Physical systems with high ground state degeneracy, such as electrons in large magnetic fields [1, 2] and geometrically frustrated spins [3], provide a rich playground for exploring emergent many-body phenomena. Quantum simulations with cold atoms offer new prospects for exploring complex phases arising from frustration and interactions [4-7] through the direct engineering of these ingredients in a well-controlled environment [8, 9]. Advances in band structure engineering, through the use of sophisticated lattice potentials made from interfering lasers, have allowed for explorations of kagome [10] and Lieb [11] lattice structures that support high-degeneracy excited energy bands. The use of internal states as synthetic dimensions [12] offers even greater flexibility in creating nontrivial band structures [13-17]. Here, using synthetic lattices based on laser-coupled atomic momentum states, we perform the first exploration of high-degeneracy ground bands in a cold atom system. By combining nearest- and next-nearest-neighbour tunnellings, we form an effective zigzag lattice that naturally supports kinetic frustration and nearly-flat quartic energy bands. In a quartic band structure with time-reversal symmetry (TRS) broken by a synthetic magnetic flux, the quench dynamics of our atoms reveal hallmark signatures of spin-momentum locking. Under preserved TRS, we demonstrate the extreme sensitivity of a nearly-flat ground band to added disorder. Furthermore, we show that the ground state localisation properties are strongly modified by an added flux, relating to a flux-dependent mobility edge due to multi-range tunnelling. Our work constitutes the first quantum simulation study on the interplay of topology and disorder [18], and opens the door to studying emergent phenomena driven by frustrated kinetics and atomic interactions
Physical systems with high ground state degeneracy, such as electrons in large magnetic fields [1, 2] and geometrically frustrated spins [3], provide a rich playground for exploring emergent many-body phenomena. Quantum simulations with cold atoms offer new prospects for exploring complex phases arising from frustration and interactions [4-7] through the direct engineering of these ingredients in a well-controlled environment [8, 9]. Advances in band structure engineering, through the use of sophisticated lattice potentials made from interfering lasers, have allowed for explorations of kagome [10] and Lieb [11] lattice structures that support high-degeneracy excited energy bands. The use of internal states as synthetic dimensions [12] offers even greater flexibility in creating nontrivial band structures [13-17]. Here, using synthetic lattices based on laser-coupled atomic momentum states, we perform the first exploration of high-degeneracy ground bands in a cold atom system. By combining nearest- and next-nearest-neighbour tunnellings, we form an effective zigzag lattice that naturally supports kinetic frustration and nearly-flat quartic energy bands. In a quartic band structure with time-reversal symmetry (TRS) broken by a synthetic magnetic flux, the quench dynamics of our atoms reveal hallmark signatures of spin-momentum locking. Under preserved TRS, we demonstrate the extreme sensitivity of a nearly-flat ground band to added disorder. Furthermore, we show that the ground state localisation properties are strongly modified by an added flux, relating to a flux-dependent mobility edge due to multi-range tunnelling. Our work constitutes the first quantum simulation study on the interplay of topology and disorder [18], and opens the door to studying emergent phenomena driven by frustrated kinetics and atomic interactions
"The many weird properties of quantum mechanics at the very small scale have led to surprising and useful discoveries that manifest at the macroscopic level, like the quantum Hall effect and high temperature superconductivity. Yet trying to understand the origin of correlated behavior from interacting quantum systems via classical simulation requires an infeasible level of computing power. Instead, we can use an easily tunable, clean quantum system as a quantum simulation of a more unwieldy system, building the same model to study the same physics, but in a more controlled environment. Our field of cold neutral atoms in optical lattices has seen success over many years as a platform for quantum simulation of various lattice models from condensed matter physics. The recent (2015) implementation of lattices not in position, but in a synthetic dimension by coupling individual quantum states with lasers has led to a more bottom-up approach to engineering lattice models. In this thesis, we present our ""momentum-space lattice"" technique in which we use individual laser frequencies to couple the momentum states of a rubidium-87 Bose-Einstein condensate, in order to create lattices with site-by-site and link-by-link precision. This technique is simple to implement experimentally, requiring just two additional common optical components (acousto-optic modulators) compared to a real-space lattice, yet is incredibly versatile. Using momentum-space lattices, we have studied the physics of artificial magnetic fields, disorder and pseudodisorder-induced localization, and atomic interactions across eight works described in this thesis. More interesting are the not-so-well-known effects that arise in the interplay among these three components of topology, disorder, and interactions, and we have made headway towards studying physics in this regime. To be more specific, in our studies we have generated an artificial magnetic field for neutral atoms, and directly observed the resulting chiral currents in both a square ladder and zigzag lattice geometry. We have further monitored the quantum walk behavior of atoms under disordered and pseudodisordered lattices, observing a transition to localization under a quasiperiodic potential. We have been able to introduce a tunable energy dependence to this localization transition (single-particle mobility edge) in two ways: with the addition of more tunneling pathways, and by modifying the form of the potential. Finally, we have studied the effects of nonlinear inter-atomic interactions in the momentum-space lattice, observing self-trapping in a double well system as well as on a full lattice, showing a skewed current-phase relationship in an analog to Josephson junction arrays, and investigating an interaction-induced shift in localization behavior under pseudodisorder. In constructing the momentum-space lattice apparatus, Eric, Bryce, and I have created a promising new platform for Hamiltonian engineering. The studies described here not only show off the capabilities of the technique, but also realize new models, reveal new physics, and provide a new perspective complementary to both real-space lattice techniques and real materials. We have observed topological edge states more directly than previous works and engineered precise lattice parameter variations unavailable to other techniques, and yet the best is still to come. With our ongoing experimental upgrades comes access to the regime of strong inter-particle interactions, which promises more challenging yet more rewarding experiments."
