Experimento da fenda dupla: dualidade onda-partícula e sua quantificação e um exemplo de tomografia

Abstract

In this work, we studied the wave-particle duality and also proposed the implementation of a minimal tomography in the same plane of detection in a model for the interference experiment with matter waves through the double slit. A quantum mechanical description of this experiment is presented, and the intermediary situations of partial knowledge of the ondulatory and corpuscular descriptions were quantied, through the quantities called visibility (V) and predictability (P), respectively, as it is usual in the literature. First, the calculations of these quantities were done for the model of the ideal case of particles sent through the obstacle with the double slit. In the second part, we pursued an aproximation with a more realistic situation and did the same calculations for the case in which the particle interacts with an environment - here, we have considered this environment made of an ideal gas of particles, for simplicity. In this case, entanglement with the environment is developed, and the state of the system becomes, after the acting of the dynamics - which is governed by a master equation - a mixed state. In both cases, we veried that the relationship P2 + V 2 1 is obeyed, and an analisys of the behaviour of these quantities were done. Finally, we proposed a minimal state tomography in the same plane in the model for the experiment here described.