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arXiv:1703.05842 · Physical Review Letters

Realizing the Haldane Phase with Bosons in Optical Lattices

Junjun Xu, Qiang Gu, Erich J. Mueller

Published Feb 23, 2018• 23 citations
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Abstract

We analyze an experimentally realizable model of bosons in a zigzag optical lattice, showing that, by rapidly modulating the magnetic field, one can tune interaction parameters and realize an analog of the Haldane phase. We explain how quantum gas microscopy can be used to detect this phase's nonlocal string order and its topological edge states. We model the detection process. We also find that this model can display supersolid correlations, but argue that they only occur at parameter values which would be challenging to realize in an experiment.

DOI
10.1103/physrevlett.120.085301

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We analyze an experimentally realizable model of bosons in a zigzag optical lattice, showing that, by rapidly modulating the magnetic field, one can tune interaction parameters and realize an analog of the Haldane phase. We explain how quantum gas microscopy can be used to detect this phase's nonlocal string order and its topological edge states. We model the detection process. We also find that this model can display supersolid correlations, but argue that they only occur at parameter values which would be challenging to realize in an experiment.
We investigate the ground-state properties of a newly discovered phase of one-dimensional lattice bosons with extended interactions [E. G. Dalla Torre et al., Phys. Rev. Lett. 97, 260401 (2006)]. The new phase, termed the Haldane insulator in analogy with the gapped phase of spin-1 chains, is characterized by a nonlocal order parameter, which can only be written as an infinite string in terms of the bosonic densities. We show that the string order can nevertheless be probed with physical fields that couple locally, via the effect those fields have on the quantum phase transitions separating the exotic phase from the conventional Mott and density wave phases. Using a field theoretical analysis, we show that a perturbation that breaks lattice inversion symmetry gaps the critical point separating the Mott and Haldane phases and eliminates the sharp distinction between them. This is remarkable given that neither of these phases involves broken inversion symmetry. We also investigate the evolution of the phase diagram with the tunable coupling between parallel chains in an optical lattice setup. We find that interchain tunneling destroys the direct phase transition between the Mott and Haldane insulators by establishing an intermediate superfluid phase. On the other hand, coupling the chains only by weak repulsive interactions does not modify the structure of the phase diagram. The theoretical predictions are confirmed with numerical calculations using the density matrix renormalization group.
The interplay between antiferromagnetic interaction and hole motion is capable of inducing conducting Haldane phases with topological features described by a finite nonlocal string order parameter. Here we show that these states of matter are captured by the one-dimensional $t\text{\ensuremath{-}}{J}_{z}$ model, which can be experimentally realized with dressed Rydberg atoms trapped onto a one-dimensional optical lattice. In the sector with vanishing total magnetization, exact calculations associated with the bosonization technique allow us to predict that both metallic and superconducting topological Haldane states can be achieved. With the addition of an appropriate magnetic field, the system enters a domain-wall structure with finite total magnetization. In this regime, the conducting Haldane states are confined in domains separated by regions where a fully polarized Luttinger liquid occurs. A procedure to dynamically stabilize such topological phases starting from a confined Ising state is also described.
We propose an optical lattice setup to investigate spin chains and ladders. Electric and magnetic fields allow us to vary at will the coupling constants, producing a variety of quantum phases including the Haldane phase, critical phases, quantum dimers, etc. Numerical simulations are presented showing how ground states can be prepared adiabatically. We also propose ways to measure a number of observables, like energy gap, staggered magnetization, end-chain spins effects, spin correlations, and the string-order parameter.
A system of ultracold atoms in an optical lattice provides a powerful platform for quantum simulation. In our laboratory, we use a quantum gas microscope to tune lattice parameters not only in a global scale but also at the level of individual sites. This allows us to control and detect the quantum state of interacting many-body systems as well as to engineer a broad class of Hamiltonians with high fidelity. Leveraging this versatility, we can realize several types of strongly correlated bosonic systems, which present intriguing behaviors and implement novel phases of matter. Analyzing snapshots of the atomic distribution with single-site resolution, we measure correlations and entanglement within these systems to reveal their main features, including non-equilibrium dynamics and quantum phase transitions. In this thesis, I present the works performed by our team for four different types of systems. First of all, I briefly introduce the behavior of a 1D disordered system in the critical regime between the thermal and the many-body-localized phases. In particular, we discuss what happens when a disordered and a non-disordered region are coupled via a single site. We find evidence for accelerated transport of thermal inclusion into the localized region, which shows the existence of a quantum avalanche, i.e. thermalization via accelerated transport throughout the localized system. In the second part, we realize a fractional quantum Hall state using an artificial gauge field, by implementing an adiabatic preparation protocol. We identify a topological phase transition in our system and characterize several key physical features expected for a Laughlin state by measuring density correlations and Hall conductivity. The next topic of this thesis relates to quantum magnetism. Mapping nearest hopping in a tilted optical lattice to spin flips, we realize a finite one-dimensional chain of 1/2-spins with closed boundary conditions. We perform an in-depth investigation on behaviors shown across the quantum phase transition between paramagnetic and antiferromagnetic ground states, including the evolution of the magnetization and Néel order parameter. Also, we find evidence for quantum superposition at the many-body level as a result of geometric frustration. In the last chapter, I report the experimental realization of a novel dipolar Bose-Hubbard Hamiltonian, based on a strongly tilted lattice system. When the tilt becomes the dominant energy scale, the Hamiltonian is fragmented, and the system behaves in a way that conserves dipole moment. Starting from a 1D chain of unity filled sites, we generate individual dipolar and anti-dipolar excitations at desired pinpoints. We observe quantum walks of these dipolar quasi-particles as well as their scattering dynamics, which allows us to study this new type of Hamiltonian using a bottom-up approach.
The rapid development of artificial gauge fields in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can support quantum Hall states, the universal edge excitations that provide the most likely experimental probe of the topological order have not been obtained. We find that the edge excitations of an interacting boson lattice model are surprisingly sensitive to interedge hybridization and edge-bulk mixing for some confining potentials. With properly chosen potentials and fluxes, the edge spectrum is surprisingly clear even for small systems with strong lattice effects such as bandwidth. Various fractional quantum Hall phases for bosons can be obtained, and the phases $\ensuremath{\nu}=1/2$ and $\ensuremath{\nu}=2/3$ have the edge spectra predicted by the chiral Luttinger liquid theory.