Flat bands in condensed matter systems can host emergent states of matter, from insulating states in twisted bilayer graphene to fractionalized excitations in frustrated magnets and quantum Hall materials. A key phenomenon in certain flat-band systems is Aharonov-Bohm caging, where particles become localized due to destructive interference caused by gauge fields. Here we report on the experimental realization of highly tunable flat-band models populated by strongly interacting Rydberg atoms. By employing synthetic dimensions, we engineer a flat-band rhombic lattice with twisted boundaries and explore the control of Aharonov-Bohm caging during non-equilibrium dynamics through a tunable gauge field. Microscopic measurements of Rydberg pairs reveal the interaction-driven breakdown of Aharonov-Bohm caging in the limit of strong dipolar interactions, where lattice bands mix. In the limit of weak interactions, where caging persists, we observe effective magnetism arising from the interaction-driven mixing of degenerate flat-band states. These observations offer insights into emergent phenomena in synthetic quantum materials and expand our understanding of quantum many-body physics in engineered lattice systems.
Complex quantum many-body systems are ubiquitous in nature, yet their behaviour often remains very challenging to predict with analytical or numerical calculations.In this thesis a different approach is presented, using ultracold fermionic 40 K atoms in a lattice with a flexible geometry, formed by interfering laser beams.This system constitutes a precisely tunable, yet very accessible complex system, which can be used to probe -or "quantum simulate" -phenomena predicted for condensed-matter systems.We demonstrate, theoretically and experimentally, how a periodically modulated system can be described by an effective Hamiltonian on longer time-scales.This approach based on Floquet theory applies even when driving the system far from equilibrium.Using oscillating magnetic field gradients, we create an effectively spin-dependent lattice, where the tunnelling rate for different internal atomic states can be freely tuned.The flexible geometry of the lattice is used to create a honeycomb lattice and study the linear band crossings -known as Dirac cones -characteristic of its band structure.We distort the lattice and use momentum-resolved interband transitions probe the deformation and movement of the Dirac cones and their eventual disappearance when moving towards a square or dimerised geometry.We show that circular modulation of a honeycomb lattice induces imaginary next-nearest neighbour tunnelling, which breaks time-reversal symmetry.In addition, a tunable site-offset is used to break inversion symmetry.We thereby realize a model proposed by F.D.M. Haldane in 1988 and study the predicted topological transition from a trivial to a Chern-insulating regime, characterised by a closing band gap.Furthermore, effects of the Berry curvature are observed in both regimes, using transverse drifts of a driven atomic cloud.Using a mixture of two internal states with tunable scattering between them, we study the Hubbard model on a variety of geometries and with a range of observables.The crossover between metal, Mott-insulator and band insulator in a two-and threedimensional Honeycomb lattice is probed by observing the double occupancy, compressibility and excitation spectrum.The addition of a site-offset leads to the appearance of a competing type of density order -an explicit charge-density wave -which is directly probed and leads to new types of excitations.At lower temperatures, magnetic correlations appear.By freezing out the dynamics of the system and adiabatically merging neighbouring sites,the probability to find singlet or triplet states on different patterns of bonds is directly probed.Using this method we study the dependence of magnetic correlations on geometry in seven different lattice structures, and crossovers between them.We find that lower connectivity quantum effects enhance short-range correlations and compare our results to sophisticated numerical approximations.Ramping the lattice from one geometry to another allows for probing the quantum dynamics of re-distributing magnetic correlations, from the sudden to the adiabatic regime.v
Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.
Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of experiments, a more general, dynamical control over site-energy and off-diagonal tunnelling disorder has been lacking. The use of atomic quantum states as synthetic dimensions has introduced the spectroscopic, site-resolved control necessary to engineer more tailored realisations of disorder. Here, we present explorations of dynamical and tunneling disorder in an atomic system by controlling laser-driven dynamics of atomic population in a momentum-space lattice. By applying static tunnelling phase disorder to a one-dimensional lattice, we observe ballistic quantum spreading. When the applied disorder fluctuates on time scales comparable to intersite tunnelling, we instead observe diffusive atomic transport, signalling a crossover from quantum to classical expansion dynamics. We compare these observations to the case of static site-energy disorder, where we directly observe quantum localisation.Cold atom quantum simulation has had challenges in realising the tailored, dynamic types of disorder relevant to real materials. Here, the authors use synthetic momentum-space lattices to engineer spatially and dynamically controlled disorder to observe ballistic, diffusive, and arrested atomic transport.
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.