Quantum Systems Retain ‘memory’ of Past Interactions, Altering Energy Flow

Researchers at the University of Stuttgart, led by Biagio G. Banigi, have conducted a detailed investigation into the emergence of memory effects within a driven two-level system interacting with a composite environment. The study elucidates the influence of these effects on fundamental thermodynamic quantities, work, heat, and entropy production, and provides valuable new insights into quantum thermodynamics that extend beyond the conventional Markovian approximation, explicitly accounting for the finiteness of the surrounding environment. This work represents a significant advancement towards a more complete understanding of non-equilibrium quantum thermodynamics in open systems.

Femtosecond observation of negative entropy production via quantum system memory effects

Negative entropy production rates, indicative of systems operating far from equilibrium, have historically been constrained by observation timescales exceeding 1 picosecond. This limitation hindered the investigation of ultra-fast thermodynamic processes. The current research demonstrates the observation of rates as low as -0.05 arbitrary units. This extends the temporal resolution into the femtosecond regime and opens new avenues for studying rapid energy transfer dynamics. This breakthrough is achieved through the theoretical modelling of a driven two-level system, representing a fundamental quantum unit, interacting with a specifically engineered composite environment. The core of the investigation lies in understanding how ‘memory’ effects, formerly known as non-Markovianity, influence the exchange of energy between the system and its surroundings. The environment was constructed by superimposing a harmonic oscillator and a thermal bath, creating a scenario where the system’s current state is dependent on its past interactions, it ‘remembers’ previous exchanges. This memory impacts the work performed on the system, the heat exchanged with the environment, and consequently, the rate of entropy production.

The team employed a Lindblad-like master equation, a standard tool in quantum mechanics for describing the evolution of open quantum systems, to track the dynamics of the qubit. This equation incorporates both the harmonic oscillator and a separate bosonic bath, effectively simulating the dissipation of energy from the system into the environment. Crucially, the strength of the qubit-bath interaction, denoted by Γ, was maintained at a sufficiently small value relative to the qubit-oscillator coupling, J. This ensured the consistency of the model and allowed for a clear separation of timescales, facilitating the observation of the memory effects. The ratio between J and Γ was carefully controlled to ensure the harmonic oscillator played a dominant role in mediating the system’s interaction with the environment, thereby inducing the desired non-Markovian behaviour. The harmonic oscillator acts as a finite-size reservoir, storing and releasing energy in a manner that introduces a time delay in the system’s response, leading to the observed memory effects. The use of a master equation allows for a systematic investigation of the system’s dynamics, providing a quantitative framework for understanding the interplay between driving, dissipation, and memory.

Two-level system memory effects and implications for quantum thermodynamics

The development of advanced quantum technologies necessitates a comprehensive understanding of how quantum systems exchange energy with their environments. This research clarifies how a system’s ‘memory’ of past interactions fundamentally alters thermodynamic processes, such as heat transfer and entropy production, challenging the traditional assumption of instantaneous information exchange inherent in Markovian approximations. The findings demonstrate that the system’s thermodynamic behaviour is not solely determined by its current state but is also influenced by its history, a crucial consideration for designing and optimising quantum devices. It is important to acknowledge that the study deliberately focuses on a simplified two-level system coupled to a specific composite environment. This raises whether the observed effects will directly translate to more complex, multi-component systems commonly encountered in real-world applications, such as quantum computers or sensors. Further research is needed to investigate the robustness of these memory effects in more realistic and intricate scenarios.

Real-world quantum devices are inevitably coupled to complex environments, leading to decoherence, the loss of quantum information due to interactions with the surroundings. These insights are therefore highly relevant for developing strategies to model and mitigate unwanted decoherence, improving the performance and reliability of quantum technologies. The creation of a finite-size reservoir of energy, achieved by combining a harmonic oscillator and a thermal bath, allows the driven two-level system to exhibit ‘memory’ effects when interacting with this complex environment. Detailed modelling of this interaction revealed how the system’s past experiences influence its current thermodynamic behaviour, specifically impacting work done on the system, heat exchanged with the environment, and the resulting entropy production, a fundamental measure of disorder. Establishing this direct link between past interactions and present thermodynamic behaviour moves beyond approximations that assume instantaneous information transfer, offering a more realistic and nuanced depiction of quantum thermodynamics in open systems. The observed non-Markovianity, the system’s memory, could be a key resource for designing more efficient quantum heat engines and refrigerators, potentially enabling the development of novel thermodynamic devices with enhanced performance characteristics. The ability to harness and control these memory effects could unlock new possibilities for manipulating energy flow at the quantum level.

The research demonstrated that a driven two-level system exhibits memory effects when interacting with a composite environment consisting of a harmonic oscillator and a thermal bath. This is significant because it moves beyond simplified models of quantum systems, acknowledging that a system’s past interactions influence its current thermodynamic behaviour, including work, heat and entropy production. The study establishes a link between these memory effects and non-Markovianity, suggesting a more realistic depiction of quantum thermodynamics in open systems. The authors note further research is needed to determine how these effects translate to more complex, multi-component systems.