PROPERTIES OF A MIXTURE OF BOSONS AND FERMIONS AT ZERO KELVIN TEMPERATURE

Abstract

Quantum materials reveal unexpected and exotic behavour when subjected to extreme conditions such as low temperature and/or high pressure. Ultra cold gases provide a very powerful tool for simulation and study of condensed matter systems. Based on recent developments on applications of quantum gases, we have to look for experimental models that can be used to probe and manipulate particles in quantum state and look at their theoretical framework in order to understand their properties. In this work, a mixture of bosons and fermions at zero Kelvin temperature is considered and its properties studied. Most theoretical work have been devoted to a system of two Bose condensates. It is in this research therefore, that we consider a system of Bose condensate with fermionic impurities and look at the properties that arise due to their interaction. The aim of this research was to determine the density distribution of bosons and fermions that are trapped in isotropic external potential and compare their density distribution for different values of ratio of their interaction strength ℎ/𝑔. Gross Pitaevski mean field equation for the boson distribution in the trap is solved by utilizing Thomas Fermi Approximation to extract the density profile of the fermions and bosons components. The results show that the Fermi gas will constitute a shell around a core of Bose condensate for ℎ > 𝑔 and it forms a core inside the Bose condensate for ℎ > 𝑔. For ℎ = 𝑔, both states exist simultaneously, the fermions has a constant spatial density where the bosons are localized. In this work, the existence of three distinct states of the system under variation of the ratio of the interaction strength ℎ/𝑔 has been confirmed.