The Density Profile Of Ideal Bose Atomic Gases In Harmonic Potential

Boson atomic gases with external harmonic trap is playing an importantrole for further understanding the crucial models for condensate matter,thefundamental principles of statistics and nonlinear physics,since the atomicinteraction and parameters for external trap can be exactly experimentallycontrolled.With the low temperature,the wave properties for atoms becomeimportant and have an exponential application in high accuracy measurementphysics.As a novel atomic interferometer,muli-modes Kaptiza-Dirac(K-D)[1]atomic interferometer was designed based on atomic K-D interaction.It’sexperimentally realization needs the knowledge of temperature dependenceof atomic density profile.Starting from quantum many body theory and quantum statistics physics,we made calculations on the density distribution function for boson atomicgases with harmonic trap in one dimension and three dimensions with thehelp of exact solutions for single particle trapped by harmonic potential.Firstly,a brief review on recently development on simulation the modelfor condensate matter and atomic interferometer is presented.Specially,thestudies on particle population[2-3]of ground state and Z[4]function for bosonatomic gases with harmonic trap are introduced.Secondly,a reduced singleparticle density distribution function is obtained by considering the normalorthogonal properties of harmonic function.Finally,the density distributionfunctions for Bose atomic gases with temperature are found with the help ofnumerical calculation for given total atom numbers(here,]000 areconsidered).When the temperature is lower than the critical temperature(Tc),a sharp condensation around original point is found for 1-D atomic densitydistribution function,which shows Bose Einstein Condensation.In the other hand,the temperature dependence of density distribution performs acontinuous behavior.To understand its behavior in high temperature,adensity distribution function with Boltzemann distribution is given under thesame conditions.The results show:a huge difference is found as expected inthe low temperature;the two distributions tend to same in the case of hightemperature(higher than 40 Tc).In the case of three dimensions,a phasetransition can be recognized by a discontinuous behavior around the criticaltemperature.Furthermore,we also have made a comparison between ourresults with the one from the local density approximation.