A Tonks Giradeau Gas in the Presence of a Local Potential

TL;DR

This paper investigates how a local potential affects the properties of a Tonks-Girardeau gas, including its condensate density and superfluidity, using analytical and numerical methods.

Contribution

It provides new insights into the impact of local impurities on the quantum state and superfluid behavior of a Tonks-Girardeau gas.

Findings

Condensate density decreases at the impurity site for repulsive potentials.

Condensate density varies with impurity strength for attractive potentials.

Superfluidity is analyzed through numerical and perturbative approaches.

Abstract

The physics of a Tonks-Giradeau Gas in the presence of a local potential is studied. In order to evaluate the single particle density matrix (SPDM) of the many-body ground state, the Wiger-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the "Bose-Einstein Condensate"(BEC) State. We find that the "BEC" state density at the positon of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Giradueau gas is discussed.