial temperature, within both the quantum theory as well as a classical reference. We conclude that to date in experiments relevant for analogue gravity, nonclassical effects have not conclusively been observed and conjecture that additional, noncommuting, observables have to be measured to this end.