Spin-flip excitation and negative energy dispersion in rotating Bose atoms.*

The fractional quantum Hall effect (FQHE) can potentially be studied in rotating Bose-Einstein condensate (BEC) [1]. A two-dimensional (2D) system of rapidly rotating BEC contained in XY-plane creates a fictitious magnetic field along Z-axis, that is perpendicular to the 2D-plane (similar to the magnetic field in a 2D electron system), which forms Landau levels (LL). Then there is a possibility of the FQHE in rapidly rotating system of dilute Bose atoms. I have studied collective spin-flip excitations (SFE) for the first three filling fractions of second and third series (2/(2p+1),3/(3p+1); p is an integer) of Jain’s composite fermion (CF) sequences [2]. I have considered short-ranged Poisson-Teller (PT) interactions between the Bose atoms as well as long range Coulomb interactions to compare the nature of the spectra with FQHE of electrons. Although very short-ranged interaction gives zero energy, as the average separation between particles will be large compared to the width of interaction, the PT interaction potential gives the freedom to control the interaction range. The nature of spectra does not depend on the range of interaction. The interesting fact is that I found anomalous negative dispersion in the excited spectra whereas there is a positive dispersion curve observed only for the Jain’s first series, i.e. for the fractions having form 1/(p+1) [3]. For the higher Jain series SFE shows negative curvature and roton minima at lower momenta; whereas for higher momenta it supports the spin-wave excitation similar as conventional ferromagnets. This phenomenon is produced by mixing of two types of spin-reversed modes: spin-wave modes with no change in LL index and spin-flip modes with decreasing LL index. This combination of two modes produces a spin-flip excitonic state of CF particle-hole pairs.

References:

[1] C. C. Chang, N. Regnault, T. Jolicoeur, J. K. Jain, Phys. Rev. A 72 (2005) 013611.

[2] N. R. Cooper, N.K. Wilkin, Phys. Rev. B 60 (1999) R16279.

[3] M. Indra, D. Majumder, Solid State Communications, 306, art. no. 113796 (2020).