Quantum Droplet In The Mixture Of Bose-Einstein Condensates

The achievement of Bose-Einstein condensation(BEC)with the advent of laser cooding in 1995.With the experimental realization BEC in ultracold atomic gase,new experimental platforms have emerged that allow us to study quantum phenomena and exotic states of matter with precise controllablity and in completely novel parameter regimes.A mean-field collapsing mixture gets into a self-bound state stabilized by LHY correction.In this thesis,we study the stability of self-bound quantum droplet and its phase diagram in q2 d,and Borromean droplet in three-component Bose mixture.In chapter 1 we explain BEC from basic principles and the droplet is formed by the inteplay of mean-field attraction and repulsive quantum fluctutions.In chapter 2we study the stability of a quantum droplet and its associated phase transitins in q2 D.The stability of a quantum droplet depends crucially on the geometry,and we note that the confinement introduces the boundary effect and another channel of a bound state to compete with the droplet.In particular,as increasing the atom number we find the soliton reentrance,while the droplet is stabilized only within a finite number window.Near the droplet-soliton transitions,they can coexist with each other as two local minima in the energy landscape.In chapter 3 we study Borromean droplet.Only the ternary bosons can form a self-bound droplet while any binary subsystems cannot.Its formation is facilitated by an additional attractive force induced by the density fluctuation of a third component,which enlarges the mean-field collapse region in comparison to the binary case and renders the formation of Borromean droplet after incorporating the repulsive force from quantum fluctuations.Outside the Borromean regime,the competition between ternary and binary droplets leads to an interesting phenomenon of droplet phase separation,manifested by double plateaus in the density profile.We further show that the transition between different droplets and gas phase can be conveniently tuned by boson numbers and interaction strengths.We summarized in Chapter 4.