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arXiv:1703.00430 · Physical review. B./Physical review. B

Realizing and adiabatically preparing bosonic integer and fractional quantum Hall states in optical lattices

Yin-Chen He, Fabian Grusdt, Adam M. Kaufman, Markus Greiner, Ashvin Vishwanath

Published Nov 3, 2017• 85 citations
arXivHTMLPDF

Abstract

We study the ground states of two-dimensional lattice bosons in an artificial gauge field. Using state-of-the-art density matrix renormalization group (DMRG) simulations we obtain the zero-temperature phase diagram for hard-core bosons at densities ${n}_{b}$ with flux ${n}_{\ensuremath{\phi}}$ per unit cell, which determines a filling $\ensuremath{\nu}={n}_{b}/{n}_{\ensuremath{\phi}}$. We find the bosonic Jain sequence $[\ensuremath{\nu}=p/(p+1)]$ states, in particular, a bosonic integer quantum Hall phase at $\ensuremath{\nu}=2$, are fairly robust in the hard-core boson limit, In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation, beginning from independent chains, and ramping up interchain couplings. Using time-dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Our proposal only utilizes existing experimental capabilities.

DOI
10.1103/physrevb.96.201103

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We study the ground states of two-dimensional lattice bosons in an artificial gauge field. Using state-of-the-art density matrix renormalization group (DMRG) simulations we obtain the zero-temperature phase diagram for hard-core bosons at densities nb{n}_{b}nb​ with flux n\ensuremathϕ{n}_{\ensuremath{\phi}}n\ensuremathϕ​ per unit cell, which determines a filling \ensuremathν=nb/n\ensuremathϕ\ensuremath{\nu}={n}_{b}/{n}_{\ensuremath{\phi}}\ensuremathν=nb​/n\ensuremathϕ​. We find the bosonic Jain sequence [\ensuremathν=p/(p+1)][\ensuremath{\nu}=p/(p+1)][\ensuremathν=p/(p+1)] states, in particular, a bosonic integer quantum Hall phase at \ensuremathν=2\ensuremath{\nu}=2\ensuremathν=2, are fairly robust in the hard-core boson limit, In addition to identifying Hamiltonians whose ground states realize these phases, we discuss their preparation, beginning from independent chains, and ramping up interchain couplings. Using time-dependent DMRG simulations, these are shown to reliably produce states close to the ground state for experimentally relevant system sizes. Our proposal only utilizes existing experimental capabilities.
We study the many-body ground states of two-component hard-core bosons in topological triangular-lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, a two-component bosonic integer quantum Hall (BIQH) effect emerges with the associated K=(0110)\mathbf{K}=(\begin{array}{cc}0& 1\\ 1& 0\end{array})K=(01​10​) matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized topological Chern number matrix $\mathbf{C}={\mathbf{K}}^{\ensuremath{-}1}$, and (iii) two counterpropagating edge branches. Moreover, with increasing nearest-neighbor repulsions, the ground state undergoes a first-order transition from a BIQH liquid to a commensurate solid order.
We study interacting two-component hard-core bosons on a square lattice for which, in the presence of staggered magnetic flux, its ground state is a bosonic integer quantum Hall (BIQH) state. By using a coupled-wire bosonization approach, we show analytically that this model exhibits a BIQH state at total charge half filling associated with a symmetry-protected topological phase under U(1)\text{U}(1)U(1) charge conservation. These theoretical expectations are verified, using the infinite density matrix renormalization group method, by providing numerical evidence for (i) a quantized Hall conductance ${\ensuremath{\sigma}}_{xy}=\ifmmode\pm\else\textpm\fi{}2$, and (ii) two counterpropagating gapless edge modes. Our model is a bosonic cousin of the fermionic Haldane model and serves as an additional case of analogy between bosonic and fermionic quantum Hall states.
We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an xyxyxy-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with xyxyxy-ferromagnetic order if the ramp crosses to regimes where the ground state is a zzz ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies.
Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\ensuremath{\nu}=1$ and find strong indications that at $\ensuremath{\alpha}=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\ensuremath{\nu}=1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.
The integer quantum Hall state occurs when Landau levels are fully occupied by fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of hard-core bosons in a multiband lattice model hosting topological flat bands with a high Chern number. The previously proposed $\ensuremath{\nu}=1/3$ fractional Chern insulating state inherited from the high Chern number C=2C=2C=2 of the lowest topological flat band is revisited by the infinite density matrix renormalization group algorithm. In particular, we numerically identify a bosonic 1/21/21/2-Laughlin-like fractional Chern insulating state at the integer fillings. We show two lower topological flat bands jointly generate an effective C=1C=1C=1 Chern band with half filling. Furthermore, we find a strictly particle-hole-like symmetry between the $\ensuremath{\nu}$ and $3\ensuremath{-}\ensuremath{\nu}$ filling in our model. These findings extend our understanding of quantum Hall states and offer a route to realize fractional states in the system with multibands and high Chern numbers.
We propose a scheme to realize the fractional quantum Hall system with atoms confined in a two-dimensional array of coupled cavities. Our scheme is based on simple optical manipulation of atomic internal states and intercavity hopping of virtually excited photons. It is shown that, as well as the fractional quantum Hall system, any system of hard-core bosons on a lattice in the presence of an arbitrary Abelian vector potential can be simulated solely by controlling the phases of constantly applied lasers. The scheme, for the first time, exploits the core advantage of coupled cavity simulations, namely, the individual addressability of the components, and also brings the gauge potential into such simulations as well as the simple optical creation of particles.