⚛️ quantum physics

Photon emission without quantum jumps

This paper argues that photon emission in quantum optical systems can be accurately modeled by solving a Schrödinger equation with a locally-acting Hamiltonian, thereby eliminating the need for the misleading concept of random quantum jumps while remaining consistent with standard quantum optical master equations.

Original authors: Thomas Hartwell, Daniel Hodgson, Huda Alshemmari, Gin Jose, Almut Beige

Published 2026-01-22

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Thomas Hartwell, Daniel Hodgson, Huda Alshemmari, Gin Jose, Almut Beige

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: No More "Magic Jumps"

Imagine you have a glowing firefly. In the old way of thinking about physics (the "Quantum Jump" view), we imagine that this firefly sits there glowing, and then—pop!—in a split second, it suddenly stops glowing and a photon (a particle of light) magically appears out of nowhere. It's like a lightbulb that doesn't dim; it just snaps from "ON" to "OFF" instantly, and a new light particle teleports into existence.

This paper argues that this "snap" view is misleading. Instead, the authors suggest that the firefly doesn't jump. It slowly fades out, like a battery draining, while the light it emits slowly flows out into the world. There is no sudden snap; it is a smooth, continuous process.

The "Schrödinger's Cat" Analogy

To explain this, the authors use a famous thought experiment involving a cat in a box.

The Old View: The cat is either alive or dead. At some random moment, it suddenly dies.
The New View: The cat is like a sick animal that gets gradually sicker. It starts healthy (the emitter is excited), gets slowly ill (the emitter is losing energy and the field is getting excited), and eventually dies (the emitter is empty, and the light is fully out).

The paper says that until someone actually opens the box to look (a measurement), the cat is in a weird, continuous state of being "partially alive and partially dead." It doesn't jump from one state to another; it transitions smoothly.

The "Antenna and Battery" Metaphor

The authors compare the atom (the light emitter) to a radio antenna connected to a finite-sized battery.

The Battery: The atom starts with a full battery (excited state).
The Antenna: As the battery drains, it sends out a signal (light).
The Process: The battery doesn't just vanish. It slowly loses energy, and that energy flows continuously into the antenna and out into the air as a wave.
The Result: The light wave moves away at the speed of light. Once it leaves the antenna, it never comes back. The antenna doesn't "re-absorb" the light it just sent out because the light is moving too fast.

In this view, the atom isn't "jumping" to a lower energy level. It is simply running out of battery power, and that power is turning into a traveling wave of light.

Why "Blips" Instead of "Jumps"?

The paper introduces a new way to think about light particles. Instead of thinking of a photon as a tiny ball that appears instantly, they describe it as a "blip" (a local excitation).

Imagine a ripple in a pond. You don't say the water "jumped" from one spot to another. The ripple forms and moves.
The authors say the atom creates these "blips" in the electromagnetic field. These blips travel away from the atom at the speed of light.
Because these blips move away so fast, the atom can't grab them back. This explains why the atom loses its energy permanently without needing to invoke a mysterious "quantum jump."

What About the "Snap" We See in Experiments?

You might ask: "But scientists see the light turn on and off in experiments. Isn't that a jump?"

The paper says: No, the jump only happens when you look.

Without a detector: The atom and the light field are in a smooth, continuous dance. The atom is slowly fading, and the light is slowly growing. Nothing jumps.
With a detector: If you place a camera or a sensor to catch the light, the act of measuring forces the system to "choose" a state. It's like taking a photo of the sick cat; the photo shows it either alive or dead. The "jump" is a result of the measurement, not the natural process of the light being created.

Why Does This Matter?

The authors claim that by viewing light emission as a smooth, continuous process (solving a standard Schrödinger equation) rather than a series of random jumps, we can understand complex situations better.

Interference: It helps explain how light from different sources can mix and interfere with each other over long distances (like in quantum computing).
Simplicity: It avoids many complicated "fixes" and assumptions that physicists usually have to add to their math to make the "jump" theory work.
Accuracy: Their math predicts that the light has a specific "color spread" (a Lorentzian spectrum), which matches what we see in real experiments, proving their smooth model works just as well as the old jump model.

Summary

In short, this paper suggests that light emission is not a sudden explosion, but a smooth draining of energy. The atom is like a battery powering an antenna, slowly sending out a wave of light. The "quantum jump" is just an illusion created when we stop to look at the result. Until we look, the universe is just a smooth, continuous flow of energy.

Technical Summary: Photon Emission without Quantum Jumps

Problem Statement
The standard paradigm for modeling spontaneous photon emission often relies on the concept of "quantum jumps," where an excited emitter is assumed to transition instantaneously and randomly to a lower energy level, generating a single photon. While this view aligns with observations of macroscopic quantum jumps in ion traps (manifesting as telegraph signals of light and dark periods), the authors argue that this perspective is misleading for quantum optical systems relying on far-field interference, such as distributed quantum computing and non-invasive photonic quantum sensing.

