Dynamic optical superlattices with topological bands

Abstract

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 tightbinding model with uniform flux and well-separated Chern bands. Our method relies only on the particles' scalar polarizability and far detuned light.In the quest to establish ultracold atoms as versatile quantum simulators of condensed-matter physics [1], a key challenge is to develop minimally invasive methods of mimicking the orbital effects of a magnetic field [2]. In solid-state systems the interplay of strong magnetic fields with Coulomb interactions gives rise to strongly correlated phases, notably the fractional quantum Hall effect [3]. Atomic systems offer prospects for studying related phenomena of either bosons or fermions with tunable interactions, using new diagnostic tools.This goal has motivated intense theoretical and experimental effort at simulating, for neutral atoms, the Lorentz force experienced by a charged particle in a magnetic field [2]. Methods demonstrated to date have included subjecting quantum gases to rapid rotation [4,5] or imprinting geometric phases via spatially dependent couplings between internal states [6]. While the latter approach can in principle be extended to reach a high (net positive) flux density [7][8][9][10][11], only a select few atomic species offer a route to introducing the requisite optical couplings without significant spontaneous-emissioninduced heating or atom loss [9][10][11][12][13].A more broadly applicable means of producing highflux gauge fields is by modulating tight-binding optical lattices periodically in time [14][15][16][17][18][19][20][21][22]. This approach can be implemented with arbitrarily far-detuned light, in principle for any atomic or molecular species. Analogous methods [23][24][25] have even been applied in solidstate systems [26] and photonic crystals [27]. Common to all these systems is a breaking of time-reversal symmetry that endows the tunneling matrix elements with Peierls-like phases [14,15,18,28], mimicking the effect of a magnetic flux though each lattice plaquette.In optical lattices, Peierls phases have been engineered by large-amplitude off-resonant shaking [15,28]; or by direct modulation of on-site energies to produce a resonant photon-assisted hopping between orbitals of distinct lattice sites [29,30]. The latter method, requiring only small modulation amplitude, is less susceptible to (multiphoton) heating processes. To date, demonstrations of this method in periodic optical lattices lead to zero average flux. Recent success in producing large uniform flux by resonant photon-assisted hopping [30] is a technical feat, requiring not only multiple optical lattice lasers but also a strong magnetic field gradient [31].Here, we present an all-op...

Light-induced gauge fields for ultracold atoms

“…In the Abelian case, fractional quantum Hall (FQH) physics could be realized. To generate and stabilize such FQH liquids, it is crucial to develop schemes leading to topological flat bands [103,178,375], namely, dispersionless bands characterized by non-zero Chern numbers, which are well separated with respect to higher energy bands [see Fig. 26 for such a configuration offered by the Hofstadter model at flux Φ = 1 /5].…”

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

“…In the recent years, it has been shown that periodic perturbations can be used as a flexible experimental knob to realize new phases not accessible in equilibrium systems [34][35][36][37], synthetic (engineered) matter [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54], and quantum motors, which are similar to a quantum ratchet [55,56]. This new line of research, which can be termed 'Floquet engineering', has motivated a renaissance of interest in periodically driven systems.…”

Colloquium: Atomic quantum gases in periodically driven optical lattices

“…Moreover, extensions of the moving-secondary-lattice and the asymmetric shaking schemes have been proposed for the creation of Haldane-type hexagonal-lattice Chern insulators, nonabelian gauge fields (spin-orbit coupling) and topological (spin-Hall) insulators, as well as Weyl semi-metals (Baur et al, 2014;Bermudez et al, 2012;Dubček et al, 2014;Kennedy et al, 2013;Struck et al, 2012). Another approach for Floquet engineering of artificial magnetic fields or spin-orbit coupling is to construct driving protocols given by a sequence of pulses during which different external fields are present (Goldman and Dalibard, 2014).…”