Nagoya University Team Models Non-Ergodic Phase Transitions for Atomic Josephson Junctions

Koichiro Furutani, from Nagoya University, and colleagues have identified a breakdown of process within a Bose-Josephson junction, revealing a new non-ergodic dynamical phase transition into a ‘running state’ not observed in Markov systems. Their exact non-Markov Langevin simulations pinpoint a zero-mode exceptional point arising from non-Markov friction as the key driver of this transition, characterised by the winding of the response function. This topological origin proves strong against quantum fluctuations and environmental backaction, as confirmed by simulations of an equivalent driven XXZ spin chain, offering potential for developing long-lived quantum memories in challenging, dissipative environments.

Modelling quantum friction using embedded dynamical variables

A sophisticated numerical technique, the Markov embedding method, was employed to unravel the intricacies of this quantum system. This method addresses the limitations of traditional Markovian approaches, which assume that a system’s future state depends only on its present state, neglecting the influence of past interactions. In reality, many quantum systems exhibit ‘memory effects’, where past interactions significantly influence current behaviour. The Markov embedding method effectively transforms a complex, non-Markovian system into a simpler, Markovian one by augmenting the system’s description with carefully calculated ‘dynamical variables’. These additional variables act as internal degrees of freedom that capture the system’s ‘memory’ of past interactions, allowing for accurate modelling of non-Markovian friction. To illustrate, consider the analogy of pushing a swing; conventional Markovian friction is akin to constant air resistance, dissipating energy regardless of the swing’s history. However, the non-Markovian friction in this system behaves as if it ‘remembers’ the initial force applied, influencing the swing’s subsequent motion. The simulations involved an ensemble average of ten thousand noise realizations, ensuring statistical robustness. The analysis was restricted to times before the system’s ‘recurrence time’, typically on the order of 10⁴ time units, to isolate the effects of non-Markovian dynamics from the finite size of the simulated environment. This careful restriction ensured the observed behaviour was genuinely due to the quantum friction, rather than artefacts of the simulation’s boundaries. The Caldeira-Leggett model, intrinsically momentum-coupled, provided the theoretical framework for these simulations, accurately describing the interaction between the Bose-Josephson junction and its environment.

Sustained Quantum Memory via a Non-Ergodic Transition in a Bose-Josephson Junction

Nagoya University scientists have established a critical initial velocity of 100π, a substantial increase from previously achievable velocities in open quantum systems. Environmental decoherence invariably led to the loss of initial quantum memory via thermalization, a process where quantum coherence is destroyed by interactions with the environment, until now. This research reveals a breakdown of that process within a Bose-Josephson junction, a superconducting circuit exhibiting quantum behaviour analogous to a Josephson junction but for bosonic particles. Precise simulations uncovered a novel, non-ergodic dynamical phase transition into a ‘running state’ where quantum properties persist, fundamentally governed by a zero-mode exceptional point originating from non-Markov friction. Ergodicity, in this context, refers to the tendency of a system to explore all accessible states over time; a non-ergodic system remains confined to a limited region of phase space, preserving its initial quantum information. The zero-mode exceptional point represents a singularity in the system’s energy landscape, where two or more energy levels coalesce, leading to enhanced stability and protection against decoherence.

Numerical simulations of an equivalent driven XXZ spin chain, a model commonly used to study quantum magnetism, confirmed the persistence of this state even with strong quantum fluctuations and environmental backaction. The XXZ spin chain provides a complementary perspective, allowing researchers to verify the robustness of the ‘running state’ in a different physical setting. Analysis of the response function revealed a dynamic winding number around zero frequency, indicating a massless double pole and the onset of the zero-mode exceptional point, key to the state’s stability. The winding number is a topological invariant that characterises the behaviour of the response function, providing a robust signature of the exceptional point. The critical velocity required for this transition increases alongside the damping parameter, suggesting a pathway towards controlling the quantum memory’s longevity and exploring its limitations. This relationship allows for fine-tuning the system’s parameters to optimise the duration of quantum coherence. Further research could investigate the influence of different environmental noise spectra on the stability of the ‘running state’.

Engineered Bose-Josephson junction exhibits persistent quantum coherence despite environmental influences

Maintaining quantum information is notoriously difficult, as interactions with the surrounding environment typically induce decoherence and thermalisation, effectively erasing delicate quantum states. These processes represent significant obstacles to the development of practical quantum technologies. A surprising durability in a specifically engineered Bose-Josephson junction was demonstrated by researchers at Nagoya University, revealing a ‘running state’ where quantum properties persist despite these interactions. This offers a promising avenue for building more resilient quantum technologies, providing a foundation for exploring long-lived quantum memories vital for advanced computation and secure communication. Quantum memories are essential components of quantum repeaters, which enable long-distance quantum communication by storing and retrieving quantum information.

The team at Nagoya University demonstrated a breakdown of expected behaviour in open quantum systems, which are typically prone to losing information through environmental interactions. Their work with a head-to-tail Bose-Josephson junction, a circuit simulating quantum dynamics, revealed this ‘running state’ where quantum properties persist, defying the usual process of thermalisation. This novel, non-ergodic dynamical phase transition is fundamentally driven by a sensitive balance point arising from a unique form of friction that ‘remembers’ past interactions, and further investigation into its behaviour over extended timescales is warranted. Understanding the long-term stability of the ‘running state’ and its susceptibility to various environmental perturbations is crucial for assessing its potential for practical applications. The discovery of this non-ergodic transition opens new avenues for exploring quantum dynamics in open systems and designing robust quantum technologies capable of operating in noisy environments.

Researchers demonstrated persistent quantum coherence within a head-to-tail Bose-Josephson junction, despite expected environmental decoherence. This finding challenges the typical loss of quantum memory in open systems, revealing a ‘running state’ where quantum properties are maintained. The transition to this state is governed by a zero-mode exceptional point arising from non-Markov friction, offering a potential platform for long-lived quantum memories. The authors suggest further investigation into the long-term stability of this ‘running state’ is necessary to fully understand its behaviour.