Density probabilities and quantum critical phenomena of a Bose-Fermi Mixture in 1D Double well potential

TL;DR

This study investigates the quantum critical behavior and density probabilities of a 1D Bose-Fermi mixture in a double well potential, revealing distinct tunneling regimes, entanglement properties, and fidelity variations influenced by interaction strengths.

Contribution

It introduces a detailed analysis of quantum critical phenomena in a 1D Bose-Fermi mixture using the two mode approximation, highlighting the effects of interactions on tunneling, entanglement, and fidelity.

Findings

Three distinct tunneling regimes identified.

Maximum entanglement occurs at specific boson-fermion couplings.

Fidelity drops deepen as boson-fermion interaction decreases.

Abstract

The time evolution of probability density, the ground-state fidelity and the entanglement of a Bose-Fermi mixture in a 1D double well potential, are studied through the two mode approximation. We found that the behaviour of the quantum return probability shows three distinct regions. The first region is characterized by a complete miscibility, and correlated tunneling of bosons and fermion. The second region is characterized by correlated sequential tunneling and in the last region we found an increase in the tunneling frequency of the two species. We found through the Von Neumann entropy, that the boson-fermion coupling allows a maximum entanglement of quantum correlations of bosons and fermions in the same value. Finally we calculated the fidelity in the $\lambda_{FF}-\lambda_{BF}$ and $\lambda_{BB}-\lambda_{BF}$ planes and we found that the drop of the two fidelities becomes deeper and deeper as the boson-fermion interaction decreases.