Chiral instabilities in Driven-Dissipative Luttinger Liquids

The interplay between Floquet driving and dissipation facilitates novel quantum phenomena in interacting systems such as 1D quantum wire. To address this, we investigate the non-equilibrium dynamics of periodically driven Luttinger liquids coupled to thermal baths. When the bath coupling satisfies detailed balance, we derive the stability conditions that suppress parametric instabilities in each bosonic mode. Furthermore, by designing a chiral coupling to the bath, we uncover a genuinely driven-dissipative phase transition between the conventional parametric instability and chiral parametric instability, where only one chirality of bosonic quasiparticles gets exponentially amplified, leading to a dynamical chiral imbalance within the Luttinger liquid.