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

Abstract

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

arXiv comment9 pages, 8 figures

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• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential
• Momentum-space interferometry with trapped ultracold atoms
• Ground state properties of a Tonks-Girardeau Gas in a periodic potential