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AIP conference proceedings

Composite Fermion Hierarchical States in Rotating Dipolar Fermi Gases

Piotr Sitko

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The systems of rotating ultracold gases of fermions is studied in the limit of the presence of quantum Hall states. The presence of composite fermion hierarchical states is investigated (other than Laughlin or Jain states). The ultra‐short ranged interaction and the dipole interaction between fermions is assumed. The results are similar to the ones found in the case of Coulomb interacting fermions (electrons).

DOI
10.1063/1.2730070

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The systems of rotating ultracold gases of fermions is studied in the limit of the presence of quantum Hall states. The presence of composite fermion hierarchical states is investigated (other than Laughlin or Jain states). The ultra‐short ranged interaction and the dipole interaction between fermions is assumed. The results are similar to the ones found in the case of Coulomb interacting fermions (electrons).
We study strongly correlated ground and excited states of rotating quasi-2D Fermi gases constituted of a small number of dipole-dipole interacting particles with dipole moments polarized perpendicular to the plane of motion. As the number of atoms grows, the system enters an intermediate regime, where ground states are subject to a competition between distinct bulk-edge configurations. This effect obscures their description in terms of composite fermions and leads to the appearance of novel quasihole ground states. In the presence of dipolar interactions, the principal Laughlin state at filling nu=1/3 exhibits a substantial energy gap for neutral (total angular momentum conserving) excitations and is well-described as an incompressible Fermi liquid. Instead, at lower fillings, the ground state structure favors crystalline order.
We study the quantum Hall states that appear in the dilute limit of rotating ultracold fermionic gases when a single hyperfine species is present. We show that the ppp-wave scattering translates into a pure hard-core interaction in the lowest Landau level. The Laughlin wave function is then the exact ground state at filling fraction $\ensuremath{\nu}=1∕3$. We give estimates of some of the gaps of the incompressible liquids for $\ensuremath{\nu}=p∕(2p\ifmmode\pm\else\textpm\fi{}1)$. We estimate the mass of the composite fermions at $\ensuremath{\nu}=1∕2$. The width of the quantum Hall plateaus is discussed by considering the equation of state of the 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.
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 investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning the direction of the dipole moments with respect to the zzz axis, the dipole-dipole interaction becomes anisotropic in the xxx-yyy plane. For a soft confining potential we find that, as we tilt the angle of the dipole moments, the system evolves from a $\ensuremath{\nu}=1/3$ Laughlin state with dipoles being polarized along the zzz axis to a series of ground states characterized by distinct mean total angular momentum, and finally to an anisotropic integer quantum Hall state. During the transition from the fractional regime to the integer regime, we find that the density profile of the system exhibits crystal-like structures. We map out the ground states as a function of the tilt angle and the confining potential, revealing the competition of the isotropic confining potential and both the isotropic and anisotropic components of the dipole-dipole interaction.
Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for electrons, can be applied to interacting bosons. Numerical evidence supporting the formation of composite fermions, each being the bound state of a boson and one flux quantum, is shown for filling fractions of the type nu=p/(p+1), both by spectral analysis and by direct comparison with trial wave functions. The rapidly rotating system of two-dimensional bosons thus constitutes an interesting example of "statistical transmutation," with bosons behaving like composite fermions. We also describe the difference between the electronic and the bosonic cases when p approaches infinity. Residual interactions between composite fermions are attractive in this limit, resulting in a paired composite-fermion state described by the Moore-Read wave function.