NASCIMENTO, L.; NASCIMENTO, Luciano.
Résumé:
In this dissertation, we will study the effects of quantum and thermal fluctuations
in dielectric material media. The basic idea here will be to consider a pulse of light,
called a probe pulse, passing through a sample of dielectric material. In this case, we will
use Cadmiun Selenide (CdSe). Material nonlinearities will be activated by a background
electric field E0
. The classic result says that this pulse will cross the sample of length (d) in
a certain time of flight (t). However, when quantized, E0 will suffer the effects of quantum
fluctuations, the so-called vacuum fluctuations. We will show that such fluctuations will
alter the time of flight of the probe pulse in the sample. To do so, we will calculate
the fractional variance for the flight time, and for a sample of CdSe of approximately
10μm it will be approximately 10−8
. Such a result could, in principle, be measured in the
laboratory. However, in a real physical experiment, fluctuations of thermal origin are also
present and they will influence the result described above. Therefore, we will also consider
the effects that thermal fluctuations have on E0 and then we will see how they will affect
the flight time of the probe pulse that passes through the CdSe sample. In particular, we
find that for a temperature T < 46K, quantum vacuum fluctuations are dominant over
fluctuations of thermal origin. To perform such calculations, we consider terms of up to
second order in the susceptibilities of the CdSe sample, since it is from these terms that
the nonlinearities appear. We also consider a test function, which, from a practical point
of view, regularizes divergent integrals that will appear in the course of the dissertation
and from a physical point of view, models the geometry of the dielectric.