Topological insulator of ultra cold atoms in bichromatic 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]
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.
Topological states in two-dimensional optical lattices
Physical Review A, 2010
We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial topological character and argue that such states can be realized within a large family of realistic optical lattice Hamiltonians with cold atoms. We focus our quantitative analysis on the properties of topological states with broken time-reversal symmetry specific to cold-atom settings. In particular, we analyze finite-size effects, multi-orbital phenomena that give rise to a variety of distinct topological states and transitions between them, the dependence on the trap geometry, and most importantly, the behavior of the edge states for different types of soft and hard boundaries. Furthermore, we demonstrate the possibility of experimentally detecting the topological states through light Bragg scattering of the edge and bulk states.
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.
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.
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.
Realistic time-reversal invariant topological insulators with neutral atoms
2010
We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near-field of an atom-chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states are localized. Our multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their remarkable versatility, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.
Optical NNN-insulators: topological obstructions in the atomistic susceptibility tensor
2021
A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational symmetry in both directions. Similarly, Wannier functions that respect time-reversal symmetry cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been enlightening and was recently extended to topological crystalline insulators which include obstructions tied to space group symmetries. In this article, we introduce a new class of two-dimensional topological materials known as opticalN -insulators that possess obstructions to constructing localized molecular polarizabilities. The opticalN -invariantN ∈ Z is the winding number of the atomistic susceptibility tensor χ and counts the number of singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the opti...
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.
Optical-lattice implementation scheme of a bosonic topological model with fermionic atoms
Physical Review A, 2014
We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one half. The scheme utilizes laser assisted and normal tunneling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the Néel antiferromagnetic ordering in the standard Fermi-Hubbard model in the Mott insulating regime.