We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize a majority of phases in the periodic table of topological insulators.
We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize a majority of phases in the periodic table of topological insulators.
Abstract. We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.
Topological matter is a popular topic in both condensed matter and cold-atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.
Owing to rapid recent progress, ultracold atomic lattice systems for simulating topological phases are now at a pivotal stage, evolving from established paradigms into increasingly versatile and programmable quantum simulators. In this review, we survey recent experimental advances across four major classes of platforms: optical lattices, including optical lattices with laser-assisted tunneling and optical Raman lattices; synthetic lattices in momentum or internal-state space; Floquet-engineered lattices; and optical tweezer arrays, all of which offer distinct capabilities for realizing and probing topological matter. For each class, we highlight representative experimental breakthroughs, the topological models that have been realized, and the advanced detection and characterization techniques employed, emphasizing how these complementary approaches collectively expand the frontier of quantum simulation. We also discuss emerging directions in strongly correlated and nonequilibrium topological phases, and conclude with an outlook on future prospects.
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
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 interatom 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 off-site interactions on top of a small on-site 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 on-site interaction Pauli forbidden, while a sizeable intersite 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 density functional theory for cold atoms, here extended to accommodate noncollinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.
A quantum simulator is a well-controlled quantum system which can be used to simulate another quantum system. Quantum degenerate gases confined by optical standing waves(optical lattices) have been considered to simulate condensed matter systems. We focus on two issues in this problem. The first one is the realization of interesting quantum phases by engineering Hamiltonians with the cold atoms toolbox. Secondly, the systems we studied are often intractable to analytical methods, which makes it a crucial issue to solve them with numerical methods. For the first issue we find several interesting phases can be studied with cold atoms in optical lattices. We show that a p-wave superfluid is stablized through a dissipation blockade mechanism. This mechanism also induces a new insulator formed by p-wave Feshbach molecules. We find that the anisotropic nature of interaction between polar molecules or dipolar atoms can be used to realize two charge density waves with different patterns and a supersolid phase which has not been found conclusively in the condensed matter system. Finally, we propose to realize a long sought spin liquid phase with hard-core bosons subject to a spin-dependent lattice and Raman induced hoppings. For the second issue we choose to numerically study these systems with the so-called tensor network algorithm which is a variational method based on the matrix(tensor) product states product states which are designed to approximate generic wave functions from their entanglement properties. In general the tensor network algorithm has advantages that it is applicable beyond one dimension, and can be used to study physical properties in the thermodynamic limit directly. We apply this method to map out the phase diagrams of the above systems. Furthermore, we show that it is capable of capturing the phase diagram of a frustrated magnetism model, the Heisenberg model on a checkerboard lattice. The great controllability and isolation from the environment of a cold atom system offer a playground to study interesting physics in strongly correlated systems. Several proposed control schemes in this thesis have been demonstrated in experiments. By providing detailed evidence from numerical simulations, this work addresses practical routes to novel quantum phases.