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arXiv:2506.05085

Collective excitation spectra of dipolar bosonic fractional quantum Hall states

Moumita Indra, Pankaj Kumar Mishra

Published Jun 5, 2025• 0 citations
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Abstract

We numerically investigate the collective excitation of spin-conserving and spin-reversed configuration of rotating diluted ultra-cold dipolar Bose gas. Rotating trapped Bose gas produces a fictitious magnetic field perpendicular to the trapping harmonic potential, which exhibits strongly correlated fractional quantum Hall states. We consider the long-range dipole-dipole interaction and compute the low lying excitations spectrum for the three fractions of the first Jain series $ν= 1/2, 1/4, 1/6$. We find that for both the spin-conserving and spin-reversed excitation the gap between the fundamental mode and the higher excitation mode increases upon increase in the filling fraction. The fundamental modes and the next higher-energy mode of excitation spectra for each of the three fractions show the presence of double roton for spin-conserving configuration only. Finally we complement our observation by calculating the spectral weight for the fundamental mode of excitation spectra which show the momenta at which the spectral weight exhibits the maxima shifts towards the lower momenta for both the excitations. Our observation for the spectral weight could be related with the inelastic Raman scattering which may be useful for the future experimental study to detect the excitation in ultracold system.

DOI
10.48550/arxiv.2506.05085

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We numerically investigate the collective excitation of spin-conserving and spin-reversed configuration of rotating diluted ultra-cold dipolar Bose gas. Rotating trapped Bose gas produces a fictitious magnetic field perpendicular to the trapping harmonic potential, which exhibits strongly correlated fractional quantum Hall states. We consider the long-range dipole-dipole interaction and compute the low lying excitations spectrum for the three fractions of the first Jain series ν=1/2,1/4,1/6ν= 1/2, 1/4, 1/6ν=1/2,1/4,1/6. We find that for both the spin-conserving and spin-reversed excitation the gap between the fundamental mode and the higher excitation mode increases upon increase in the filling fraction. The fundamental modes and the next higher-energy mode of excitation spectra for each of the three fractions show the presence of double roton for spin-conserving configuration only. Finally we complement our observation by calculating the spectral weight for the fundamental mode of excitation spectra which show the momenta at which the spectral weight exhibits the maxima shifts towards the lower momenta for both the excitations. Our observation for the spectral weight could be related with the inelastic Raman scattering which may be useful for the future experimental study to detect the excitation in ultracold system.
Abstract We have studied the collective spin-conserving collective excitation spectra in rotating diluted ultra-cold Bose atoms. Double roton-minima have been observed in the fractional quantum Hall (FQH) states for the two filling fractions (ν) of the first series of Jain's composite fermion sequences. The obtained roton-minima for ν = 1/4 are at the wave-vectors 1.26 and 2.38 and the roton-minima for ν = 1/6 have been shifted to 1.08 and 2.06. Such shift of roton-minima is attributed due to strong correlation between the particles in bosonic FQH-system. Moreover, the number of roton minima observed depends upon number of attached fluxes as well as the ranges of interaction between the particles.
We have studied collective spin density excitations 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 spectras 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.
We investigated the excitation spectra for the rotating Bose system in the fractional quantum Hall effect regime considering short-ranged Po¨schl-Teller and long-ranged Coulomb type interaction. We found the anomalous negative dispersion in the excited spectra for Jain's second and third series, whereas conventional spin-wave positive dispersion is observed in the case of Jain's first series. The higher order Jain series display negative curvature with roton minima at lower momenta and exhibit spin-wave excitation similar to conventional ferromagnets at higher momenta. This anomalous spin-flip excitonic state of particle-hole pairs arises due to the merging of two types of spin-reversed modes i.e. spin-wave with no change in Landau level (LL) index and spin-flip with decreasing LL index.
We apply the magneto-roton theory of the fractional quantum Hall effect to study the collective excitation spectrum of rotating dipolar Fermi gases. The predicted spectrum has a finite energy gap in the long wavelength limit and a roton minimum at finite wave vector. The roton minimum being deepened from filling factor 1/3 to filling factor 1/5 is a signature of incipient crystallization near filling factor 1/7. We also demonstrate that there are no low-lying single-particle excitations below the roton mode. The fractional-quantum-Hall fluid rotating dipolar fermions behaves as an incompressible superfluid at low temperature.
Collective modes capture the dynamical aspects of fractional quantum Hall (FQH) fluids. Depending on the active degrees of freedom, different types of collective modes can arise in a FQH state. In this work, we consider spinful FQH states in the lowest Landau level (LLL) along the Jain sequence of fillings ν=n/(2n±1)ν{=}n/(2n{\pm}1)ν=n/(2n±1) and compute the Coulomb dispersion of their spin-flip and spin-conserving collective modes in the spherical geometry. We use the LLL-projected density-wave and composite fermion (CF) exciton states as trial wave functions for these modes. To evaluate the dispersion of density-wave states, we derive the commutation algebra of spinful LLL-projected density operators on the sphere, which enables us to extract the gap of the density-wave excitations from the numerically computed density-density correlation function, i.e., the static structure factor, of the FQH ground state. We find that the CF excitons provide an accurate description of the collective modes at all wavelengths, while the density-wave states fail to do so. Specifically, the spin-flip density wave reliably captures the spin-flip collective mode only for the Laughlin and Halperin states, and that too only in the long-wavelength limit. Interestingly, for spin-singlet primary Jain states, the spin-conserving density mode is inaccurate even in the long-wavelength regime. We show that this discrepancy stems from the presence of an additional high-energy spin-conserving parton mode, similar to that found in fully polarized secondary Jain states at ν=n/(4n±1)ν{=}n/(4n{\pm}1)ν=n/(4n±1). We propose an ansatz for this parton mode and compute its Coulomb dispersion in the singlet state at ν=2/5ν{=}2/5ν=2/5. The predicted parton mode can be observed in circularly polarized inelastic light scattering experiments.
The long-term goal of our study is to perform a simulation on a rapidly rotating gas of ultracold bosonic atoms. When the rotation frequency is close to the harmonic trap frequency, the trapping force is compensated by the centrifugal force and only the Coriolis force remains, analogous to the Lorentz force. The quantum Hall effect regime is reached when the number of vortices is larger than the number of atoms. In this work, we demonstrate a variety of excitations of the fractional quantum Hall states of composite fermions and ultracold two-dimensional rapidly rotating bosonic atoms. Second, we can also check directly whether there is a relationship between these two phenomena by calculating the energy of N = 8 bosons in the ground state of the harmonic oscillator and a few-boson elementary excitations for the Bose–Laughlin state at the half filling factor.