Communication
Collective spin density excitation of fractional quantum Hall states in dilute ultra-cold Bose atoms

https://doi.org/10.1016/j.ssc.2019.113796Get rights and content

Highlights

  • •

    First time we have calculated the spin-reversed excitations in fractional quantum Hall effect of Bose particles, considering different types of interaction.

  • •

    Low energy collective excitation is similar with the spin-wave excitation.

Abstract

We have studied collective spin density excitation of fractional quantum Hall effect (FQHE) in rotating Bose–Einstein condensation for the three filling fractions of first series of Jain’s composite fermion sequences. We have considered short-ranged contact interactions between the Bose atoms as well as long range Coulomb interactions to compare the nature of the spectra with FQHE of electrons. Using Monte-Carlo method for finite but large number of particles, the lowest order collective modes of spin-reversed sectors is calculated here, by computing the energy differences of the respective excitons from the fully polarized ground states.

Section snippets

Delta function interaction

Cooper, Wilkin and others applied the idea [6], [9], [22] to map interacting bosons onto non-interacting spin-less fermions and considered delta (δ) function interaction between the Bose atoms. For ultra-cold dilute bosons, the scattering between the atoms eventuates only in the s-wave. The effective interactions between the bosons at low energy limit, can be represented by a constant U0=4πħ2as∕m in momentum space, where m is the mass of each particle and as is the s-wave scattering length.

This

Wave function & calculation procedures

As the spherical geometry has no edge, it is beneficial to study the bulk properties of FQHE with finite number of electrons. In our numerical calculations, we thus formulate composite fermion wave function in spherical geometry [25], [28]. It is thought that, N number of correlated electrons are moving on the surface of a sphere, subjected to a radial magnetic field. The magnetic field is assumed to emerge from a ‘magnetic monopole’ of strength Q at the center of sphere, which produces a total

Results & discussion

Previous studies by Chang et al. [5] show that the CF description of Bose atoms worsens with increasing n along the CF sequence [equation (2)] and the mapping is also quantitatively very accurate for the ground state and excited state at ν=1∕2. We have also seen that the CF result well agrees with the exact diagonalization for ν=1∕4,1∕6 filling fractions. So the CF wave function is very good wave function for those states. That is why we have studied here the spin-reversed collective excitation

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

It is our pleasure to thank Sutirtha Mukherjee for sharing his exact diagonalization result with us. Moumita thanks DST INSPIRE (Ref: IF160850), India for the financial support.

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