Quebra de simetria em condensados de Bose-Einstein confinados por um potencial funil
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2021-04-09
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Universidade Federal de Goiás
Resumo
Theoretically predicted in 1923-1924 by Bose and Einstein and experimentally
obtained only in 1995, the Bose-Einstein condensate became an important laboratory for
the investigation of various quantum phenomena, such as the Josepshon oscillations, the
study of vortex, use as interferometers, etc. Using mean-field theory to include the effects
of the average interaction between particles, in the 1960s, Gross and Pitaevskii obtained
an equation capable of describing the dynamics of a diluted gas at a temperature of 0 K.
Dimensional reduction models for the Gross-Pitaevskii equation were developed for several
types of confining potentials in order to simplify numerical calculations and reproduce
accurate results. For condensates with a strong attractive strength, confined by doublewell
potentials, it is known that the phenomenon of spontaneous symmetry breaking
occurs. In this state, the particle population between wells becomes asymmetrical, in
contrast with the symmetry of the confining potential.
In this work, we consider a condensate in the self-focusing regime, confined
transversely by a funnel-like potential and axially by a double well formed by the
combination of two inverted Pöschl-Teller potentials. We used an effective equation,
obtained by means of a variational method for the Gross-Pitaevskii equation, to analyze
the symmetry break of the probability density of the wave function that describes the
condensate. This symmetry break was observed for several interaction strength values
as a function of the minimum potential well. A quantum phase diagram was obtained,
in which it is possible to recognize the three phases of the system: symmetric phase
(Josepshon), asymmetric phase (spontaneous symmetry breaking - SSB), and collapsed
states, i.e., when the solution becomes singular, which does not represent the physical
system, showing a validity limit for the model under consideration. We analyzed our
symmetric and asymmetric solutions using the real-time evolution method, in which it
was possible to confirm the stability of the results. Finally, a comparison with the cubic
nonlinear Schrödinger equation in one dimension and the Gross-Pitaevskii equation in
three dimensions is performed for the purpose of analyzing the accuracy of the effective
equation used here.
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Citação
MIRANDA, B. M. Quebra de simetria em condensados de Bose-Einstein confinados por um potencial funil. 2021. 52 f. Dissertação (Mestrado em Física) - Instituto de Física, Universidade Federal de Goiás, Goiânia, 2021.