A single fermion in a Bose Josephson Junction

TL;DR

This paper investigates the tunneling behavior of a single fermion in a Bose-Einstein condensate within a double-well potential, revealing a resonance phenomenon and proposing a fermion-based interferometer.

Contribution

It provides analytical descriptions of fermion-boson tunneling resonances and demonstrates their application in constructing a Mach-Zehnder interferometer.

Findings

Identification of a tunnel resonance at strong boson-fermion interaction

Analytical expressions for the resonance lineshape using degenerate Brillouin-Wigner theory

Design of a fermion-based Mach-Zehnder interferometer for population transfer

Abstract

We consider the tunneling properties of a single fermionic impurity immersed in a Bose-Einstein condensate in a double-well potential. For strong boson-fermion interaction, we show the existence of a tunnel resonance where a large number of bosons and the fermion tunnel simultaneously. We give analytical expressions for the lineshape of the resonance using degenerate Brillouin-Wigner theory. We finally compute the time-dependent dynamics of the mixture. Using the fermionic tunnel resonances as beam splitter for wave-functions, we construct a Mach-Zehnder interferometer that allows complete population transfer from one well to the other by tilting the double-well potential and only taking into account the fermion's tunnel properties.