Pietro Pelliconi - Princeton University

Monitoring low-rank SYK in a dissipative cavity: photon loss, quantum chaos, and quantum trajectories

The Sachdev-Ye-Kitaev model is an all-to-all interacting disordered model whose relevance ranges from quantum chaos to holographic quantum gravity. Cavity-QED platforms offer a promising route toward implementing closely related boson-fermion models, commonly known as Yukawa-SYK, in which cavity modes mediate all-to-all interactions through disordered QED-like vertices. In the dispersive regime, these systems realize an effective low-rank SYK dynamics for the fermionic degrees of freedom.

In this presentation, we study the effect of photon loss on the quantum chaotic dynamics of low-rank SYK. Photon loss is a natural dissipative channel in cavity QED, but in this setting it plays a particularly interesting role: the same cavity modes that mediate the chaotic all-to-all interactions also provide the dominant channel through which information leaks out of the system. This creates an interplay between scrambling, relaxation, and measurement.

We present preliminary results for two-point and four-point correlation functions in this dissipative regime, with the goal of understanding how photon loss modifies anomalous relaxation, out-of-time-ordered correlators, and Lyapunov growth. We then discuss the unraveling of quantum trajectories, in particular photon-detection statistics. Under natural assumptions, the waiting-time distribution of emitted photons encodes thermal information about the effective low-rank SYK model, allowing one to reconstruct its partition function.