Recent advances in ultrafast experimental techniques, material fabrication, and innovative cavity designs have unlocked the potential for photo-engineering metastable phases in an increasing range of quantum materials and simulators. The progress has opened fundamental questions about emergent, non-thermal phases that lack equilibrium counterparts. In contrast to the remarkable experimental progress, theory still cannot systematically describe, classify, or predict metastable phases. Existing theories either rely on phenomenological descriptions, which are hard to connect to specific systems, or focus on complex microscopic aspects, which obscure the mechanism of metastability. Developing a theory that integrates phenomenological intuition with predictive system-specific microscopic modelling would greatly aid the search for novel metastable phases.
This project is about establishing such a theory by merging the phenomenological Landau-Ginzburg description with advanced, microscopic computational tools based on the time-dependent Keldysh theory, e.g. Dynamical mean-field theory. Such a fundamental development will enable us to classify metastability scenarios and identify their signatures in microscopically calculated response functions, enabling compar- isons with state-of-the-art experimental probes. The framework will facilitate the control of metastability, exemplified in three timely experimental setups: a) coherent switching protocols in Mott insulators with strong lattice coupling, b) a novel super-radiant phase in a current-driven excitonic insulator within a cavity, and c) long-lived many-body hybrids of light and matter in a cavity quantum simulator. Realising these metastable states could enable transformative quantum technologies, such as ultrafast Mott switches, voltage-tunable excitonic lasers, and quantum memory devices in cavity-based quantum simulators. This project will enhance our control over metastability, opening new frontiers in quantum technology.
