Observing Time-Dependent Energy Level Renormalisation in an Ultrastrongly Coupled Open System

TL;DR

This paper experimentally demonstrates time-dependent energy level shifts in a strongly coupled open quantum system, revealing the role of memory effects and correlations in energy renormalisation, with implications for quantum thermodynamics.

Contribution

It provides the first direct experimental observation of dynamic energy level renormalisation due to ultra-strong coupling and memory effects in an open quantum system.

Findings

Observed up to 15% shift in system energy levels

Shift accurately predicted by an open system ansatz

Results align with generalized Lamb shift predictions

Abstract

Understanding how strong coupling and memory effects influence the energy levels of open quantum systems is a complex and challenging problem. Here, we show these effects by probing the transition frequency of an open two-level system within the Jaynes-Cummings model, experimentally realised using Ramsey interferometry in a single trapped 25Mg+ ion. Measurements of the system, coupled to a single-mode environment, reveal a time-dependent shift in the system's energy levels of up to 15% of the bare system frequency. This shift, accurately predicted using an open system ansatz of minimal dissipation, results purely from ultra-strong system-mode interactions and the buildup of correlations. Time-averaged measurements converge to the dispersive Lamb shift predictions and match dressed-state energies, indicating that this observed shift represents a generalised Lamb shift applicable across all coupling and detuning regimes. Our findings provide direct evidence of dynamic energy level renormalisation in strongly coupled open quantum systems, although the total system-environment Hamiltonian is static; this underscores the significance of memory effects in shaping the reduced system's energy landscape. These results offer more profound insights into Hamiltonian renormalisation, essential for strong-coupling quantum thermodynamics and advancements in all quantum platforms.