Collision Properties Of Symmetric Two-dimensional Quantum Droplets

In recent years,in the field of ultracold atoms,a new state of matter,quantum droplet of atoms,is found to exist stably at several orders of magnitude thinner than air.It is well known that ultracold atoms in the gas phase are usually trapped by an external potential,and they expand freely when the external potential is turned off.Petrov first proposed in 2015 that binary Bose mixtures of dilute weakly interacting atomic gases could form selfbound droplets.In the case of attractive inter-and repulsive intraspecies interactions,the system energy has a minimum value at a finite density corresponding to a liquid state.The stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang(LHY)correction.Quantum droplets have been successfully realized in experiments on dipolar Bose gases of 164Dy,168Er atoms,the homonuclear mixture of 39K and the heteronuclear 39K-87Rb mixture.Quantum droplet states of ultracold atoms are self-bound and can survive in the vacuum for considerable long time without trapping which is completely different from the behavior of gases.In order to further study the dynamics of quantum droplets,collision of quantum droplets becomes an important tool.The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross-Pitaevskii equation(GPE)in two dimensions by including a logarithmic correction term in the usual contact interaction.When the relative phase is 0,we find the merged droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets.With increasing collision momentum the colliding droplets may separate into two,or even more,and finally into small pieces of droplets.When the relative phases are π/2 or π,the collisions between droplets are only separated or evaporated.For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area or in the strip areas located on both sides of the system and the damped oscillation of the quadrupole mode.A stability peak for the existence of droplets emerges at the critical particle number Nc(?)48 for the quasi-Gaussian and flat-top shapes of the droplets.