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Quantum Optics Journal of the European Optical Society Part B

Spontaneous emission and non-locality in quantum mechanics

B. Crosignani, Paolo Di Porto

Published Jun 1, 1994• 3 citations
Publisher

Abstract

We describe a thought experiment in which the decay rate of an ensemble of excited atoms turns out to depend on both the efficiency and geometry of the counters used to detect the emitted photons. This quantum mechanical effect, of intrinsically non-local nature, implies an enhancing of the atomic decay rate and is present under experimental conditions completely different from those giving rise to the freezing of atomic decay corresponding to quantum Zeno effect.

DOI
10.1088/0954-8998/6/3/001

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We describe a thought experiment in which the decay rate of an ensemble of excited atoms turns out to depend on both the efficiency and geometry of the counters used to detect the emitted photons. This quantum mechanical effect, of intrinsically non-local nature, implies an enhancing of the atomic decay rate and is present under experimental conditions completely different from those giving rise to the freezing of atomic decay corresponding to quantum Zeno effect.
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.
We investigate the decay of an excited two-level atom under a situation where the emitted photon is detected by the conventional photon counting measurement. We discuss an imperfect measurement with finite probability of failing in counting the emitted photon. By analyzing the extended quantum system including the measurement apparatus, we have calculated the survival probability of the excited atom, as well as the response of the apparatus and the errors in the measurement. The decay rate under the measurement is obtained in a simple form. It is shown that not only the response time of the detector but also the measurement error play crucial roles in modification of the decay rate. The conditions to observe the quantum Zeno effect and the anti-Zeno effect are also clarified for the case of Lorentzian form factor.
Abstract We study the measurement-induced enhancement of the spontaneous decay for a two-level subsystem, where measurements are treated as couplings between the excited state and an auxiliary state rather than the von Neumann's wave function reduction. The photon radiated in a fast decay of the atom, from the auxiliary state to the excited state, triggers a quasi-measurement, as opposed to a projection measurement. Our use of the term “quasi-measurement” refers to a “coupling-based measurement”. Such frequent quasi-measurements result in an exponential decay of the survival probability of atomic initial state with a photon emission following each quasi-measurement. Our calculations show that the effective decay rate is of the same form as the one based on projection measurements. The survival probability of the atomic initial state obtained by tracing over all the photon states is equivalent to that of the atomic initial state with a photon emission following each quasi-measurement.
To build up a collective emission, the atoms in an ensemble must coordinate their behavior by exchanging virtual photons. We study this non-Markovian process in a subwavelength atom chain coupled to a one-dimensional (1D) waveguide and find that retardation is not the only cause of non-Markovianity. The other factor is the memory of the photonic environment, for which a single excited atom needs a finite time, the Zeno regime, to transition from quadratic decay to exponential decay. In the waveguide setup, this crossover has a time scale longer than the retardation, thus impacting the development of collective behavior. By comparing a full quantum treatment with an approach incorporating only the retardation effect, we find that the field memory effect, characterized by the population of atomic excitation, is much more pronounced in collective emissions than that in the decay of a single atom. Our results maybe useful for the dissipation engineering of quantum information processings based on compact atom arrays.