CommunicationCollective spin density excitation of fractional quantum Hall states in dilute ultra-cold Bose atoms
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 () 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 in momentum space, where is the mass of each particle and 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, 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 along the CF sequence [equation (2)] and the mapping is also quantitatively very accurate for the ground state and excited state at . We have also seen that the CF result well agrees with the exact diagonalization for 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.
References (35)
- et al.
Phys. Rev. B
(1984) - et al.
Phys. Rev. Lett.
(1982)Phys. Rev. B
(1982)et al.Phys. Rev. Lett.
(1983) Phys. Rev. Lett.
(1989)Phys. Rev. B
(1990)- et al.
Science
(1995) - et al.
Phys. Rev. A
(2005) - et al.
Phys. Rev. B
(1999) Rev. Modern Phys.
(2001)- et al.
Rev. Modern Phys.
(1999) - et al.
Phys. Rev. Lett.
(2001)
Nuovo Cimento Soc. Ital. Fis. B
Phys. Rev. Lett.
Phys. Rev. Lett.
Front. Phys.
Phys. Rev. Lett.
Phys. Rev. Lett.
Phys. Rev. Lett.
Phys. Rev. Lett.
Cited by (5)
Spin-flip excitation and negative energy dispersion in rotating Bose atoms
2024, Journal of Physics Condensed MatterCollective Excitation of Bosonic Quantum Hall State
2024, Journal of Low Temperature PhysicsDouble roton-minima in bosonic fractional quantum Hall states
2023, Physica Scripta