Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0808.0439

Collective Excitations of Rotating Dipolar Fermi Gases in the Fractional Quantum Hall Regime

Szu-Cheng Cheng

Published Aug 4, 2008• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0808.0439

Related papers

Roton instabilities and correlated Wigner crystals of rotating dipolar fermions in the fractional quantum Hall regime

Shih-Da Jheng, Tsin-Fu Jiang, Szu-Cheng Cheng

We point out that the Wigner crystal (WC) state of rotating dipolar fermions in the lowest Landau level is strongly correlated. From intra-Landau-level excitations of the fractional quantum Hall effect (FQHE) liquid, we find that the roton minimum of the excitation spectrum at $\ensuremath{\nu}=1/7$ becomes negative, indicating an absence of the FQHE state, which is supposed to be the ground state of the system. Therefore, we show that the Hartree-Fock theory of the WC does not predict the correct ground-state energy in the lowest Landau level. There exists a strong correlation effect on the Wigner crystallization of rotating dipolar gases.

arXiv:1305.3494•Physical Review A•Nov 4, 2013•5 citations

Excitation Spectrum and Stability from a Filled Landau Level in Rotating Dipolar Fermi Gases

Szu-Cheng Cheng

We apply the equation-of-motion method to study the collective excitation spectrum from a filled Landau level in rotating dipolar Fermi gases. The predicted excitation spectrum of rotating dipolar Fermi gases can exhibit a roton-minimum character. This roton character is tunable by varying the dipole interaction strength and confining potential. An increase of the dipole interaction strength makes the roton minimum becoming zero, and the system becomes unstable. We also obtain a condition for the dynamical stability of rotating dipolar Fermi gases.

arXiv:0809.4972•Sep 29, 2008•0 citations

Collective excitation spectra of dipolar bosonic fractional quantum Hall states

Moumita Indra, Pankaj Kumar Mishra

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.

arXiv:2506.05085•Jun 5, 2025•0 citations

Fractional Quantum Hall States in Ultracold Rapidly Rotating Dipolar Fermi Gases

M. A. Baranov, Klaus Osterloh, Maciej Lewenstein

We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultracold two-dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction nu = 1/3 is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow us to realize these very interesting highly correlated states in future experiments.

arXiv:cond-mat/0404329•Physical Review Letters•Feb 24, 2005•131 citations

Correlation effect on the roton minimum of the rotating dipolar Fermi gas

Jing-Nuo Wu, Y. L. Chiang, Hsin-Chien Huang +1 more

[[abstract]]The collective-excitation spectrum from a filled Landau level in a rotating dipolar Fermi gas is investigated through the equation of motion method. The predicted excitation spectrum exhibits a roton structure which is affected by the strength of dipolar interactions and trapping potential. The correlation effect on the roton minimum is observed by varying the dipolar interaction strength. An increase of the dipolar interaction strength leads to a deeper roton minimum. The roton minimum can even become zero, where the system exhibits instability, as the dipolar strength approaches a critical value. As the dynamical stability of the system is studied through the roton structure, we find that this zero-value roton minimum is a precursor of the occurrence of a bubble crystal.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 30, 2011•1 citation

Analytic Wavefunctions for Collective Modes in Fractional Quantum Hall Fluids

Bo Yang

We show model wavefunctions for neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair excitations" works for the magneto-roton modes of single-component Abelian and non-Abeliean FQH states, as well as neutral fermion mode for the Moore-Read (MR) state. The analytic wavefunctions enable computations in the thermodynamic limit previous inaccessible to numerics, and the long wavelength limit of the neutral energy gap of the magneto-roton modes can be interpreted as fusion of charges in two-dimensional plasma picture, extending the plasma analogy to neutral excitations. A lattice diagrammatic method of representing these many-body wavefunctions and FQH elementary excitations is also presented.

arXiv:1303.6299•Mar 25, 2013•1 citation
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.
We point out that the Wigner crystal (WC) state of rotating dipolar fermions in the lowest Landau level is strongly correlated. From intra-Landau-level excitations of the fractional quantum Hall effect (FQHE) liquid, we find that the roton minimum of the excitation spectrum at $\ensuremath{\nu}=1/7$ becomes negative, indicating an absence of the FQHE state, which is supposed to be the ground state of the system. Therefore, we show that the Hartree-Fock theory of the WC does not predict the correct ground-state energy in the lowest Landau level. There exists a strong correlation effect on the Wigner crystallization of rotating dipolar gases.
We apply the equation-of-motion method to study the collective excitation spectrum from a filled Landau level in rotating dipolar Fermi gases. The predicted excitation spectrum of rotating dipolar Fermi gases can exhibit a roton-minimum character. This roton character is tunable by varying the dipole interaction strength and confining potential. An increase of the dipole interaction strength makes the roton minimum becoming zero, and the system becomes unstable. We also obtain a condition for the dynamical stability of rotating dipolar Fermi gases.
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.
We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultracold two-dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction nu = 1/3 is well described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow us to realize these very interesting highly correlated states in future experiments.
[[abstract]]The collective-excitation spectrum from a filled Landau level in a rotating dipolar Fermi gas is investigated through the equation of motion method. The predicted excitation spectrum exhibits a roton structure which is affected by the strength of dipolar interactions and trapping potential. The correlation effect on the roton minimum is observed by varying the dipolar interaction strength. An increase of the dipolar interaction strength leads to a deeper roton minimum. The roton minimum can even become zero, where the system exhibits instability, as the dipolar strength approaches a critical value. As the dynamical stability of the system is studied through the roton structure, we find that this zero-value roton minimum is a precursor of the occurrence of a bubble crystal.
We show model wavefunctions for neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair excitations" works for the magneto-roton modes of single-component Abelian and non-Abeliean FQH states, as well as neutral fermion mode for the Moore-Read (MR) state. The analytic wavefunctions enable computations in the thermodynamic limit previous inaccessible to numerics, and the long wavelength limit of the neutral energy gap of the magneto-roton modes can be interpreted as fusion of charges in two-dimensional plasma picture, extending the plasma analogy to neutral excitations. A lattice diagrammatic method of representing these many-body wavefunctions and FQH elementary excitations is also presented.