Neutral Collective Excitation of Fractional Quantum Hall Effect in Rotating Bose Einstein condensation

Debashis Das, Saswata Sahu, and Dwipesh Majumder Department of Physics, Indian Institute of Engineering Science and Technology, Howrah, W B, India

Fractional quantum Hall effect (FQHE) occurs due to the strong Coulomb interaction between electrons in 2D system in presence of the perpendicular magnetic field. The natural quasi- particle of FQHE is the composite fermion (CF), each electron in the lowest Landau level captures an even number of flux quanta and form CF. So the CF experience reduced amount of magnetic field, in this magnetic field CF forms new kind of Landau level called $\Lambda$ levels, and the FQHE of strongly interacting electron can be mapped into the integer quantum Hall effect of non-interacting CFs.

After the discovery of Bose-Einstein condensation (BEC), FQHE in rapidly rotating BEC of charge neural dilutes Bose gas in a harmonic trapped at low temperature has been proposed. The neural atoms do not interact with the magnetic field, but the rotation in the confinement potential plays a similar mathematical role of magnetic field in the two-dimensional electron system, sometimes this field refers as synthetic magnetic field, though the experimentally we don't have any observation in this filed. The CF realization of Bose atomic system is simply attaching an odd number of vortices with each atom. There are details studies of the ground state properties of this system in the literature, but the little attention has been given to the collective excitations study except for some exact diagonalization calculation for the small number of particles. We have studied the collective excitations of the various filling fraction in the Jain's series. The most of the cases interaction between the atoms is the short-range delta-function interaction. It is very difficult to handle delta-function interaction potential in the quantum Monte-Carlo calculation, to remove this difficulty we have used Poschl-Teller interaction potential, with suitable adjusted parameter so that we can tune the interaction. Some of the observed BEC such as the dilute gas of Cesium atoms have the permanent dipole moment. We have included the dipole-dipole interaction in our calculation to study such system. In addition, we have considered Coulomb interaction to see the nature of collective excitations and compare with the electronic FQHE. In our study, we have seen that the nature of collective excitations of FQHE of Bose gas has similar characteristics as that of the FQHE of the electron.