Coulomb Interaction Achieves Efficiency Gains in Quantum Otto Cycle Simulations

Researchers are increasingly exploring quantum thermodynamics to develop highly efficient energy conversion technologies. Salvatore Gatto, Alessandra Colla, and Heinz-Peter Breuer, alongside Michael Thoss and colleagues from the University of Freiburg, the Università degli Studi di Milano, and INFN, now present a detailed analysis of a quantum Otto cycle implemented within the Anderson impurity model. Their work, utilising a minimal dissipation approach with hierarchical equations of motion, reveals how Coulomb interactions and strong coupling to the environment can significantly influence the cycle’s performance and even enhance its efficiency. This understanding is crucial for designing future quantum heat engines and refrigerators operating in complex many-body systems, potentially paving the way for novel nanoscale thermodynamic devices

The team achieved this breakthrough by combining a decomposition of the time-evolution generator, based on the principle of minimal dissipation, with the numerically exact hierarchical equations of motion (HEOM) method. This innovative methodology allows for the investigation of operating regimes within the quantum thermal machine, and a detailed examination of the effects of Coulomb interactions, strong system-reservoir coupling, and energy level alignments. The study reveals that Coulomb interaction can significantly alter operating regimes and, surprisingly, may even enhance the efficiency of the cycle under specific conditions.

The research establishes a framework for analysing quantum thermodynamics beyond the weak-coupling regime, addressing a critical challenge in the field where conventional assumptions often break down. By uniquely decomposing the generator of the system dynamics into dissipative and Hamiltonian contributions, the scientists defined an Effective Hamiltonian, denoted as KS, which accounts for the system’s internal energy, including contributions from interaction with the environment. Experiments show that this approach provides a robust means of defining key thermodynamic quantities like work, heat, and entropy production, even in scenarios with strong system-environment coupling and significant memory effects. The team’s work opens new avenues for understanding how energy can be attributed to the system itself and how this influences thermodynamic behaviour.

Notably, the study unveils an intriguing result: while Coulomb interaction generally hinders efficiency when energy levels are positioned above the Fermi energy, it can actually improve performance when levels lie below. This finding is robust, persisting even when alternative definitions of energy and work are employed, suggesting a fundamental aspect of the system’s behaviour. Researchers meticulously analysed the cycle efficiency’s dependence on energy level alignment and the strength of Coulomb interaction, focusing on two distinct regimes of the single-impurity Anderson model. This detailed analysis provides valuable insights into the complex interplay between these parameters and their impact on the overall thermodynamic performance.

Furthermore, the work explores how the effective Hamiltonian KS deviates from the bare system Hamiltonian HS due to interaction with the leads, and how this deviation influences the thermodynamic behaviour of the cycle. By comparing the expectation value of KS to perturbative estimates based on the system-environment coupling strength, the scientists gained a deeper understanding of the system’s internal energy and its relationship to the external environment. The team’s findings have significant implications for the development of future quantum technologies, particularly in the design and optimisation of quantum thermal machines and the exploration of novel thermodynamic protocols. This research provides a solid foundation for further investigations into the fascinating realm of quantum thermodynamics and its potential applications.

Quantum Otto Cycle Analysis via Hierarchical Equations

Scientists investigated the thermodynamic performance of a periodic quantum Otto cycle utilising the single-impurity Anderson model as a working medium. The research team decomposed the time-evolution generator applying the principle of minimal dissipation, subsequently combining this with the numerically exact hierarchical equations of motion (HEOM) method to analyse the operating regimes of the thermal machine. This approach enabled detailed investigation into the effects of Coulomb interactions, strong system-reservoir coupling, and energy level alignments on cycle performance. Results demonstrate that Coulomb interaction can alter operating regimes and potentially enhance efficiency under specific conditions.

The study pioneered a revised formulation of thermodynamic laws, uniquely decomposing the generator of system dynamics into dissipative and Hamiltonian terms, defining an effective Hamiltonian, KS. Researchers engineered a system where a central interacting system alternates between coupling to fermionic environments at differing temperatures. The working medium, described by the single-impurity Anderson model, features a single electronic level capable of double occupancy with opposite spin, incorporating on-site Coulomb repulsion. To simulate the time evolution, scientists harnessed the numerically exact HEOM method, allowing for analysis across a broad parameter range and detailed examination of the quantum thermal machine’s operating regimes.

