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arXiv:2408.15928 · Nature Communications

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

Alessandra Colla, Florian Hasse, Deviprasath Palani, Tobias Schaetz, Heinz‐Peter Breuer, Ulrich Warring

Published Mar 13, 2025• 10 citations
arXivHTMLPDF

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.

DOI
10.1038/s41467-025-57840-4

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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.
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Quantum thermodynamics seeks to address the emergence of thermodynamic laws, which govern how energy is exchanged between physical systems, from a quantum mechanical description of light and matter. As such, the workhorse model for an underlying description of such energy exchange processes is the open quantum system: a quantum system which may interact with an external environment. Open quantum systems are well-understood in regimes where the interaction between the system and the environment is weak enough that perturbative methods may be employed to arrive at dynamical equations of motion for the evolution of the system. How to tackle the strong coupling regime is an open question and much research is still being devoted in this area. In this project we employ a technique developed for studying an open quantum system in regimes of strong reservoir coupling in problems in thermodynamics which have so far been restricted to the weak coupling regime. We spend some time developing our strong coupling framework and then use it to analyse a quantum heat engine to find that strong coupling leads to a particular set of operational costs which are not present in more well-understood weak coupling versions. We also identify effects purely quantum in nature, present in the engine cycle only at strong coupling, which lead to a degradation in the engine's performance. Finally we address the issue of quantum coherence more generally in archetypal open quantum system models beyond weak coupling, and identify a thermodynamic cost to its erasure.
Explaining the influence of strong coupling in the dynamics of open quantum systems is one of the most challenging issues in the rapidly growing field of quantum thermodynamics. By using a particular definition of heat, we develop an approach to study the thermodynamics in the strong-coupling regime, which takes into account quantum resources such as coherence and entanglement. We apply the method to calculate the time-dependent thermodynamic properties of a system and an environment interacting via the generalized amplitude-damping channel. The results indicate that the transient imbalance between heat dissipated and heat absorbed that occurs in the process is responsible for the generation of system-environment entanglement.
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We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to the time-local generator of the reduced dynamics. We derive a general expression for the effective Hamiltonian and develop a recursive perturbative expansion that expresses it in terms of system-bath interaction terms and bath correlation functions. This expansion provides a systematic tool for analyzing energy renormalization effects across different coupling regimes. Applying our framework to paradigmatic spin systems, we reveal how environmental correlations influence energy shifts and eigenbasis rotations, offering insights into strong-coupling effects and non-Markovian quantum thermodynamics.