Interactions Steer Quantum Particles Even Without Direct Energy Input

Researchers at the University of Vienna, led by Pietro Borchia, demonstrate that density-density interactions can effectively transfer non-reciprocity, the property of directional behaviour, between different parts of an open quantum system. Their investigation centres on a one-dimensional lattice of spin-½ fermions, and establishes the exact solvability of the system’s dynamics, illuminating how interactions reshape the behaviour of excitations. These interactions can induce directional movement even in parts of the system not directly connected to the external environment, suggesting a broadly applicable mechanism for controlling many-body quantum dynamics. The findings provide a key understanding of how interactions can spread non-reciprocal dynamics within quantum systems, potentially impacting the design of future quantum technologies.

Exact solution reveals interaction-driven directional transport in open quantum systems

An exact solution to the Lindbladian dynamics has been achieved for a system comprising 128 sites, representing a significant advancement beyond previous methods that relied on approximations such as the no-click approximation. The Lindbladian master equation is a standard tool in open quantum systems to describe the time evolution of a density matrix, accounting for the system’s interaction with its environment. The no-click approximation, often used to simplify these calculations, can introduce inaccuracies, particularly in strongly interacting systems. This breakthrough, therefore, represents a key leap forward in understanding open quantum many-body systems, allowing for a more accurate and detailed analysis of their behaviour. Enabled by a one-dimensional lattice of spin-½ fermions with Hatsugai-Kohmoto interactions, the exact solution allows detailed analysis of how density-density interactions transfer non-reciprocal dynamics and directional behaviour between different degrees of freedom within the system. The Hatsugai-Kohmoto interaction, a specific type of long-range interaction, is crucial for achieving this solvability and facilitates the exploration of non-reciprocal effects.

Remarkably, these interactions induce directional drift even in spin sectors not directly coupled to the engineered reservoir, demonstrating a new method for controlling energy flow. The engineered reservoir represents the external environment with which the quantum system interacts, and typically introduces dissipation and decoherence. This observation suggests that the interactions effectively ‘relay’ the non-reciprocal behaviour throughout the system. The drift was quantified by examining the first moment of the real space Green’s function, revealing a rightward shift with increasing interaction strength. The Green’s function provides information about the propagation of excitations within the system, and its first moment represents the average position of these excitations. A similar mechanism was observed in a driven-dissipative Fermi-Hubbard chain, suggesting broader applicability beyond the specific model, evidenced by momentum-selective dressing of the particle conserving sector. The Fermi-Hubbard model is a cornerstone of condensed matter physics, describing interacting fermions on a lattice, and the observation of similar behaviour strengthens the generality of the findings. This momentum-selective dressing refers to the modification of the energy spectrum of the system due to interactions, which further contributes to the non-reciprocal transport. It establishes a key principle, broadening understanding of how to engineer non-reciprocal dynamics in quantum materials and circuits, offering a pathway towards novel devices such as quantum ratchets and directional amplifiers.

Hatsugai-Kohmoto interactions enable control despite limitations in realistic quantum system

Reservoir engineering offers increasingly precise control over quantum systems, yet achieving this control often demands complex, finely-tuned interactions. The research reveals a surprising route to directional control, not through direct manipulation of the reservoir, but via interactions that redistribute these effects within the system itself. This redistribution is achieved through density-density interactions, where the density of particles at one location influences the behaviour of particles at another. However, the current model relies on all-to-all connectivity, a specific and potentially restrictive form, and it remains unclear whether this mechanism functions with more localized or realistic interactions. All-to-all connectivity implies that every particle interacts directly with every other particle in the system, which is rarely the case in real materials.

While simplifying calculations and allowing exact solutions, these interactions may not fully reflect the complexity of real physical systems. The challenge lies in translating these findings to systems with more realistic interactions, such as those mediated by short-range forces. Interactions between particles now establish a route to control quantum systems by redistributing directional behaviour. Specifically, density-density interactions can transfer non-reciprocity, a one-way flow of energy or information, between different parts of an open quantum system, differing from traditional methods requiring direct manipulation of each component. This is significant because it opens up possibilities for controlling quantum systems without needing to directly address every individual element. The work utilised a one-dimensional lattice of spin-½ fermions, particles with intrinsic angular momentum, featuring this specific type of connection allowing for precise control. These fermions are fundamental building blocks of many quantum systems, and their behaviour is crucial for understanding the properties of materials. The use of a one-dimensional lattice simplifies the analysis while still capturing the essential physics of interaction-mediated non-reciprocity. Further research will be needed to explore the robustness of this mechanism in more complex and realistic scenarios, potentially paving the way for the development of novel quantum devices and materials with tailored directional properties.

The research demonstrated that density-density interactions can transfer non-reciprocity, a one-way flow of energy, between different parts of a quantum system. This is important because it offers a new method for controlling quantum systems without directly manipulating each individual component. Researchers investigated this phenomenon using a one-dimensional lattice of spin-½ fermions with all-to-all interactions, establishing an exactly solvable model for interaction-mediated non-reciprocal dynamics. The authors note that further work is needed to test this mechanism in more complex systems.