We introduce an all-optical approach to producing high-flux synthetic magnetic fields for neutral atoms or molecules by designing intrinsically time-periodic optical superlattices. A single laser source, modulated to generate two frequencies, suffices to create dynamic interference patterns which have topological Floquet energy bands. We propose a simple laser setup that realizes a tight-binding model with uniform flux and well-separated Chern bands. Our method relies only on the particles' scalar polarizability and far-detuned light.
We introduce an all-optical approach to producing high-flux synthetic magnetic fields for neutral atoms or molecules by designing intrinsically time-periodic optical superlattices. A single laser source, modulated to generate two frequencies, suffices to create dynamic interference patterns which have topological Floquet energy bands. We propose a simple laser setup that realizes a tight-binding model with uniform flux and well-separated Chern bands. Our method relies only on the particles' scalar polarizability and far-detuned light.
We propose a scheme to dynamically generate optical flux lattices with nontrivial band topology using amplitude-modulated Raman lasers and radio-frequency (rf) magnetic fields. By tuning the strength of Raman and rf fields, three distinct phases are realized at unit filling for a unit cell. Respectively, these three phases correspond to normal insulator, topological Chern insulator, and semimetal. Nearly nondispersive bands are found to appear in the topological phase, which promises opportunities for investigating strongly correlated quantum states within a simple cold-atom setup. The validity of our proposal is confirmed by comparing the Floquet quasienergies from the evolution operator with the spectrum of the effective Hamiltonian.
We theoretically explore the optical flux lattices produced for ultra-cold atoms subject to laser fields where both the atom-light coupling and the effective detuning are spatially periodic. We analyze the geometric vector potential and the magnetic flux it generates, as well as the accompanying geometric scalar potential. We show how to understand the gauge-dependent Aharonov-Bohm singularities in the vector potential, and calculate the continuous magnetic flux through the elementary cell in terms of these singularities. The analysis is illustrated with a square optical flux lattice. We conclude with an explicit laser configuration yielding such a lattice using a set of five properly chosen beams with two counterpropagating pairs (one along the x axes and the other y axes), together with a single beam along the z axis. We show that this lattice is not phase-stable, and identify the one phase-difference that affects the magnetic flux. Thus armed with realistic laser setup, we directly compute the Chern number of the lowest Bloch band to identify the region where the non- zero magnetic flux produces a topologically non-trivial band structure.
We present a general framework for engineering two-dimensional subwavelength topological optical lattices using spatially dependent atomic dark states in a Λ -type configuration of the atom-light coupling. By properly designing the spatial profiles of the laser fields inducing coupling between the atomic internal states, we show how to generate subwavelength Kronig-Penney-like geometric scalar potential accompanied by narrow and strong patches of the synthetic magnetic field localized in the same areas as the scalar potential. These sharply peaked magnetic fluxes are compensated by a smooth background magnetic field of opposite sign, resulting in zero net flux per unit cell while still enabling topologically nontrivial band structures. Specifically, for sufficiently narrow peaks, their influence is minimum, and the behavior of the system in a remaining smooth background magnetic field resembles the Landau problem, allowing for the formation of nearly flat energy bands with unit Chern numbers. Numerical analysis confirms the existence of ideal Chern bands and the robustness of the topological phases against nonadiabatic effects and losses. This makes the scheme well suited for simulating quantum Hall systems and fractional Chern insulators in ultracold atomic gases, offering a platform for exploring strongly correlated topological phases with high tunability.
