Quantum Reflection Of A Bose-Einstein Condensate With A Dark Soliton

Bose Einstein condensation(BEC)is the aggregation of the lowest energy states of bosons in momentum space when the temperature of the system is low enough(generally in the order of nK).It is considered to be a new macroscopic state of matter besides solid state,liquid state,gas state and plasma state.Since the Bose Einstein condensate has been confirmed in experiments,it has attracted the research interests of scientists in different fields.The theoretical and experimental research of Bose Einstein condensate has always been a hot issue in physics.Moreover,BEC has wide application prospects in superconductivity,superfluidity,particle physics,quantum information,atomic laser and quantum simulation.With the development of atomic chip and nanotechnology,BEC has been applied to atomic devices and precision measurement.The interaction between aggregates and solid surface has also become a new research direction.The interaction of ground state condensate and bright soliton condensate with external potential has been well studied.The main work of this paper is to analyze and study the dynamic process of the interaction between the condensate containing dark soliton structure and the step potential field(potential well or barrier),and reveal the non mediocre influence of dark soliton structure on quantum reflection.In the first part of this paper,we give a brief overview and description of Bose-Einstein condensates,introduce the mean field treatment of BEC system and the corresponding Gross-Pitaevskii(GP)equation to describe its dynamic process.Dark solitons in BEC and quantum reflection of condensates are introduced.In the second part,we study the dynamic process of reflection between the Bose Einstein condensate with dark soliton structure and the barrier or well by solving the GP equation,and further discuss that the asymptotic reflectance of the condensate is affected by several parameters,such as the orientation Angle of the dark soliton and the width of the barrier or well.The cosine function between the asymptotic reflectance Rs of the condensate in the dark soliton state and the orientation angle ? of the dark soliton is obtained,i.e.,R_s?cos[?(?-?/2)].It is found that the asymptotic reflectance of the condensate is affected by two characteristic lengths.For the potential of barrier and well,the asymptotic reflectivity R_s shows different variation rules with the variation of potential width.For the potential well,the length of the dark soliton in the condensate determines the sensitivity width of the potential well,while for the barrier,the attenuation length of the matter wave in the barrier region determines the sensitivity width of the potential barrier.We also study the time evolution of the density distribution of the system during the reflection process and reveal the different behavior of matter waves in different regions of external potential.In the third part,we discuss the quantum reflection process of the interaction between an expansion-dominated condensate and an infinite wide potential well,and compare it with the quantum reflection of a condensate whose center of mass motion dominates.The results show that the expansion velocity of the condensate also has a certain influence on the reflectivity,the larger the expansion velocity of the condensate,the smaller the reflectivity.In the fourth part,we study the effect of the steepness of the potential well change on the quantum reflection of the dark soliton condensate.The results show that the steeper the potential well change is,the more obvious the quantum effect is.The last part is a brife summary of this work and a brief outlook of the development and research prospects in this field.