Photon emission without quantum jumps

TL;DR

This paper challenges the standard view that photon emission necessarily involves quantum jumps by treating the emitter and the free radiation field as a closed quantum system evolving under a locally acting Hamiltonian. By solving the Schrödinger dynamics for $H=H_E+H_F+H_{int}$ with a point-like two-level emitter, it shows that the excited-state population decays exponentially while energy is transferred coherently into the field, yielding a single-photon wave packet and a Lorentzian emission spectrum centered at $ω_0$ with width $Γ$. The approach remains consistent with master-equation descriptions, preserves energy, and provides a versatile framework for modeling far-field interference and complex environments without invoking quantum jumps, with potential applications in distributed quantum computing and non-invasive photonic sensing.

Abstract

When modelling photon emission, we often assume that the emitter experiences a random quantum jump. When a quantum jump occurs, the emitter transitions suddenly into a lower energy level, while spontaneously generating a single photon. However, this point of view is misleading when modelling quantum optical systems which rely on far-field interference effects for applications like distributed quantum computing and non-invasive photonic quantum sensing. In this paper, we highlight that the dynamics of an emitter in the free radiation field can be described by simply solving a Schroedinger equation based on a locally-acting Hamiltonian without invoking the notion of quantum jumps. Our approach is nevertheless consistent with quantum optical master equations.

Figures (3)

• Figure 1: Schematic illustration of the generation of a single photon by an initially excited emitter with two internal electronic states. Suppose the excited state $|1_{\rm E} \rangle$ of the emitter corresponds to an alive cat, while $|0_{\rm E} \rangle$ denotes its ground state and corresponds to a dead cat. Utilising an analogy with Schrödinger's cat, the ability to treat the emitter and its surrounding radiation field as a closed quantum system which can be analysed with the help of a Schrödinger equation implies that the cat is in general both dead and alive and can transition continuously from being alive to being dead. This is in contrast to the common view which suggests that the cat is always either alive or dead.
• Figure 2: (a) Probability density $p_r(t)$ in Eq. (\ref{['oma2']}) to detect a photon at time $t$ a distance $r$ away from an initially excited emitter ($|\beta|^2 = 1$) as a function of $r$ for three different times $t_1<t_2<t_3$. The figure shows that the generated photonic wave packet has an exponentially increasing amplitude and travels at the speed of light, $c$, away from the emitter. (b) The same probability density $p_r(t)$ as a function of the time $t$ for three different distances $r_1<r_2<r_3$. An observer placed at $r$ sees the wave packet arriving after some time $r/c$; afterwards its amplitude decreases exponentially in time.
• Figure 3: Probability density $p_{\omega}$ in Eq. (\ref{['oma22']}) of the eventually emitted photon having the frequency $\omega$ for different decay rates $\Gamma_1 < \Gamma_2 < \Gamma_3$. Our calculations confirm in a relatively straightforward way that the spectrum of the emitted light is Lorentzian in agreement with experiments MollowMollow2Mollow3.