Wormholes and Superconductivity: Linking Quantum Systems with Traversable Connections.

Research demonstrates a connection between two weakly coupled Yukawa-SYK models and a traversable wormhole, evidenced by anomalous scaling in fermionic Green’s functions and a unique Andreev-revival detectable via ac-Josephson current. This suggests critical effects persist even within superconductivity, offering a potential observational signature.

The theoretical exploration of wormholes, once confined to the realm of general relativity and science fiction, receives renewed attention through investigations into condensed matter physics. Recent work suggests that analogous structures, exhibiting properties akin to traversable wormholes, may emerge within specific quantum systems. Researchers at the Instituut-Lorentz, Leiden University, namely Aravindh S. Shankar, Jasper Steenbergen, Stephan Plugge, and Koenraad Schalm, detail such a possibility in their paper, “A Josephson wormhole in coupled superconducting Yukawa-SYK metals”. They demonstrate that a particular arrangement of coupled superconducting materials, modelled using the Yukawa-SYK (Sachdev-Yeager-Kitaev) model – a theoretical framework used to understand strongly correlated quantum systems – can give rise to a hybrid state resembling a ‘thermofield-double’ which is holographically dual to a wormhole connecting two black holes. This exotic state is characterised by unique signatures in the fermionic Green’s function, specifically anomalous scaling of revival oscillations and an Andreev-revival, potentially detectable through measurements of the ac-Josephson current.

Current research concentrates intensely on strongly correlated electron systems, materials where interactions between electrons dominate their behaviour, exceeding the predictions of conventional metallic models. The Sachdev-Ye-Kitaev (SYK) model, a solvable model of interacting fermions, emerges as a crucial analytical tool within this field, offering a framework to investigate non-Fermi liquid behaviour – a state of matter where electrons do not behave as independent particles, defying traditional descriptions. Several studies explore variations of the SYK model, particularly those incorporating Yukawa interactions – interactions mediated by a scalar field – to better represent realistic materials and quantum phase transitions, points where a material undergoes a fundamental change in its properties.

Investigations reveal that coupling two Yukawa-SYK models via weak tunneling – a quantum mechanical effect where particles pass through a barrier – creates a unique hybrid state, resembling a superconducting thermofield-double (TFD). A TFD is a specific quantum state representing thermal equilibrium between two systems, and its emergence here suggests a connection to exotic phenomena. This state exhibits characteristics of both superconductivity – the lossless flow of electrical current – and a traversable wormhole, a theoretical tunnel connecting two distant points in spacetime. Researchers identify anomalous scaling in fermionic Green’s functions – mathematical functions describing the propagation of electrons – alongside a distinctive Andreev-revival within the anomalous Green’s function, as key signatures of this hybrid state.

The existence of the TFD/wormhole state demonstrates a surprising resilience of certain critical effects even within superconducting materials. This finding challenges conventional understanding and suggests that superconductivity does not necessarily negate the presence of these more exotic quantum phenomena. Furthermore, the observed Andreev-revival – a specific type of excitation related to the pairing of electrons – presents a potentially detectable signature of the TFD/wormhole state through measurements of the ac-Josephson current, a phenomenon occurring in superconducting junctions.

Theoretical work complements these investigations, providing foundational background in many-body physics – the study of systems with many interacting particles – and exploring the connections between the SYK model and holographic duality, specifically the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. This duality proposes a relationship between gravitational theories in higher dimensions and quantum field theories, offering a novel approach to understanding strongly correlated systems.

Studies also examine the model’s implications for quantum chaos, information scrambling – the rapid dispersal of information within a quantum system – and the behaviour of Lyapunov exponents, which quantify the rate of separation of nearby trajectories in chaotic systems. These combined efforts represent a significant advancement in the theoretical understanding of complex quantum materials and their potential applications.

Specifically, the anomalous scaling of revival oscillations within these Green’s functions serves as a key indicator. Revival oscillations represent the periodic reappearance of initial quantum states after a time evolution, and their anomalous scaling suggests a departure from conventional behaviour. Furthermore, the observation of an Andreev-revival in the anomalous Green’s function – a unique phenomenon related to the pairing of electrons – provides further evidence for the existence of the hybrid superconducting state and its connection to the traversable wormhole.

Crucially, certain critical effects persist even within superconductivity, challenging conventional understanding of how these phenomena interact. The ability to detect these effects experimentally could revolutionise our understanding of quantum gravity and the fundamental nature of reality.

This research opens new avenues for exploring the connection between quantum entanglement, spacetime geometry, and the emergence of exotic quantum phases of matter. By combining theoretical insights with advanced experimental techniques, researchers are paving the way for a new era of discovery in condensed matter physics and quantum gravity.

Researchers utilise sophisticated analytical techniques, relying heavily on many-body theory and advanced mathematical tools to unravel the complex interactions between electrons in strongly correlated materials. By analysing the behaviour of these systems, they gain insights into the emergence of novel quantum phenomena.

This work builds upon decades of research in condensed matter physics and quantum field theory, pushing the boundaries of our understanding of quantum phenomena. By combining theoretical insights with advanced computational techniques, researchers are making significant progress in unraveling the mysteries of strongly correlated materials. The potential applications of this research are vast, ranging from the development of new materials with enhanced properties to the exploration of fundamental questions about the nature of reality.