The single-particle density matrix and the momentum distribution of dark 'solitons' in a Tonks-Girardeau gas

摘要

We study the reduced single-particle density matrix (RSPDM), the momentumdistribution, natural orbitals and their occupancies, of dark "soliton" (DS)states in a Tonks-Girardeau gas. DS states are specially tailored excitedmany-body eigenstates, which have a dark solitonic notch in theirsingle-particle density. The momentum distribution of DS states has acharacteristic shape with two sharp spikes. We find that the two spikes arisedue to the high degree of correlation observed within the RSPDM between themirror points ($x$ and $-x$) with respect to the dark notch at $x=0$; thecorrelations oscillate rather than decay as the points $x$ and $-x$ are beingseparated.