The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo

TL;DR

This paper investigates the pinning quantum phase transition in a Tonks-Girardeau gas using ground state fidelity and Loschmidt echo, providing insights into equilibrium and out-of-equilibrium dynamics with experimental relevance.

Contribution

It introduces the use of ground state fidelity and Loschmidt echo as diagnostic tools for the pinning transition in a Tonks-Girardeau gas, including out-of-equilibrium analysis.

Findings

Fidelity sharply decreases at the transition point.

Loschmidt echo dynamics reflect fidelity properties.

Results align with recent experimental observations.

Abstract

We study the pinning quantum phase transition in a Tonks-Girardeau gas, both in equilibrium and out-of-equilibrium, using the ground state fidelity and the Loschmidt echo as diagnostic tools. The ground state fidelity (GSF) will have a dramatic decrease when the atomic density approaches the commensurate density of one particle per lattice well. This decrease is a signature of the pinning transition from the Tonks to the Mott insulating phase. We study the applicability of the fidelity for diagnosing the pinning transition in experimentally realistic scenarios. Our results are in excellent agreement with recent experimental work. In addition, we explore the out of equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find all properties of the ground state fidelity are reflected in the Loschmidt echo dynamics i.e., in the non equilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential.