Parametric Instabilities of Correlated Quantum Matter

TL;DR

This paper develops a framework for manipulating collective bosonic excitations in correlated quantum matter through parametric driving, revealing insights into quantum geometry and enabling new non-equilibrium states.

Contribution

It introduces a general theoretical framework for parametric amplification of collective modes in broken-symmetry phases, with case studies relevant to current quantum materials.

Findings

Parametric driving can amplify collective bosonic modes.

Squeezing of the bosonic vacuum relates to ground state hierarchy.

Parametric modes can induce observable high-amplitude modulations.

Abstract

Collective bosonic excitations are a fascinating aspect of broken-symmetry correlated phases. A wealth of such phases emerged in tailored moir\'e heterostructures, where, in addition, new direct knobs of control exist. Our work explores how the associated collective bosonic modes can be directly manipulated and amplified via parametric driving. As we show, parametric driving is closely related to many-body quantum geometry, as it reveals information about the fidelity susceptibility of the underlying ground state with respect to changes in the control knobs of the interacting system. The parametric response hinges on the tunability of the hierarchy of competing ground states, which we show manifests as squeezing of the bosonic mode vacuum. Furthermore, parametrically-driven modes can produce a high-amplitude modulation in the system that could be easily observed, and could also be used to produce a new non-equilibrium prethermal states with different symmetries. We derive a general framework for parametric amplification of collective bosonic modes in broken-symmetry phases, and provide case-studies of current relevance. Elucidating the connection between the dynamics of these excitations and microscopic electronic observables is key to harnessing their immense potential.