Ground state properties of a Tonks-Girardeau Gas in a periodic potential

Abstract

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.

9 pages, 10 figures

References in corpus (9)

• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Universal correlations of trapped one-dimensional impenetrable bosons
• Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• Momentum distribution for a one-dimensional trapped gas of hard-core bosons
• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Ground State Properties of a Tonks-Girardeau Gas in a Split Trap
• Ground states of hard-core bosons in one dimensional periodic potentials
• The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas

Cited by in corpus (5)

• Correlation versus commensurability effects for finite bosonic systems in one-dimensional lattices
• Generalised Kronig-Penney model for ultracold atomic quantum systems
• The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces