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arXiv:1407.7935 · Physical Review B

Existence of strong-pairing quantum Hall phase in bilayer cold-atom systems with dipolar interactions

Yuhui Zhang, Edward H. Rezayi, Kun Yang

Published Oct 2, 2014• 12 citations
arXivHTMLPDF

Abstract

We study bilayer fermionic cold-atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth- and first-order Haldane pseudopotentials, at a total Landau-level filling factor of 1/2. Our numerical results on the TCTP model indicate that a Haldane-Rezayi state describes the critical point between strong and weak $d$-wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.

DOI
10.1103/physrevb.90.165102

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We study bilayer fermionic cold-atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth- and first-order Haldane pseudopotentials, at a total Landau-level filling factor of 1/2. Our numerical results on the TCTP model indicate that a Haldane-Rezayi state describes the critical point between strong and weak ddd-wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.
We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C = ±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν t = 1 2 + 1 2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/lB is driven. The critical point at d c/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB < d c/lB , the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r = 0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/lB > d c/lB , a crossover from the d → d c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.
In the limit of very fast rotation atomic Bose-Einstein condensates may entirely reside in the lowest two-dimensional Landau level (LLL). For small enough filling factor of the LLL, one may have formation of fractional quantum Hall states. We investigate the case of bosons with dipolar interactions as may be realized with chromium-52 atoms. We show that at a filling factor equal to unity the ground state is a Moore-Read (or Pfaffian) paired state as is the case of bosons with purely sss-wave scattering interactions. This Pfaffian state is destabilized when the interaction in the sss-wave channel is small enough and the ground state is a stripe phase with unidimensional density modulation. For filling factor 1/3, we show that there is formation of a Fermi sea of ``composite fermions.'' These composites are made of one boson bound with three vortices. This phase has a wide range of stability and the effective mass of the fermions essentially depends only on the scattering amplitude in momentum channels larger or equal to 2. The formation of such a Fermi sea opens up a new possible route to detection of the quantum Hall correlations.
We study a rapidly rotating gas of unpolarized spin-1/2 ultracold fermions in the two-dimensional regime when all atoms reside in the lowest Landau level. Due to the presence of the spin degree of freedom both sss-wave and ppp-wave interactions are allowed at ultralow temperatures. We investigate the phase diagram of this system as a function of the filling factor in the lowest Landau level and in terms of the ratio between sss- and ppp-wave interaction strengths. We show that the presence of attractive interactions induces a wide regime of phase separation with formation of maximally compact droplets that are either fully polarized or composed of spin-singlets. In the regime with no phase separation, we give evidence for fractional quantum Hall states. Most notably, we find two distinct singlet states at the filling $\ensuremath{\nu}=2/3$ for different interactions. One of these states is accounted for by the composite fermion theory, while the other one is a paired state for which we identify two competing descriptions with different topological structures. This paired state may be an Abelian liquid of composite spin-singlet Bose molecules with Laughlin correlations. Alternatively, it may be a known non-Abelian paired state, indicated by good overlaps with the corresponding trial wave function. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for $\ensuremath{\nu}=1/2$ and the permanent state of Moore and Read for $\ensuremath{\nu}=1$. For purely repulsive interactions, we also find evidence for a gapped Halperin state at $\ensuremath{\nu}=2/5$.
In a bilayer system of fermionic dipoles, full control over the strength of the attractive interactions between two layers leads to the BCS-BEC crossover. Here, using the BCS mean-field theory, we study such a crossover in symmetric bilayers of ultracold dipolar fermions with their dipole moments perpendicular to layers. In particular, we investigate how the pairing between two layers and the many-body screening of interlayer interaction affect each other. We compare results for pairings obtained with three different approximations for the interlayer interactions, namely, bare dipole-dipole interaction, the random-phase approximation for screening obtained in the normal phase, and the self-consistent superfluid phase screening within the random-phase approximation. We find that at weak couplings the screening further suppresses the pairing, while at strong couplings, the screening is suppressed due to the pairing gap in the quasiparticle spectrum. Therefore a self-consistent treatment of both screening and pairing on equal footings is necessary for obtaining the correct picture of the phase diagram and order parameter at both small and large layer spacings and densities. We also notice that the signals of highly speculated density-wave instability in dipolar bilayers only appear in the normal phase screened interlayer interaction.
We study phase transitions in bilayer and trilayer bosonic quantum Hall systems. In the absence of interlayer tunneling and interaction, each layer is chosen to have filling factor ν=1/2ν=1/2ν=1/2 or 111 to realize the Laughlin state or the Moore-Read state. By tuning interlayer tunneling and/or interaction, multiple phases can be generated. In the absence of interlayer interaction, three phase transitions appear when interlayer tunneling becomes sufficiently strong: (1) from two decoupled ν=1/2ν=1/2ν=1/2 Laughlin states to the Moore-Read state in bilayer systems; (2) from one ν=1/2ν=1/2ν=1/2 Laughlin state plus one ν=1ν=1ν=1 Moore-Read state to the Read-Rezayi Z3\mathbb{Z}_{3}Z3​ state in bilayer systems; (3) from three decoupled ν=1/2ν=1/2ν=1/2 Laughlin states to the Read-Rezayi Z3\mathbb{Z}_{3}Z3​ state in trilayer systems. Numerical calculations suggest that these transitions are third-order ones. We propose non-Abelian Chern-Simons-Higgs theory to describe them. If both interlayer tunneling and interaction are present, one-component or multi-component composite fermion liquids and Jain states can be realized. This leads to intricate phase diagrams that host multiple phase transitions and possibly exotic critical points.
We study the properties of dipolar fermions trapped in one-dimensional bichromatic optical lattices and show the existence of fractional topological states in the presence of strong dipole-dipole interactions. We find some interesting connections between fractional topological states in one-dimensional superlattices and the fractional quantum Hall states: (i) the one-dimensional fractional topological states for systems at filling factor ν=1/p have p-fold degeneracy, (ii) the quasihole excitations fulfill the same counting rule as that of fractional quantum Hall states, and (iii) the total Chern number of p-fold degenerate states is a nonzero integer. The existence of crystalline order in our system is also consistent with the thin-torus limit of the fractional quantum Hall state on a torus. The possible experimental realization in cold atomic systems offers a new platform for the study of fractional topological phases in one-dimensional superlattice systems.