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Imagine a slide with three dips: the deepest one is a stable position for a ball, the middle one is precarious. A slight push and the ball rolls down. Yet, constant vibration of the right strength can hold it in the middle hollow for a long time.

In the 1950s, physicists Lee and Yang discovered that all states of matter are separated by invisible points in the world of imaginary numbers. These points, called Lee-Yang zeros, outline the phases. Stable phases are tucked far away, while shaky (metastable) ones creep up to the real axis. Research has shown: vibration shifts these zeros, and the shaky state becomes stable. The stronger the forcing, the more real the hidden phase becomes.

Terahertz light pulses act like that very 'shaking', only electromagnetic. By controlling light, we can program material properties. The most surprising part: the distance from a Lee-Yang zero to the real axis precisely determines the required vibration intensity. Entropy of the system behaves like a coordinate on an imaginary map, and spectroscopy becomes a control panel.

Original abstract

as written by the authors arXiv:2606.08004

Metastable phases (MPs) are energetically unfavorable states typically suppressed in equilibrium phase diagrams. Rather than remaining ''hidden'', we show that they exist in the complex plane of thermal fields, as regions delineated by Lee-Yang zeros (LYZs). We demonstrate this numerically in a toy model with a tunable density of states featuring three Gaussian peaks and in a more realistic periodically driven system. In both cases, as artificial parameters or drive amplitudes increase, the LYZs bounding the MP approach the real axis and split into separated branches, signaling the emergence and stabilization of the MP within the enlarged gap between two adjacent stable phases. In the driven system, the imaginary part of LYZs correlates with drive strength, linking Lee-Yang theory to terahertz matter manipulation. These findings provide a scheme to describe MPs in phase diagram analysis. By viewing periodic drives as complex thermal fields, it also offers a new perspective for understanding and engineering non-equilibrium collective states.