Non-Hermitian Models Reveal Two-Qubit System’s Exceptional Points in Heat Flow

Scientists at Universit`a di Napoli Federico II, led by Grazia Di Bello, have elucidated a new connection between non-Hermitian Hamiltonians and conventional Lindblad dynamics in nonequilibrium open quantum systems. The findings offer potential benefits for extending phase diagrams and improving sensing capabilities. Focusing on a two-qubit system designed to conduct heat, the study shows that exceptional points, features of non-Hermitian physics, arise specifically within local master equations under strong, non-equilibrium conditions. Comparing fully Lindblad and non-Hermitian descriptions, and even hybrid approaches, advances understanding of quantum jumps and exceptional points, while also suggesting a practical architecture for experimental investigation using circuit-QED platforms. Emergence of exceptional points clarifies links between energy flow and non-Hermitian quantum Exceptional points, singularities in a quantum system’s parameter space, now emerge with a clear threshold of strong nonequilibrium conditions, previously unobservable in global master equations. Their presence in local master equations reveals a previously hidden link between non-Hermitian Hamiltonians and conventional quantum dynamics. Establishing this connection proved difficult before, particularly regarding the emergence of these points. Dr. Johannes Fink and colleagues at the University of Siegen utilised a minimal two-qubit setup mediating a heat current to compare different mathematical descriptions of quantum behaviour, bypassing approximations often needed when modelling energy loss. The significance of this lies in the ability to accurately model open quantum systems, which are constantly interacting with their environment, leading to dissipation and decoherence, major obstacles in quantum technology development. A spectrum of behaviours bridging the two theoretical frameworks was revealed through further analysis of hybrid models, combining standard ‘Lindblad’ descriptions of energy dissipation with non-Hermitian approaches. Lindblad master equations are the standard tool for describing the evolution of open quantum systems, ensuring physically realistic, completely positive, trace-preserving dynamics. However, they can become computationally expensive for complex systems. Non-Hermitian Hamiltonians, while seemingly violating fundamental principles of quantum mechanics, offer a mathematically convenient way to describe certain aspects of open system dynamics, potentially simplifying calculations and revealing novel phenomena. This work builds on previous investigations into quantum jumps, sudden transitions in a quantum system’s state, and identifies a circuit-QED platform as a potential avenue for experimental verification of these findings. Circuit-QED, utilising superconducting circuits to mimic quantum systems, provides a highly controllable and measurable environment for testing these theoretical predictions. Currently, the analysis focuses on a minimal system and does not yet demonstrate how these principles translate to more complex, practically relevant quantum devices, such as those with many interacting qubits. The two-qubit setup, designed to simulate heat transfer, allowed the team to deliberately bypass approximations commonly used when modelling energy loss. Typically, researchers employ techniques like the Born-Markov approximation to simplify the description of the environment, but these can introduce inaccuracies, particularly when the system-environment coupling is strong. By carefully controlling the interaction between the qubits and their environment, the researchers were able to maintain a more accurate representation of the energy flow. Increasingly, scientists are turning to non-Hermitian physics to model open quantum systems, hoping to unlock new capabilities in sensing and computation. A persistent tension exists between the promise of these models and their practical application, as many theoretical advantages rely on ‘postselection’, effectively cherry-picking successful outcomes from numerous attempts. This approach, while powerful, limits the immediate applicability of some theoretical predictions and motivates the search for phenomena observable without it. Postselection introduces a bias, as it only considers a subset of all possible outcomes, potentially masking the true underlying dynamics. Exceptional points emerge from realistic interactions in open quantum systems Exceptional points, unusual conditions where a quantum system’s behaviour changes dramatically, emerge only under specific conditions, namely within ‘local master equations’ describing how a system interacts with its immediate surroundings. Strong disturbances to a system’s equilibrium are necessary for these points, clarifying a key condition for their observation and demonstrating they are not simply a mathematical quirk. The emergence of these points, alongside their non-Hermitian counterparts, establishes a direct link between the behaviour of open quantum systems and non-Hermitian physics, moving beyond scenarios requiring postselection, the practice of only considering successful experimental outcomes. The local master equation focuses on the immediate interactions of the qubits with their environment, providing a more detailed and accurate description of the dynamics compared to global master equations which treat the entire system as a whole. This is crucial because the environment’s influence is often highly localised. Further investigation focused on quantifying the strength of these disturbances and their impact on the system’s overall dynamics. The researchers found that the exceptional points appear when the rate of heat current between the qubits exceeds a certain threshold, indicating that strong driving forces are necessary to induce this non-Hermitian behaviour. This threshold provides a crucial parameter for experimental control and verification. The implications of this work extend beyond fundamental quantum mechanics. The ability to engineer and control exceptional points in open quantum systems could lead to novel sensing schemes, where the sensitivity of the system is enhanced due to the singular nature of these points. Furthermore, understanding the interplay between Lindblad dynamics and non-Hermitian Hamiltonians could pave the way for designing more robust and efficient quantum devices, less susceptible to environmental noise and decoherence.

The team’s findings suggest that the 01 to 1 GHz range, typical for circuit-QED experiments, is well-suited for observing these effects. The next step involves extending this analysis to more complex systems with multiple qubits and exploring the potential for utilising these phenomena in practical quantum technologies. The research highlights the importance of considering both Hermitian and non-Hermitian descriptions when modelling open quantum systems, offering a more complete and nuanced understanding of their behaviour. The research demonstrated that exceptional points, singularities in a system’s behaviour, emerge in a two-qubit setup when heat current exceeds a specific threshold. This matters because it shows how to create these points without needing to discard experimental data, offering a more realistic approach to harnessing their potential for enhanced sensing. The findings suggest that circuit-QED platforms operating in the 0.1 to 1GHz range are suitable for observing these effects. Future work will likely focus on expanding this understanding to systems with more qubits and investigating applications in robust quantum device design. 👉 More information🗞 Local and Global Master Equations through the Lens of Non-Hermitian Physics🧠 ArXiv: https://arxiv.org/abs/2603.23011 Tags: