Topological states in two-dimensional optical lattices (original) (raw)
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Topological insulators and metals in atomic optical lattices
Physical Review A, 2009
We propose the realization of topological quantum states with cold atoms trapped in an optical lattice. We discuss an experimental setup that generates a two-dimensional hexagonal lattice in the presence of a light-induced periodic vector potential, which represents a realization of the Haldane model with cold atoms. We determine theoretically the conditions necessary for observing the topological states and show that two of the key conditions are: 1) the realization of sharp boundaries and 2) the minimization of any smoothly varying component of the confining potential. We argue that, unlike their condensed matter counterparts, cold atom topological quantum states can be i) "seen", by mapping out the characteristic chiral edge states, and ii) controlled, by controlling the periodic vector potential and the properties of the confining potential. arXiv:0901.3921v1 [cond-mat.mes-hall]
Topological insulator of ultra cold atoms in bichromatic optical lattices
We investigate the effect of a strong bichromatic deformation to the mathbbZ2\mathbb{Z}_{2}mathbbZ2 topological insulator in ultracold atomic system proposed by B. B\'eri and N. R. Cooper, Phys.Rev.Lett. 107, 145301 (2011). Large insulating gap of this system allows for examination of strong perturbations. We conclude that the mathbbZ2\mathbb{Z}_{2}mathbbZ2 topological character of the system is robust against a large global perturbation which breaks the inversion symmetry but preserves the time-reversal symmetry.
arXiv (Cornell University), 2023
We investigate fermionic 6 Li F = 1/2 atoms in a 2D spin-dependent optical lattice potential (SDOLP) generated by intersecting laser beams with a superposition of polarizations. The effective interaction of a Li atom with the electromagnetic field contains a scalar and vector (called as fictitious magnetic field, B fic) contribution. We calculate the band structure of Li atoms in the SDOLP as a function of the laser intensity and an external magnetic field Bext = Bextẑ. We also calculate the Chern numbers of the SDOLP and show that depending on Bext, the system is an ordinary insulator, an Abeliean topological insulator (TI), or a non-Abelian TI. Introducing a blue-detuned laser potential, VBD(y) = VBD,0(y)Θ(|y| − Ly/2), results in edges for the SDOL. We calculate the resulting edge states (some of which are topological) and study their density, current density, spincurrent density and correlate the edge states with the Chern numbers.
Science advances, 2017
Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfaces act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial...
Interaction effects and quantum phase transitions in topological insulators
We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T=0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.
Direct imaging of topological edge states in cold-atom systems
Proceedings of the National Academy of Sciences, 2013
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes -guaranteed by the existence of non-trivial topological invariants -have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas, and imaging its time-evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.
Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
Physical Review Letters, 2010
Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.
Topological transitions of interacting bosons in one-dimensional bichromatic optical lattices
Physical Review A, 2014
Ultra-cold atoms in 1D bi-chromatic optical lattices constitute a surprisingly simple system for the study of topological insulators. We show that bosons in 1D bi-chromatic lattices present as a general feature the existence at equal fractional filling of Mott-insulator phases with different topological character. These different phases are a direct consequence of the bosonic and interacting nature of the particles and the topological nature of the Bloch bands. We demonstrate that the associated hidden topological transitions may occur both as a function of the superlattice strength and due to inter-site interactions. We discuss in addition the topological character of incommensurate density wave phases in quasi-periodic superlattices.
Physical Review Letters, 2015
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator", has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large offsite interactions on top of a small onsite interaction. Here we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in A and B sublattices makes the onsite interaction Pauli-forbidden, while a sizeable inter-site interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt the density functional theory for cold-atoms, here extended to accommodate non-collinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.