Observing time-dependent energy level renormalisation in an ultrastrongly coupled open system.

Abstract

Understanding how strong coupling and memory effects influence energy levels in open quantum systems is a fundamental challenge. Here, we experimentally probe these effects in a two-level open system coupled to a single-mode quantum environment, using Ramsey interferometry in a trapped ion. Operating in the strong coupling regime, we observe both dissipative effects and time-dependent energy shifts of up to 15% of the bare system frequency, with the total system effectively isolated from external environments. These dynamic shifts, likely ubiquitous across quantum platforms, arise solely from ultra-strong system-mode interactions and correlation build-up and are accurately predicted by the minimal-dissipation Ansatz. Our approach identifies these as generalised Lamb shifts, matching conventional predictions on time-average. We provide experimental fingerprints supporting the Ansatz of minimal-dissipation, thereby suggesting it as a testable quantum thermodynamics framework and establishing a foundation for future benchmarks in strong-coupling quantum thermodynamics and related technologies.