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arXiv:1310.3709 · Physical Review B

Quantum Hall phases of two-component bosons

Tobias Graß, David Raventós, Maciej Lewenstein, Bruno Juliá-Díaz

Published Jan 13, 2014• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.89.045114

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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 \ensuremathν=2\ensuremath{\nu}=2\ensuremathν=2 to the Halperin phase at filling factor \ensuremathν=2/3\ensuremath{\nu}=2/3\ensuremathν=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 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 $\ensuremath{\nu}=k/3+k/3$ (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.
We investigate the feasibility of many candidate quantum Hall states for two-component bosons in the lowest Landau level. We identify interactions for which spin-singlet incompressible states occur at filling factors $\ensuremath{\nu}=2/3$, 4/54/54/5, and 4/34/34/3, and partially spin-polarized states at filling factors 3/43/43/4 and 3/23/23/2, where ``spin'' serves as a generic label for the two components. We study ground states, excitations, edge states, and entanglement spectrum for systems with up to 16 bosons and construct explicit trial wave functions to clarify the underlying physics. The composite fermion theory very accurately describes the ground states as well as excitations at $\ensuremath{\nu}=2/3$, 4/54/54/5, and 3/43/43/4, although it is less satisfactory for the $\ensuremath{\nu}=3/2$ state. For $\ensuremath{\nu}=4/3$ a ``non-Abelian spin-singlet'' state, which is the exact ground state of a three-body contact interaction, has been proposed to occur even for a two-body contact interaction; our trial wave functions are very accurate for the excitations of the three-body interaction, but they do not describe the excitations of the two-body interaction very well. Instead, we find that the $\ensuremath{\nu}=4/3$ state is more likely to be a spin-singlet state of reverse-flux-attached composite fermions at filling ${\ensuremath{\nu}}^{*}=4$. We also consider incompressible states at integral filling factors $\ensuremath{\nu}=1$ and 2. The incompressible state at $\ensuremath{\nu}=1$ is shown to be well described by the parton-based Jain spin-singlet wave function, and the incompressible state at $\ensuremath{\nu}=2$ as the spin-singlet state of reverse-flux-attached composite fermions at ${\ensuremath{\nu}}^{*}=2$, which provides an example of the bosonic integer topological phase.
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 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 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 the quantum Hall phases that appear in the fast-rotation limit for Bose-Einstein condensates of spinless bosonic atoms. We use exact diagonalization in a spherical geometry to obtain low-lying states of a small number of bosons as a function of the angular momentum. This allows us to understand or guess the physics at a given filling fraction $\ensuremath{\nu}$, the ratio of the number of bosons to the number of vortices. This is also the filling factor of the lowest Landau level. In addition to the well-known Bose-Laughlin state at $\ensuremath{\nu}=1∕2$, we give evidence for the Jain principal sequence of incompressible states at $\ensuremath{\nu}=p∕(p\ifmmode\pm\else\textpm\fi{}1)$ for a few values of ppp. There is a collective mode in these states whose phenomenology is in agreement with standard arguments coming, e.g., from the composite-fermion picture. At filling factor 1, the potential Fermi sea of composite fermions is replaced by a paired state, the Moore-Read state. This is most clearly seen from the half-flux nature of elementary excitations. We find that the hierarchy picture does not extend up to the point of transition towards a vortex lattice. While we cannot come to any definite conclusions, we investigate the clustered Read-Rezayi states and show evidence for incompressible states at the expected ratio of flux versus number of Bose particles.