Standard approaches typically utilize master equations to describe the time evolution of the emitter's density matrix. These equations, while experimentally successful, are often non-intuitive, require multiple ad hoc approximations (e.g., rotating wave, Born, and dipole approximations), and do not inherently describe the unitary dynamics of the combined emitter-field system. Furthermore, the quantum jump approach approximates the time delay between emission and detection, potentially neglecting interference effects that occur before a photon reaches a detector.

Methodology
The authors propose an alternative framework where the emitter and the surrounding free radiation field are treated as a single, closed quantum system evolving unitarily according to the Schrödinger equation. The methodology rests on three core pillars:

Locality and "Blips": Instead of decomposing the electromagnetic field into momentum-space modes, the authors utilize a position-space description. The field is quantized using "blips"—bosons localized in position that act as local carriers of light. This approach distinguishes between field observables and local carriers, allowing for a local description that avoids the non-commutativity issues often cited as a barrier to local field quantization.
Locally-Acting Hamiltonian: The system is governed by a Hamiltonian $H = H_E + H_F + H_{int}$ . Crucially, the interaction Hamiltonian $H_{int}$ is constructed to be locally acting at the emitter's position. It couples the atomic lowering operator $\sigma_-$ to the creation operator of a local field excitation $a^\dagger(0)$ . This form ensures causality (solving Fermi's two-atom problem) and naturally incorporates the second law of thermodynamics without requiring the rotating wave approximation or the Wigner-Weisskopf approximation.
Analytical Solution: The authors solve the Schrödinger equation for this closed system analytically using a Dyson series expansion. They track the evolution of the pure state vector $|\psi(t)\rangle$ of the combined emitter-field system, rather than tracing out the field to obtain a master equation immediately.

Key Results
The analytical solution yields the following specific results:

Exponential Decay without Jumps: The excited state population of the emitter decreases exponentially over time ( $e^{-\Gamma t}$ ). However, this decay is not the result of a stochastic jump but a continuous, coherent transfer of energy from the emitter to the field. The emitter transitions from an "alive" (excited) state to a "dead" (ground) state via a continuous superposition, analogous to a Schrödinger's cat transitioning from alive to dead through an "ill" state.
Photon Wave Packet Dynamics: The emitted photon is described as a wave packet with an exponentially decreasing amplitude that propagates away from the source at the speed of light $c$ . The probability density of detecting a photon at distance $r$ and time $t$ is non-zero only for $0 \le r \le ct$ , strictly adhering to causality.
Lorentzian Spectrum: By performing a Fourier analysis on the disentangled photon state after the emission process is complete, the authors derive the spectrum of the emitted light. The result is a Lorentzian distribution centered at the atomic transition frequency $\omega_0$ , with a linewidth proportional to the spontaneous decay rate $\Gamma$ . This matches experimental observations without invoking complex eigenvalues or continuous environmental monitoring.
Consistency with Master Equations: By tracing out the field degrees of freedom from the derived pure state, the authors recover the standard quantum optical master equation for the emitter's density matrix. This demonstrates that the standard master equation is a valid description of the emitter's reduced dynamics, but it emerges here from a fundamental unitary evolution without the need for the approximations typically required in its derivation.

Significance and Claims
The paper claims to provide a more intuitive and physically transparent picture of photon emission by treating it as a coherent, continuous process within a closed system. The significance of this approach includes:

Avoidance of Approximations: The model derives standard results (exponential decay, Lorentzian spectrum) without relying on the rotating wave, dipole, or Wigner-Weisskopf approximations, or the assumption of complex eigenvalues.
Handling of Interference: Because the dynamics are described by a pure state vector of the field, the approach naturally accommodates far-field interference effects and long-range atomic interactions. This is particularly relevant for scenarios where emitted light interferes before detection, a situation where the quantum jump approach (which assumes immediate collapse upon detection) may be insufficient.
Control and Applications: The authors suggest that this framework offers new tools for quantum technology. Specifically, it allows for the direct modeling of pulse shaping and the potential application of quantum control to correct unwanted changes in the emitter's state without requiring quantum feedback control. It also facilitates the modeling of complex environments, such as emitters near partially transparent mirrors or in plasmonic cavities, by directly accounting for delays and interference.

In summary, the paper argues that the "quantum jump" is an artifact of measurement and coarse-grained observation, whereas the underlying physical reality of photon emission in a free field is a continuous, unitary evolution governed by a locally-acting Hamiltonian.