We have studied the collective excitation of Bose–Einstein condensate of short-range weak interacting atoms with spin–orbit coupling (SOC) in two dimensions in the liquid phase. In our study, we have included Rashba, Dresselhaus, as well as Raman SOC. The study of Bogoliubov excitation shows that in small interactions, only phonon modes are present, and for higher interactions, roton modes start to appear. Energy spectra contain two roton modes in relatively strong interacting atomic systems.

We have studied the collective excitation of fractional quantum Hall effect (FQHE) in the rotating Bose-Einstein condensate (BEC) using CF theory at the filling fraction ν = 1/2. The roton type of excitation in the FQHE of electron system is established over the years for all the filling fraction, whereas the collective excitation at ν = 1/2 filling fraction in the rotating BEC shows no roton minimum. We have investigated this using composite fermion theory with the Pöschl-Teller interaction potential between the particles. We have seen that the long range interaction will give the roton, whereas short range interaction gives no roton minimum.

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We have studied the effect of time-independent repulsive random impurity potential on the quantum droplets of Bose-Einstein condensation of two different species of Bose atoms in two dimensions. We have solved the Gross-Pitaevskii equation to get the density profile and the energy of the condensate. In our study, we found that quantum droplets are incredibly robust against the non-chemical reactive impurity.