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arXiv:1802.07988 · Physical Review A

Bosonic quantum Hall states in single-layer two-dimensional optical lattices

Rukmani Bai, Soumik Bandyopadhyay, Sukla Pal, Kuldeep Suthar, D. Angom

Published Aug 7, 2018• 28 citations
arXivHTMLPDF

Abstract

Quantum Hall (QH) states of two-dimensional (2D) single-layer optical lattices are examined using the Bose-Hubbard model (BHM) in the presence of an artificial gauge field. We study the QH states of both the homogeneous and inhomogeneous systems. For the homogeneous case, we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes ranging from $2\ifmmode\times\else\texttimes\fi{}2$ to $5\ifmmode\times\else\texttimes\fi{}5$. We then consider the inhomogeneous case, which is relevant to experimental realization. In this case, we use CGMF and exact diagonalization (ED). The ED studies are using lattice sizes ranging from $3\ifmmode\times\else\texttimes\fi{}3$ to $4\ifmmode\times\else\texttimes\fi{}12$. Our results show that the geometries of the QH states are sensitive to the magnetic flux $\ensuremath{\alpha}$ and cluster sizes. For homogeneous systems, among various combinations of $1/5\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1/2$ and filling factor $\ensuremath{\nu}$, only the QH state of $\ensuremath{\alpha}=1/4$ with $\ensuremath{\nu}=1/2,\phantom{\rule{0.16em}{0ex}}1,\phantom{\rule{0.16em}{0ex}}3/2$, and 2 occur as ground states. For other combinations, the competing superfluid (SF) state is the ground state and QH state is metastable. For BHM with envelope potential, all the QH states observed in homogeneous systems exist for box potentials, but none exist for the harmonic potential. The QH states also persist for very shallow Gaussian envelope potential. As a possible experimental signature, we study the two-point correlations of the QH and SF states.

