Coherent States Demonstrate Origin of Classical Fields in Quantum Electrodynamics, Impacting Laser-Matter Interactions

Classical electromagnetic fields underpin our understanding of countless physical processes, ranging from the interaction of lasers with matter to the behaviour of systems in intense fields, yet their fundamental quantum origin remains a complex question. Keita Seto from the National Institute for Fusion Science, along with colleagues, now provides a first-principles formulation that explains how these classical fields emerge directly from quantum electrodynamics (QED) through the use of coherent states of light. The team demonstrates that scattering amplitudes calculated using these coherent states naturally give rise to an effective description involving background fields, clearly distinguishing the coherent laser component from other quantum fluctuations. This achievement establishes a robust and universally applicable framework for QED with coherent backgrounds, allowing for the consistent inclusion of effects like field depletion and backreaction, and unifying operator-based and functional approaches to strong-field physics.

Beginning with the operator formulation of QED, the study demonstrates how scattering amplitudes between coherent states naturally result in an effective description using background fields, crucially maintaining a distinction between the coherent laser mode and other quantized photon degrees of freedom. This framework enables the consistent inclusion of effects beyond the fixed background approximation, such as depletion and backreaction, without presupposing any specific field strength or intensity regime.

Coherent States Define Classical Electromagnetic Fields

Scientists have established a foundational framework for quantum electrodynamics (QED) with coherent background fields, systematically deriving classical electromagnetic fields from the quantum theory of light. This work clarifies how classical fields emerge from the underlying quantum description, moving beyond simply postulating their existence, and provides a rigorous basis for strong-field QED. The team began with the operator formulation of QED, examining scattering amplitudes between coherent states of the electromagnetic field and other particles, maintaining a clear distinction between the laser mode and other quantum photons. Experiments revealed that the conventional generating functional used in QED, with a prescribed background field, arises as a natural consequence of fixed coherent state boundary conditions, demonstrating a direct link between established methods and this new formulation.

Researchers reformulated these scattering amplitudes using a path integral representation, confirming that both operator-based and functional approaches yield equivalent physical results, offering complementary perspectives on the same phenomena. The study successfully incorporates effects beyond the standard fixed background approximation, such as depletion and backreaction, without limitations on field strength or intensity, expanding the scope of applicable scenarios. Measurements confirm that the Gupta-Bleuler condition, essential for defining physically admissible states, can be adapted to coherent states within the Heisenberg picture, effectively defining coherent laser electromagnetic fields. Specifically, the team demonstrated that the expectation value of the electromagnetic field in a coherent state is defined by the sum of its positive and negative frequency components, establishing a precise mathematical description of the classical field arising from quantum origins. This intensity-independent foundation allows standard strong-field QED formulations to emerge as specific, well-defined cases, solidifying the framework’s versatility and broad applicability. The breakthrough delivers a unified view of QED in background fields, clarifying the conceptual validity of classical backgrounds and their limitations.

Classical Fields Emerge From Quantum Electrodynamics

This research establishes a foundational framework for understanding how classical electromagnetic fields emerge from the principles of quantum electrodynamics, specifically through the use of coherent states of the electromagnetic field. Scientists have demonstrated that these coherent states provide a natural origin for background fields routinely used in describing interactions between light and matter, offering a consistent way to separate the coherent laser component from other quantum fluctuations. The team successfully derived a path integral formulation that incorporates effects like laser depletion and backreaction, phenomena occurring when the laser’s energy is not constant, without the need for approximations typically employed in strong-field quantum electrodynamics. The achievement unifies several existing approaches to the problem, including operator-based methods and conventional path integral formulations, presenting them as specific instances within a more general and consistent quantum framework.

Importantly, the work clarifies how standard strong-field QED arises as a limiting case, simplifying complex calculations while maintaining full quantum consistency. The authors acknowledge that their formulation relies on specific boundary conditions for the coherent field, defining its behavior at infinite distances, and that gauge constraints are enforced before performing the functional integral, a standard procedure in quantum field theory. Future research may explore applications of this framework to increasingly complex scenarios, potentially refining calculations of non-linear quantum electrodynamic effects and furthering our understanding of light-matter interactions at extreme intensities.