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arXiv:1205.2169 · Physical Review A

Quantum Hall states in rapidly rotating two-component Bose gases

Shunsuke Furukawa, Masahito Ueda

Published Sep 17, 2012• 39 citations
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Abstract

We investigate strongly correlated phases of two-component (or pseudospin-$1/2$) Bose gases under rapid rotation through exact diagonalization on a torus geometry. In the case of pseudospin-independent contact interactions, we find the formation of gapped spin-singlet states at the filling factors $\ensuremath{\nu}=k/3+k/3$ ($k/3$ filling for each component) with integer $k$. We present numerical evidences that the gapped state with $k=2$ is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the ratio of the intercomponent-to-intracomponent interactions.

DOI
10.1103/physreva.86.031604

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We investigate strongly correlated phases of two-component (or pseudospin-1/21/21/2) Bose gases under rapid rotation through exact diagonalization on a torus geometry. In the case of pseudospin-independent contact interactions, we find the formation of gapped spin-singlet states at the filling factors \ensuremathν=k/3+k/3\ensuremath{\nu}=k/3+k/3\ensuremathν=k/3+k/3 (k/3k/3k/3 filling for each component) with integer kkk. We present numerical evidences that the gapped state with k=2k=2k=2 is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the ratio of the intercomponent-to-intracomponent interactions.
The recent production of synthetic magnetic fields acting on electroneutral particles, such as atoms or photons, has boosted interest in the quantum Hall physics of bosons. Adding pseudospin 1/2 to the bosons greatly enriches the scenario, as it allows them to form an interacting integer quantum Hall (IQH) phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor $\ensuremath{\nu}=2$ to the Halperin phase at filling factor $\ensuremath{\nu}=2/3$, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, such as non-Abelian spin singlet (NASS) states.
We study strongly correlated phases of a pseudo-spin-12\frac{1}{2}21​ Bose gas in an artificial gauge field using the exact diagonalization method. The atoms are confined in two dimensions and interact via a two-body contact potential. In Abelian gauge fields, pseudospin singlets are favored by pseudo-spin-independent interactions. We find a series of incompressible phases at fillings $\ensuremath{\nu}=2k/3$. By comparison with the non-Abelian spin singlet (NASS) states, constructed as zero-energy eigenstates of a (k+1)(k+1)(k+1)-body contact interaction, we classify the nontrivial topology of the states. An additional spin-orbit coupling is shown to switch between NASS-like states and spin-polarized phases from the Read-Rezayi series.
We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-12\frac{1}{2}21​) Bose gases in a high synthetic magnetic field in the space of the total filling factor and the ratio of the intercomponent coupling ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ to the intracomponent one g>0g>0g>0. Using exact diagonalization, we find that when the intercomponent coupling is attractive (${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}<0$), the product states of a pair of nearly uncorrelated quantum Hall states are remarkably robust and persist even when $|{g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}|$ is close to ggg. This contrasts with the case of an intercomponent repulsion, where a variety of spin-singlet quantum Hall states with high intercomponent entanglement emerge for ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}\ensuremath{\approx}g$. We interpret this marked dependence on the sign of ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ in light of pseudopotentials on a sphere, and also explain recent numerical results in two-component Bose gases in mutually antiparallel magnetic fields where a qualitatively opposite dependence on the sign of ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ is found. Our results thus unveil an intriguing connection between multicomponent quantum Hall systems and quantum spin Hall systems in minimal setups.
We study two-component (or pseudospin-1/2) Bose gases in a strong synthetic magnetic field. Using exact diagonalization, we show that a bosonic analog of an integer quantum Hall state with no intrinsic topological order appears at the total filling factor ν=1+1 when the strengths of intracomponent and intercomponent interactions are comparable with each other. This provides a prime example of a symmetry-protected topological phase in a controlled setting of quantum gases. The real-space entanglement spectrum of this state is found to be comprised of counterpropagating chiral modes consistent with the edge theory derived from an effective Chern-Simons theory.
We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-12\frac{1}{2}21​) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ to the intracomponent coupling g>0g>0g>0. This time-reversal-invariant setting represents a bosonic analog of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ up to as large as ggg. For ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}=\ensuremath{-}g$, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses in the thermodynamic limit.
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 $\ensuremath{\nu}=2/5$.