Experiments employed the HEOM method to simulate the dynamics of the single-impurity Anderson model, a crucial step in modelling the quantum Otto cycle. The team meticulously simulated the system’s dynamics, focusing on the interplay between the system and its environment, particularly at strong coupling strengths. This method achieves a numerically exact solution, circumventing limitations of conventional approaches in regimes of strong system-environment coupling. The system’s internal energy, including contributions from environmental interactions, was then compared to perturbative estimates based on the system-environment coupling strength, providing a robust validation of the model.

Furthermore, the study analysed how the effective Hamiltonian, KS, deviates from the bare system Hamiltonian, HS, due to lead interactions, and how this deviation influences thermodynamic behaviour. Researchers explored the impact of Coulomb interaction on cycle efficiency, revealing an intriguing result: while Coulomb interaction typically hinders efficiency when energy levels are above the Fermi energy, it can actually enhance performance when levels are below. This finding proves robust across different definitions of energy and work, suggesting a fundamental effect of Coulomb interactions on the cycle’s thermodynamic properties.

Coulomb interactions enhance quantum Otto cycle

Scientists have achieved a detailed analysis of a periodic Otto cycle operating on the single-impurity Anderson model, employing a novel decomposition of the time-evolution generator based on the principle of minimal dissipation. The research, combined with the numerically exact hierarchical equations of motion (HEOM) method, meticulously examines the operating regimes of this quantum thermal machine and investigates the effects of Coulomb interactions, strong system-reservoir coupling, and energy level alignments. Results demonstrate that Coulomb interaction significantly alters the operating regimes and, surprisingly, can enhance the efficiency of the cycle under specific conditions. Experiments revealed that the efficiency is heavily influenced by the alignment of energy levels relative to the Fermi energy.

The team measured a distinct performance variation depending on whether the energy levels reside above or below the Fermi level, with Coulomb interactions exhibiting contrasting effects in each regime. Specifically, when energy levels are above the Fermi energy, Coulomb interaction generally hinders efficiency, while below the Fermi level, it can actually improve performance. This finding is robust, persisting even when alternative definitions of energy and work are applied, suggesting a fundamental relationship between Coulomb interactions and cycle efficiency. Data shows a comprehensive analysis of the effective Hamiltonian, KS, and its deviation from the bare system Hamiltonian, HS, due to interaction with the leads.

Scientists recorded how this deviation influences the thermodynamic behaviour of the cycle, providing insights into the system’s internal energy and the contribution of system-environment interactions. Measurements confirm that the effective Hamiltonian accurately accounts for the system’s internal energy, aligning with perturbative estimates based on the system-environment coupling strength. The breakthrough delivers a refined understanding of thermodynamic quantities in strongly coupled quantum systems, addressing challenges in defining work, heat, and entropy production beyond the weak-coupling regime. Tests prove the efficacy of the minimal dissipation principle in uniquely decomposing the generator of the system dynamics, separating dissipative and Hamiltonian contributions. This work provides a foundation for further exploration of quantum thermal machines and their potential applications in nanoscale energy conversion and quantum technologies, opening avenues for designing more efficient and robust quantum devices.

Coulomb Interactions Enhance Quantum Otto Cycle Efficiency b

Scientists have conducted a comprehensive study of the thermodynamics of a periodic quantum Otto cycle implemented on a single-impurity Anderson model. Employing the hierarchical equations of motion (HEOM) method, they provided a numerically exact treatment of the system to explore the impact of strong system-reservoir coupling and Coulomb interactions. The research utilised definitions of work and heat grounded in the principle of minimal dissipation to analyse the cycle’s thermodynamic properties. The findings demonstrate that Coulomb interactions significantly modify the thermodynamic performance of the cycle, altering operational regimes and influencing both heat exchanges and work output.

Notably, the presence of interaction can enhance efficiency in specific regimes due to the population dynamics of doubly occupied states, which favourably affect the cycle’s energy balance. This enhancement was consistently observed across different thermodynamic definitions used in the analysis, suggesting the potential for exploiting strong correlations to improve quantum thermal machines. The authors acknowledge that their study focuses on a specific model and parameter range, representing a limitation to broader generalisations. Future research could extend this framework to multi-level impurities or explore more complex reservoir engineering strategies. Such investigations may reveal novel operational modes and optimisation techniques for nanoscale quantum engines, potentially leading to advancements in quantum technologies.