DOI
10.1103/physreva.98.023606

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Quantum Hall (QH) states of two-dimensional (2D) single-layer optical lattices are examined using the Bose-Hubbard model (BHM) in the presence of an artificial gauge field. We study the QH states of both the homogeneous and inhomogeneous systems. For the homogeneous case, we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes ranging from 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 to 5\ifmmode×\else\texttimes\fi55\ifmmode\times\else\texttimes\fi{}55\ifmmode×\else\texttimes\fi5. We then consider the inhomogeneous case, which is relevant to experimental realization. In this case, we use CGMF and exact diagonalization (ED). The ED studies are using lattice sizes ranging from 3\ifmmode×\else\texttimes\fi33\ifmmode\times\else\texttimes\fi{}33\ifmmode×\else\texttimes\fi3 to 4\ifmmode×\else\texttimes\fi124\ifmmode\times\else\texttimes\fi{}124\ifmmode×\else\texttimes\fi12. Our results show that the geometries of the QH states are sensitive to the magnetic flux \ensuremathα\ensuremath{\alpha}\ensuremathα and cluster sizes. For homogeneous systems, among various combinations of 1/5\ensuremath≤\ensuremathα\ensuremath≤1/21/5\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1/21/5\ensuremath≤\ensuremathα\ensuremath≤1/2 and filling factor \ensuremathν\ensuremath{\nu}\ensuremathν, only the QH state of \ensuremathα=1/4\ensuremath{\alpha}=1/4\ensuremathα=1/4 with \ensuremathν=1/2,1,3/2\ensuremath{\nu}=1/2,\phantom{\rule{0.16em}{0ex}}1,\phantom{\rule{0.16em}{0ex}}3/2\ensuremathν=1/2,1,3/2, and 2 occur as ground states. For other combinations, the competing superfluid (SF) state is the ground state and QH state is metastable. For BHM with envelope potential, all the QH states observed in homogeneous systems exist for box potentials, but none exist for the harmonic potential. The QH states also persist for very shallow Gaussian envelope potential. As a possible experimental signature, we study the two-point correlations of the QH and SF states.
In this research, we study the bosonic fractional quantum Hall (FQH) states in a system of ultracold bosons in a two-dimensional optical lattice in the presence of a synthetic magnetic field, described by the bosonic Harper–Hofstadter Hamiltonian. We use the cluster Gutzwiller mean-field and exact diagonalization techniques in our work. We obtain incompressible states as ground states at various filling factors similar to those of the FQH states. We focus in particular on the ν = 1/2 FQH state, and it is characterized by the two-point correlation function and the many-body Chern number. We further investigate the effect of dipolar interaction on the ν = 1/2 FQH state. We find that the dipolar interaction stabilizes the FQH state against the competing superfluid state.
We investigate quantum phases of the Bose-Bose mixtures in a two dimensional (2D) square lattice under artificial magnetic flux. Our analysis employs the inhomogeneous Dynamical Gutzwiller Mean-Field Theory (DGMFT) to investigate ground state within the two-component Bose-Hubbard model. The results based on various inter-component interactions and magnetic flux. In the case of weak inter-component interaction (wherein the inter-component interactions remain subordinate to intra-component interactions, symbolically expressed as |Uab|≤U), we observe a multitude of captivating quantum phases within the Bose-Bose mixtures. These include the emergence of the jagged density-wave supersolid(SS) phase, the latticed-like density-wave SS phase, and counterflow superfluid (CFSF) phase. Notably, the introduction of artificial magnetic flux expands the range of existence for CFSF phase. In the case of strong inter-component interaction(wherein the inter-component interactions surpass intra-component interactions, symbolically expressed as Uab>U), we delve deeper into the classification of the spatially separated phase, aptly termed the phase separated supersolid (P-SS).
In this paper, we investigate the quantum phases of two-component bosons in a non-Hermitian optical lattice system featuring a nonreciprocal hopping phase factor. Our analysis focuses on the Bose–Hubbard model in a two-dimensional (2D) square lattice, utilizing the inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT) to examine the ground state. The impact on quantum phases of the inter component interaction varies in the weak-interaction (the inter-component interactions are smaller than intra-component interactions, i.e., [Formula: see text]) and in the strong-interaction (the inter-component interactions are bigger than intra-component interactions, i.e., [Formula: see text]) regime. In the weak regime, we observe a diverse range of quantum phases, including vortex-like liquid, MI islands (the Mott insulator (MI) islands periodically distributed in the superfluid (SF) background) and SF islands (the SF islands periodically distributed in the MI background), and the inter-component counterflow superfluid (CFSF) phases. In the strong regime, we observe phase separation of the two-component bosons.
We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. [Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.
We study incompressible ground states of bosons in a two-dimensional rotating square optical lattice. The system can be described by the Bose-Hubbard model in an effective uniform magnetic field present due to the lattice rotation. To study ground states of the system, we map it to a frustrated spin model, followed by Schwinger boson mean-field theory and projective symmetry group analysis. Using symmetry analysis, we identify bosonic fractional quantum Hall states, predicted for bosonic atoms in rotating optical lattices, with possible stable gapped spin-liquid states within the Schwinger boson formalism. In particular, our results indicate that previously obtained fractional quantum Hall states induced by the lattice potential, and with no counterpart in the continuum [M\"oller and Cooper, Phys. Rev. Lett. 103, 105303 (2009)], correspond to ``$\ensuremath{\pi}$-flux'' spin-liquid states of the frustrated spin model.
Abstract Ground-state phases of the ultracold bosons in 2D optical lattices subject to artificial magnetic flux are studied by the inhomogeneous Gutzwiller variational method. Results show that the density of a vortex increases linearly with the magnetic flux per plaquette. For a smaller magnetic flux, no supersolid (SS) states are present. The superfluid (SF) states are vortex liquids of either particle-type or hole-type, depending on whether the average filling is greater or less than the integer number. For a larger magnetic flux, regular density-wave states, which also exhibit superfluidity of either particle-type or hole-type, appear at the boundary between the Mott insulator and the SF. Moreover, the uniform SF phases differ to the conventional SF by carrying convection super-current and coreless vorticity. The convection super-current or vorticity in the SS phases assemble in pairs or stripes, as well as checkerboards, according to the flux strength per unit cell.