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arXiv:1104.0100 · Physical Review A

Quantum Hall effects in fast-rotating Fermi gases with anisotropic dipolar interaction

Ruizhi Qiu, Su-Peng Kou, Zi-Xiang Hu, Xin Wan, S. Yi

Published Jun 28, 2011• 30 citations
arXivHTMLPDF

Abstract

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 $z$ axis, the dipole-dipole interaction becomes anisotropic in the $x$-$y$ 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 $z$ 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.

DOI
10.1103/physreva.83.063633

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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 \ensuremathν=1/3\ensuremath{\nu}=1/3\ensuremathν=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.
For the fast rotating quasi-two-dimensional dipolar fermions in the quantum Hall regime, the rotational symmetry in the two-body interaction breaks when the dipole moment has an in-plane component that can be tuned by an external field. Assuming that all the dipoles are polarized in the same direction, we perform the numerical diagonalization for finite size systems on a torus. We find that while $\ensuremath{\nu}=1/3$ Laughlin state is stable in the lowest Landau level (LLL), it is not stable in the first Landau level (1LL); instead, the most stable Laughlin state in the 1LL is the $\ensuremath{\nu}=2+1/5$ Laughlin state. These FQH states are robust against moderate introduction of anisotropy, but large anisotropy induces a transition into a compressible phase in which all the particles are attracted and form a bound state. We show that such phase transitions can be detected by the intrinsic geometrical properties of the ground states alone. The anisotropy and the phase transition are systematically studied with the generalized pseudopotentials and characterized by the intrinsic metric, the wave function overlap, and the nematic order parameter. We also propose simple model Hamiltonians for this physical system in the LLL and 1LL, respectively.
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 analyze the ground state of a system of dipolar bosons moving in the XYXYXY plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle $\ensuremath{\alpha}$ with respect to the ZZZ axis. We use the path-integral ground-state method to analyze the static properties of the system as both $\ensuremath{\alpha}$ and the density nnn vary over a wide range where the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them. We find that, in addition to a superfluid gas and a solid phase, the system reaches a stripe phase at large tilting angles that is entirely induced by the anisotropic character of the interaction. We also show that the quantum phase transition from the gas to the stripe phase is of second order and report approximate values for the critical exponents.
Recent experimental advances in creating stable dipolar systems, including polar molecules with large electric dipole moments, have led to vigorous theoretical activities. Here we discuss our work on homogeneous 2D dipolar bosons with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane, i.e. for non-zero tilt angles. Using Bogoliubov-de Gennes equations, we obtain T=0 excitation spectrum of the dipolar Bose gas, and explore instabilities at varying tilt angle, density and dipolar coupling. We map out a phase diagram a function of tilt angle, dipole strength and density. We find the development of maxon-roton behavior leading to roton instabilities at large densities for small tilt angles, and at low densities for large tilt angles. The behavior is anisotropic in k-space; accordingly the roton instabilities occur in the k y direction, suggestive of inhomogeneity and stripe phase, with density mode becoming soft in the y direction. Our results compare favorably with existing Quantum Monte Carlo calculations for non-zero tilt angles.
In this thesis we study the effects of the dipole-dipole interaction on the physics of ultracold quantum gases, both bosonic and fermionic, within the theoretical framework provided by the mean-field regime. This kind of interaction takes place in ultracold atomic gases (for instance 52Cr or 164Dy) due to their atomic magnetic dipole moment, and in ultracold molecular gases due to the magnetic or electric dipole moment. \n \nIn the case of quantum gases of bosonic atoms, or Bose-Einstein condensates, the dipole-dipole interaction can be studied within mean-field approximation using the Gross-Pitaevskii equation, which now contains a new non-linear term due to the dipole-dipole interaction. We investigate, on the one hand dipolar condensates confined in harmonic traps, and on the other dipolar condensates confined in toroidal traps. In the harmonic geometry, our focus is on the study of the ground state and the quantized vortex state, where the density profile is characterized as well as some properties leading to the process of vortex formation, such as the critical frequency and the energy barrier that has to be overcome to bring the vortex from the surface to the centre of the gas. We finish the study of dipolar condensates in harmonic traps by dynamically simulating the precession frequency of an off-center vortex in a non-rotating condensate. \n \nIn the toroidal geometry the dipolar effects are strongly magnified when the polarization axis of the dipoles is perpendicular to the trap symmetry axis. In this case, the anisotropic structure of the density can be understood as the response of the system to the double-well effective potential along the ring. We have studied the dynamics of this system when the initial number of atoms in the left and right wells is imbalanced, predicting Josephson and self-trapping oscillations depending on the initial condition. This has led us to name this new system as Self-induced Josephson Junction. We have studied in detail the self-trapping regime and we have seen that the particle flux inversion is closely related to the crossing of vortices across the Josephson junctions. This result opens the door to establishing a more direct connection between the phase-slip regime, widely addressed in superfluid helium, and the self-trapping regime of condensates. \n \nIn the case of quantum gases of fermionic dipolar particles, we have studied how the radial quadrupole mode allows one to distinguish between hydrodynamic and collisionless regimes. We have analytically calculated the frequency of this mode in the mean-field approximation, generalizing the results from the Thomas-Fermi approximation for trapped ideal Fermi gases. On the one hand, we observe that the frequency in the hydrodynamic regime is smaller than in non-dipolar Fermi gases, while in the collisionless regime the frequency is larger or smaller than that corresponding to the non-interacting system depending on the geometry of the harmonic trap. On the other hand, we predict that reducing the trap deformation (aspect ratio) an observable jump in the frequency of the radial quadrupole mode would take place, which would correspond to the transition between the collisionless and hydrodynamic regimes, for instance when the gas undergoes the transition to the superfluid state.
We examine the two-dimensional spin-orbit-coupled bosons in the presence of an anisotropic dipolar interaction in square lattices. The spin-orbit coupling leads to finite-momentum superfluid and supersolid states, while the nearest-neighbour interaction induces crystalline characteristics in the quantum phases of soft-core bosons. We employ site-decoupled Gutzwiller ansatz and mean-field decoupling theory to obtain the phase diagrams and investigate the effects of the tilt of magnetic dipoles with respect to the polarization axis. Our study reveals the intriguing quantum phase transition of checkerboard finite-momentum phase-twisted and phase-stripe states into their stripe counterparts at a magic tilt angle, at which the off-site interaction along one of the directions becomes zero. At smaller tilt angles, the checkerboard charge-density-wave phase intervened by two compressible finite-momentum phases, and at strong spin-orbit coupling strengths, the phase-twisted supersolid and superfluid phases emerge. At larger tilt angles, a transition between the striped order of phase-twisted states and phase-stripe states occurs. The inclusion of off-site inter-component correlation leads to density-correlated phases, lattice-induced supersolid, and ferromagnetic quantum phases. Our study highlights novel finite-momentum crystal phases of spin-orbit-coupled dipolar bosons and provides a parameter space to observe them in quantum gas experiments.