The realization of fractional quantum Hall (FQH) states in cold atomic gases is a long-standing goal in quantum simulation. Established approaches, including rapidly rotating gases and tight-binding lattices, are often hampered by low interaction energies and small many-body energy gaps. While optical flux lattices (OFLs) can achieve higher effective magnetic flux densities, standard two-state configurations generate highly non-uniform fields, and extensions to multi-state systems introduce significant experimental complexity. Here, we present a new paradigm for engineering robust FQH phases in OFLs using only two internal atomic states. We show that the introduction of an additional scalar potential provides a generic mechanism for creating Chern bands that are simultaneously essentially flat and ideal.'' These desirable properties arise by tuning lattice parameters to certain N-flat manifolds (N=1,2,…), where the 1-flat manifold shares its origin with certainmagic-angle’’ conditions familiar from moiré materials. A central result is the design of a dark-state OFL whose adiabatic Hamiltonian is exactly of Aharonov-Casher (AC) form. This exact AC equivalence guarantees perfectly flat, exactly ideal Chern bands in the adiabatic limit. This method allows for precise tuning of band flatness and stabilizes both Abelian and non-Abelian FQH phases. Our scheme is compatible with existing experimental capabilities using vector polarizability, opening practical routes to exploring strongly correlated topological physics with cold atoms.
The realization of fractional quantum Hall (FQH) states in cold atomic gases is a long-standing goal in quantum simulation. Established approaches, including rapidly rotating gases and tight-binding lattices, are often hampered by low interaction energies and small many-body energy gaps. While optical flux lattices (OFLs) can achieve higher effective magnetic flux densities, standard two-state configurations generate highly non-uniform fields, and extensions to multi-state systems introduce significant experimental complexity. Here, we present a new paradigm for engineering robust FQH phases in OFLs using only two internal atomic states. We show that the introduction of an additional scalar potential provides a generic mechanism for creating Chern bands that are simultaneously essentially flat and "ideal". These desirable properties arise by tuning lattice parameters to certain N-flat manifolds (N=1,2,…), where the 1-flat manifold shares its origin with certain "magic-angle" conditions familiar from moiré materials. A central result is the design of a dark-state OFL whose adiabatic Hamiltonian is exactly of Aharonov-Casher (AC) form. This exact AC equivalence guarantees perfectly flat, exactly vortexable Chern bands in the adiabatic limit. This method allows for precise tuning of band flatness and stabilizes both Abelian and non-Abelian FQH phases. Our scheme is compatible with existing experimental capabilities using vector polarizability, opening practical routes to exploring strongly correlated topological physics with cold atoms.
The present chapter discusses methods by which topological Bloch bands can be prepared in cold-atom setups. Focusing on the case of Chern bands for two-dimensional systems, we describe how topological properties can be triggered by driving atomic gases, either by dressing internal levels with light or through time-periodic modulations. We illustrate these methods with concrete examples, and we discuss recent experiments where geometrical and topological band properties have been identified. Introduction Ultracold atoms constitute a promising physical platform for the preparation and exploration of novel states of matter [1, 2, 3]. In particular, the engineering of topological band structures with cold-atom systems, together with the capability of tuning interactions between the particles, opens an interesting route toward the realization of intriguing strongly correlated states with topological features, such as fractional topological insulators and quantum Hall liquids [4]. This chapter is dedicated to the preparation and the detection of topological band structures characterized by nonzero Chern numbers [5]. Such Chern bands , which constitute the building blocks for realizing (fractional) Chern insulators [6, 7], arise in two-dimensional (2D) systems presenting time-reversal-symmetry (TRS) breaking effects. For instance, nontrivial Chern bands naturally appear in the Harper-Hofstadter model [8], a lattice penetrated by a uniform flux, where they generalize the (nondispersive) Landau levels to the lattice framework. Additionally, Chern bands also appear in staggered flux configurations, such as in Haldane's honeycomb-lattice model [9] or in lattice systems combining Rashba spin-orbit coupling and Zeeman (exchange) fields. The atoms being charge neutral, “magnetic” fluxes cannot be simply produced by subjecting optical lattices to “real” magnetic fields. It is the aim of this chapter to review several schemes that have been recently implemented in laboratories with the goal of realizing synthetic magnetic fields leading to Chern bands for cold atoms. Our presentation is complementary to that of Chapter 15, as we focus on synthetic magnetic fields in lattice-based systems for which the flux density can be made very large (with magnetic length comparable to interparticle spacing). The chapter is structured as follows: Section 14.2 describes how the Chern number is related to physical observables defined in a lattice framework. In particular, it clarifies the link between recent Chern-number measurements performed in cold bosonic gases and the more conventional (electronic) quantum Hall effect.