Researchers Model Photon Emission Without Jumps, Revealing Dynamics Consistent with Optical Systems and Equations

Conventional models of photon emission rely on the idea of sudden, random jumps between energy levels, but this approach presents challenges when simulating complex optical systems, particularly those leveraging far-field interference for applications like distributed computing. Thomas Hartwell, Daniel Hodgson, and Huda Alshemmari, all from the University of Leeds, alongside Gin Jose and Almut Beige, demonstrate an alternative method that accurately describes photon emission without invoking these jumps. Their research presents a new theoretical framework based on the Schrodinger equation and a locally-acting Hamiltonian, offering a more consistent approach for modelling the dynamics of light-emitting systems. This advancement promises to improve the accuracy and efficiency of simulations for a range of optical technologies, potentially paving the way for more sophisticated designs and applications.

Localized Photons, Quantum Paradoxes, and Causality

Researchers are exploring the fundamental nature of photons and their behaviour, particularly the challenges of defining a photon’s position without encountering paradoxes related to causality. This work delves into the theoretical foundations of light-matter interactions, seeking to reconcile quantum mechanics with our classical understanding of the world. A central question is whether a photon can be truly localized without potentially allowing signals to travel faster than light, violating established physical principles. The research focuses on concepts including the Quantum Zeno effect, which suggests frequent measurement can effectively freeze a quantum system’s evolution.

Researchers are also exploring models that describe photons confined to a smaller space, investigating how these models affect the energy and momentum of emitted light. The work treats quantum systems as ‘open’, interacting with their environment, and uses mathematical tools called ‘master equations’ to describe their evolution, drawing upon ‘Molecular Quantum Electrodynamics’ which describes light and matter interactions at the molecular level. The research establishes a historical context, referencing earlier work on quantum jumps and photon localization, then delves into the mathematical and theoretical underpinnings of quantum optics. A significant portion explores the paradoxes that arise when attempting to pinpoint a photon’s location, and the potential for causality violations, investigating models of local photon Hamiltonians. The team also considers recent advances in controlling open quantum systems, suggesting ways to overcome decoherence and maintain quantum coherence.

Continuous Evolution of Quantum Emitter Dynamics

Researchers have developed a new way to model how excited atoms emit light, moving away from the traditional idea of abrupt quantum jumps. Instead, they use the Schrödinger equation, governed by a locally-acting Hamiltonian, to accurately describe the interaction between the atom and the surrounding radiation field, aligning with established quantum optical models like master equations without requiring approximations. The team introduces ‘single-excitation states’ to represent field excitations originating from a point-like source, propagating outwards from the emitter, utilizing a mathematical technique called a ‘Dyson series expansion’ to define the emitter and field’s evolution over time. This technique reveals that the emitter’s state changes continuously, with the probability of remaining excited decreasing exponentially, mirroring expected decay behaviour.

Scientists calculated coefficients, c₀(t) and cᵣ(t), describing the probability amplitudes for the emitter remaining excited or transitioning to a lower energy level with a photon emitted in a specific direction, exhibiting a Lorentzian structure consistent with experimental observations. The calculations demonstrate that the probability of detecting a photon at a given distance and time is proportional to the square of cᵣ(t), and integrating this probability over all distances yields a total probability of one, confirming energy conservation. Researchers proved that the predicted probability of not detecting a photon, p₀(t), remains identical whether the radiation field is observed continuously or only at a single point in time, highlighting the robustness of the model. The calculations reveal that the generated photonic wave packet propagates outwards from the emitter at the speed of light with an exponentially decreasing amplitude, accurately depicting the emission process and providing a new perspective on quantum optical systems.

Coherent Emission Modeled with Schrödinger Equation

Researchers have developed a novel approach to modelling photon emission, moving beyond traditional methods that rely on the concept of random jumps between energy levels. This work demonstrates that the dynamics of an emitter can be accurately described using the Schrödinger equation based on a locally-acting Hamiltonian, offering a consistent alternative to standard quantum optics models. The team successfully calculated the time evolution of a point-like emitter analytically, revealing that the emitter’s energy decreases exponentially as it coherently transfers energy into the surrounding field. Experiments and calculations show the emitted light possesses a Lorentzian spectrum, aligning closely with established experimental observations.

The results demonstrate a pure state of the emitter and surrounding field evolves predictably over time, provided no measurements are made to disturb the system. The team’s calculations align with the quantum jump approach, a widely used method, but without requiring approximations; their Hamiltonian directly corresponds to the conditional non-Hermitian Hamiltonian used in that approach. Importantly, the predicted probability of not detecting a photon, p₀(t), remains consistent whether the field is observed continuously or only at a single point in time. Further analysis reveals the emitted light propagates outwards from the source as a wave packet with an exponentially increasing amplitude, travelling at the speed of light. The probability density of detecting a photon at a given distance and time, pr(t), is directly proportional to the square of the amplitude, and integrates to one when considered over all distances, confirming energy conservation. This approach accurately predicts the observed spectrum of emitted light, validating its consistency with experimental data and offering a new perspective on the fundamental processes governing photon emission.

Continuous Emission Models Atom-Field Interaction Precisely

This research demonstrates that the emission of light from an excited atom can be accurately modelled not as a series of random jumps to lower energy levels, but as a continuous process governed by a standard Schrödinger equation. The team shows that by describing the atom and the surrounding radiation field with a locally-acting Hamiltonian, they can reproduce the predictions of established quantum optical master equations without relying on approximations.