Light-Matter Circuits Unlock Control of Quantum Entanglement at Any Strength

Luiz H. Santos, Emory University, and colleagues have mapped the structure and scaling of light-matter entanglement in hybrid quantum systems where quantum materials interact strongly with photons. The team presents an exactly solvable framework, reinterpreting the Power, Zienau, Woolley transformation as a light-matter quantum circuit, offering new insight into controlling and probing quantum correlations within these complex systems and advances the development of nonlocal coupling methods. This framework reveals an emergent dipole symmetry dynamically imposed by the photon field, and shows that both light-matter and spatial entanglement scale logarithmically with system size, a behaviour distinct from typical one-dimensional critical systems.

Logarithmic scaling reveals entanglement growth in light-matter quantum circuits

Light-matter entanglement measures now scale logarithmically with system size, a sharp departure from previously observed extensive or area law scaling. Quantified as S∞∼α/2 log L, this logarithmic scaling emerges when strong coupling resolves a single collective coordinate within the material, something impossible with earlier understandings of entanglement in these hybrid systems. Reinterpreting the Power, Zienau, Woolley transformation as a ‘light-matter quantum circuit’ enabled scientists and the Max Planck Institute of Quantum Optics to perform exact calculations of entanglement across all coupling strengths. The Power-Zienau-Woolley (PZW) transformation is a mathematical technique originally developed to describe the interaction between light and matter in certain physical systems, typically involving polaritons. Its reinterpretation as a quantum circuit provides a novel approach to analysing the entanglement properties, allowing for a more tractable mathematical treatment of the complex interactions.

The dipole fluctuations, a collective coordinate resolved by the photon, grow as Lα/2, directly controlling the observed entanglement within a half-filled Su-Schrieffer-Heeger (SSH) chain. This scaling persists even across the SSH phase diagram, demonstrating strong durability, and the prefactor α/2 is not fixed, evolving with coupling strength to reach a maximum at the chain’s critical point. The Su-Schrieffer-Heeger chain is a one-dimensional model system in condensed matter physics, known for its topological properties and the emergence of localised states at its boundaries. Using this model allows for a precise investigation of entanglement scaling due to its relative simplicity and well-understood characteristics. The observation that the prefactor α/2 is not constant but varies with coupling strength is significant, indicating a tunable relationship between the coupling and the degree of entanglement. Unlike logarithmic entanglement found in critical systems, this entanglement arises in topologically trivial states and stems from non-local photon coupling, not conformal invariance; the circuit couples the photon’s position to the material’s dipole moment, allowing exact calculations at all coupling strengths. Conformal invariance is a property of certain physical systems that leads to logarithmic scaling of entanglement at critical points, but this new finding demonstrates that similar scaling can occur without the need for this symmetry, highlighting the unique role of the nonlocal photon coupling.

Entanglement scaling in a Su-Schrieffer-Heeger chain reveals logarithmic behaviour

Hybrid light-matter systems are increasingly attracting attention as a means of controlling quantum behaviour, but understanding how entanglement, a key quantum connection, scales within these materials has proven difficult. A logarithmic scaling of entanglement was observed, differing from more conventional patterns, though the framework was applied specifically to a half-filled Su-Schrieffer-Heeger chain. Whether these findings will hold true for more complex quantum materials or different geometrical arrangements remains an open question. The difficulty in analysing entanglement scaling stems from the complex interplay between the quantum material and the photon field, requiring sophisticated theoretical tools and computational methods to accurately model the interactions.

Despite current limitations to broader material application, this detailed analysis of entanglement scaling offers important insight into designing future quantum technologies. The observed logarithmic relationship in the chain provides a foundational step towards controlling quantum behaviour within these hybrid systems. This analysis establishes a framework for interpreting complex interactions and clarifies the role of collective coordinates in managing entanglement, though further investigation into different materials and configurations is required. By reimagining the Power-Zienau-Woolley transformation as a ‘light-matter quantum circuit’, scientists and the Max Planck Institute of Quantum Optics could model how light interacts with the collective behaviour of electrons within a material. This approach uncovered an ‘emergent dipole symmetry’ dynamically imposed by the photon field, restructuring entanglement through long-range correlations than local criticality. The emergent dipole symmetry arises from the coupling between the photon and the material’s dipole moment, effectively aligning the dipoles and creating a coherent state that enhances entanglement. This long-range correlation is crucial, as it allows for entanglement to be sustained over larger distances within the system, overcoming the limitations of local interactions.

The logarithmic scaling, S∞∼α/2 log L, is particularly noteworthy because it suggests that the entanglement does not saturate with system size L, unlike extensive scaling (linear with L) or area law scaling (proportional to the surface area). This implies that the entanglement can be sustained and even enhanced as the system grows, potentially enabling the creation of more robust and scalable quantum devices. The fact that the scaling is logarithmic, rather than linear, suggests that the entanglement is distributed in a non-trivial way across the system, with correlations extending over long distances. This has implications for quantum information processing, where long-range entanglement is essential for certain protocols. Further research will focus on extending this framework to explore other quantum materials, such as those exhibiting strong correlations or topological properties, and to investigate the effects of different geometrical arrangements and coupling strengths on entanglement scaling. Understanding these factors will be crucial for realising the full potential of hybrid light-matter systems for quantum technologies.

By modelling light’s interaction with electrons in a one-dimensional quantum chain, researchers demonstrated how entanglement between light and matter can be controlled and sustained. This work revealed an ‘emergent dipole symmetry’ which restructures entanglement via long-range correlations, allowing it to persist over greater distances than previously understood. The entanglement exhibited logarithmic scaling, meaning it does not diminish as the system increases in size. The authors intend to extend this framework to explore other quantum materials and geometrical arrangements to further understand entanglement scaling.