Dissipative parametric resonance in a modulated 1D Bose gas

We synthesize results of previous works to give a coherent and self-consistent account of parametric resonance in a modulated quasi-1D Bose gas in the presence of a dissipative mechanism. The resonant behaviour is shown to be largely in line with the predictions of a phenomenological model published in 2014, while the associated dissipation rate is consistent with that derived in 2022 from three-wave mixing processes between the produced quasiparticles and thermal fluctuations. Particular emphasis is put on the evolution of entanglement for opposite momenta quasiparticles which is a signature of their vacuum origin.