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arXiv:cond-mat/0702266 · Physical Review Letters

Strongly Correlated States of Ultracold Rotating Dipolar Fermi Gases

Klaus Osterloh, N. Barberán, Maciej Lewenstein

Published Oct 17, 2007• 57 citations
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Abstract

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.

DOI
10.1103/physrevlett.99.160403

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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 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 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.
We study the competition between the Wigner crystal and the Laughlin liquid states in an ultracold quasi-two-dimensional rapidly rotating polarized fermionic dipolar gas, and find that the Wigner crystal has a lower energy below a critical filling factor. We examine the quantum crystal to liquid transition for different confinements in the third direction. Our analysis of the phonon spectra of the Wigner crystal taking into account the phonon-phonon interactions also shows the stability of the Wigner crystal for sufficiently low filling factors (nu < 1/7).
We study ultracold Rydberg-dressed Bose gases subject to artificial gauge fields in the fractional quantum Hall (FQH) regime. The characteristics of the Rydberg interaction gives rise to interesting many-body ground states different from standard FQH physics in the lowest Landau level (LLL). The non-local but rapidly decreasing interaction potential favors crystalline ground states for very dilute systems. While a simple Wigner crystal becomes energetically favorable compared to the Laughlin liquid for filling fractions ν<1/12\nu<1/12ν<1/12, a correlated crystal of composite particles emerges already for ν≤1/6\nu \leq 1/6ν≤1/6 with a large energy gap to the simple Wigner crystal. The presence of a new length scale, the Rydberg blockade radius aBa_BaB​, gives rise to a bubble crystal phase for ν≲1/4\nu\lesssim 1/4ν≲1/4 when the average particle distance becomes less than aBa_BaB​, which describes the region of saturated, almost constant interaction potential. For larger fillings indications for strongly correlated cluster liquids are found.
We show that dipolar interactions have dramatic effects on the ground states of rotating atomic Bose gases in the weak-interaction limit. With increasing dipolar interaction (relative to the net contact interaction), the mean field, or high filling factor, ground state undergoes a series of transitions between vortex lattices of different symmetries: triangular, square, "stripe," and "bubble" phases. We also study the effects of dipolar interactions on the quantum fluids at low filling factors. We show that the incompressible Laughlin state at filling factor nu = 1/2 is replaced by compressible stripe and bubble phases.