Abstract
Abstract In this manuscript, we explore the effects of continuous measurements upon the quantized electromagnetic field through a series of simple examples. For this purpose, we consider the Srinivas-Davies model to describe the optical field dynamics probed continuously by a photodetector. Through the application of this continuous photodetection model to some specific situations, it is possible to cover some basic concepts of quantum mechanics such as the principle of superposition, the collapse of the wave function, the probabilistic character of the possible outcomes associated with projective measurements, as well as some advanced topics such as the description of open quantum systems, irreversible processes in quantum mechanics, decoherence and dissipation associated with non-unitary evolution of quantum systems. Besides, we also consider the important concept of entanglement between two electromagnetic fields and how it is affected by the photodetection process. This work aims to provide complementary material for undergraduate and graduate students interested in the effects of measuring devices acting on quantum systems.
Highlights
The postulates of Quantum Mechanics (QM), following the Copenhagen interpretation, establish the foundations to describe nature at the microscopic scale
We are interested in exploring the concepts raised above, considering continuous measurements applied to the quantized optical field via photodetection
The conditioned state (37) is the state that emerges from the continuous photodetection process when it is known how many photons were counted during the probing time t; if it is not known how many photons were counted during the probing time we usually describe our lack of information about the state through the unconditioned state, which is the state obtained averaging the conditioned state (37) over all possible k counts weighted by the photocouting probability distribution (39)
Summary
The postulates of Quantum Mechanics (QM), following the Copenhagen interpretation, establish the foundations to describe nature at the microscopic scale. Despite an extensive literature [6,7,8,9,10,11,12,13,14,15] about this subject, we care about being quite pedagogical to help advanced undergraduate and graduate students interested in the effects of measuring devices acting on quantum systems This kind of problem is becoming increasingly important given the significant quantum-based technologies advancements [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31].
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