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arXiv:2505.22164

The dynamics of spontaneous emission

M. Baldo

Published May 28, 2025• 0 citations
arXivHTMLPDF

Abstract

The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.

DOI
10.48550/arxiv.2505.22164

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The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.
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Vacuum fluctuations play a central role in spontaneous emission. Recently, it has been suggested that these fluctuations could also be fundamental in the absorption dynamics, breaking the superposition inherent to the linear quantum evolution. We analyze the consistency of that proposal with previous results in double spontaneous emission. Moreover, for the case of single absorption by two atoms, we present a test based on the time dependence of the subsequent spontaneous emission patterns, which can experimentally settle the question. This test is more viable than the original proposal, built on the Casimir effect. Our approach also allows for the comparison between the time scales of vacuum fluctuations as a disentangling mechanism and an emission trigger.
A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way progressively since the early days of the theory. We summarize the main historical steps and then we outline how the randomness gains to be depicted by using tools adapted to Markov processes. We consider a model system corresponding to experimental situations, namely a single two-level atom submitted to a monochromatic light triggering transitions from the ground to the excited state. After a short summary of present quantum approaches, we explain how a general "kinetic-like" Kolmogorov equation yields the statistical properties of the fluorescent light radiated by the atom which makes at once Rabi oscillations between the two states, and random quantum jumps with photo-emission. As an exemple we give the probability distribution of the time intervals between two successive emitted photons by using the Kolmogorov equation.
Among theories of the physical world, quantum mechanics remains a topic of lively discussions on its so-called interpretation. For some it remains an open question to understand how deterministic equations of this theory, as established long ago, may combine with a fundamental uncertainty. We consider the process of spontaneous emission by an atom interacting with infinite number of degrees of freedom of the electromagnetic field. There is uncertainty in the evolution of the photo-emission process which was characterized as Markovian by using the equations of quantum mechanics when the decay of the atom is due to the coupling with the vacuum field. The Markovian property leads us naturally to describe spontaneous emission by using the classical Kolmogorov equation for the probability evolution of a parameter defining the state of the atom. We explain that Everett’s many-worlds interpretation weld together our description, and appears therefore as a consequence of the equations of quantum mechanics, that solves in this case the riddle of deterministic equations describing random events.
A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
We demonstrate a new type of weak measurement based on the dynamics of spontaneous emission. The pointer in our scheme is given by the Lorentzian distribution characterizing atomic exponential decay via emission of a single photon. We thus introduce weak measurement, so far demonstrated nearly exclusively with laser beams and Gaussian statistics, into the quantum regime of single emitters and single quanta, enabling the exploitation of a wide class of sources that are abundant in nature. We describe a complete analogy between our scheme and weak measurement with conventional Gaussian pointers. Instead of a shift in the mean of a Gaussian distribution, an imaginary weak value is exhibited in our scheme by a significantly slower-than-natural exponential distribution of emitted photons at the postselected polarization, leading to a large shift in their mean arrival time. The dynamics of spontaneous emission offer a broader view of the measurement process than is usually considered within the weak measurement formalism. Our scheme opens the path for the use of atoms and atomlike systems as sensitive probes in weak measurements, one example being optical magnetometry.