Quasiparticle decay in a one-dimensional Bose-Fermi mixture

In the past 20 years, the developpement of highly controlled experimental setups of ultradcold atoms has opened new ways of investigating low-dimensional mixtures of quantum fluids. In particular, one can realize Bose-Fermi mixtures (BFM) where the physical properties of the system can be probed at arbitrary coupling strength through Feshbach resonance. The usual starting point for the theoretical description of one-dimensional BFM is done in terms of a two-component Luttinger liquid. Although this low-energy approach can succesfully describe various phenomena, it fails at describing the decay rate of excitations.
Using a microscopic hydrodynamic description accounting for the various anharmonicities of the theory, we study the effect of the Bose-Fermi couling on the decay rate of excitations [1]: at weak interaction, one branch of elementary excitations is well described by the Bogoliubov spectrum. Identifying the leading process of decay, we obtain the decay rate of these excitations for different regime of coupling and masses of bosons and fermions. We show that the decay rate can dramatically change by tuning the ratio of masses and interactions.

[1] B. Reichert, A. Petković, Z. Ristivojevic, Phys. Rev. B 95, 045426 (2017)