Coherence and Classical Emergence in the Scovil and Schulz-DuBois Laser Model

Abstract

This thesis investigates the quantum dynamics of a three-level laser system described by the Scovil and Schulz--DuBois model with emphasis on the emergence of classical laser behaviour. In particular we study the time evolution from an initially coherent quantum field. We compare closed Jaynes--Cummings dynamics with open Lindblad dissipator dynamics including hot and cold Markovian reservoirs, which provide lasing gain in the cavity field. This provides a unified setting for studying coherence, dissipation, and phase-space dynamics. We determine if the decoherence of the system can be predetermined by Jaynes--Cummings model and a Schawlow-Townes like estimate for a strong and weak coupling regime, respectively.

Numerically, we show that the model follows the expected quantum optical behaviour. The numerical implementation was improved substantially through vectorisation and by benchmarking two integrators. The fourth-order Runge--Kutta method was found to be significantly more efficient than the forward Euler method, yielding an improvement in computational speed by a factor of $\sim 80$ for the parameter ranges considered.

From the simulation we find that the Jaynes--Cummings model holds for the strong--coupling regime and that indicators like the Husimi Q--function must be interpreted together with density-matrix-based observables to confirm quantum coherence. In the open system the coherence decays over time and the cavity field evolves toward a phase-averaged, annular shaped distribution in phase space, consistent with the expected steady-state behaviour of a laser. In the weak--coupling regime, the fitted coherence lifetime agrees well with a Schawlow-Townes-like phase diffusion estimate. This suggests that the Schawlow--Townes description becomes appropriate once coherent Jaynes--Cummings dynamics no longer dominate the cavity evolution.

Popular Abstract

Lasers are used in barcode scanners, fibre optics, medicine, manufacturing, and everyday optical devices. Although they are often thought of simply as narrow beams of light, their operation is rooted in quantum physics. They are built from quantum rules, and their behaviour reveals how order, randomness, and light are connected at a fundamental level. In pursuit of further applicability of lasers as a part of the second quantum revolution, this thesis studies a simple yet powerful model of a laser system: the Scovil and Schulz-DuBois model.

At its core, the model describes a quantum system that can only occupy three allowed energy states. Energy is supplied from one side of the system and removed from another, so that the system is driven far away from ordinary equilibrium. This imbalance is what makes laser action possible. The key physical process is stimulated emission: one photon can trigger the release of another photon with the same colour, direction, and phase. The emitted photons act like a group of musicians playing in perfect synchrony.

We try to understand how a strongly quantum state gradually becomes more classical. To make this visible, the system is first prepared in a coherent light state. This is the closest quantum analogue to the kind of monochromatic light produced by a laser, despite the quantum origins of the light production. When the light starts in a coherent state, its behaviour changes in a striking way. The system goes through oscillations caused by coherent energy exchange between the atom and the light field in the Jaynes--Cummings model. The system oscillations can fade and later return, a phenomenon known as collapse and revival. This is a genuinely quantum effect, which we study: the system does not evolve as one single tone, but as a combination of many slightly different ones, which first interfere destructively and later reassemble.

A particularly revealing way to visualise this is through the Husimi Q-function. Rather than treating the light as a point in ordinary space, this gives a kind of map of its quantum state. In this map, a purely quantum superposition can appear as two separate peaks. The two-peak structure reflects the dressed-state dynamics of the coupled atom and light field. In the thesis, this bimodal structure is observed directly in a system without other disturbances. Together with other coherence measures, it supports the interpretation that the light field contains coherent quantum structure.

The role of the environment is just as important. The thermal reservoirs act like background noise in a concert hall: they do not immediately stop the music, but they gradually make the precise timing harder to maintain. In the same way, the reservoirs wash out the phase coherence of the light field, a process known as decoherence, and the system evolves toward a phase-averaged, more classical laser-like state.

Overall, the thesis shows how quantum coherence in a simple laser model can evolve into the more classical, phase-averaged behaviour associated with laser light. This helps clarify how quantum optical systems connect microscopic coherence with macroscopic laser behaviour.

• author: Christov, Oskar
• supervisor: Andreas Wacker
• organization: Mathematical Physics; Department of Physics
• course: FYSK04 20261
• year: 2026
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Coherence, Scovil and Schulz-DuBois, Open quantum system, Jaynes-Cummings, Lindblad
• language: English
• id: 9237009
• date added to LUP: 2026-06-15 07:03:03
• date last changed: 2026-06-15 07:03:03