Atom arrays with sub-wavelength lattice constant can exhibit fascinating optical properties. For example, the combination of $V$-type level structure and magnetic fields can yield topological band structures, making the neutral atomic excitations behave like charged particles in a magnetic field. Up to now, much of our understanding of these systems (and arrays in general) focuses on the single-excitation regime. Here, we go beyond the single-excitation level to show that such systems can give rise to few-particle Laughlin-like states. In particular, we consider small honeycomb ``flakes,'' where the harmful divergences near the light cone can be smeared out by finite-size effects. By choosing an appropriate value of magnetic field we thereby obtain an energy spectrum and eigenstates resembling those of Landau levels. The native hard-core nature of atomic excitations then gives rise to multi-excitation Laughlin-like states. This phenomenon occurs not only in samples of tens of sites, but also in a minimal nanoring system of only six sites. Next, considering two-particle Laughlin-like states, we show that they can be driven by uniform light, and that correlations of the output light contain identifying fingerprints of these states. We believe that these results are a step towards new paradigms of engineering and understanding strongly-correlated many-body states in atom-light interfaces.
Atom arrays with sub-wavelength lattice constant can exhibit fascinating optical properties. For example, the combination of V-type level structure and magnetic fields can yield topological band structures, making the neutral atomic excitations behave like charged particles in a magnetic field. Up to now, much of our understanding of these systems (and arrays in general) focuses on the single-excitation regime. Here, we go beyond the single-excitation level to show that such systems can give rise to few-particle Laughlin-like states. In particular, we consider small honeycomb ``flakes,'' where the harmful divergences near the light cone can be smeared out by finite-size effects. By choosing an appropriate value of magnetic field we thereby obtain an energy spectrum and eigenstates resembling those of Landau levels. The native hard-core nature of atomic excitations then gives rise to multi-excitation Laughlin-like states. This phenomenon occurs not only in samples of tens of sites, but also in a minimal nanoring system of only six sites. Next, considering two-particle Laughlin-like states, we show that they can be driven by uniform light, and that correlations of the output light contain identifying fingerprints of these states. We believe that these results are a step towards new paradigms of engineering and understanding strongly-correlated many-body states in atom-light interfaces.
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 optical properties of subwavelength arrays of atoms or other quantum emitters have attracted significant interest recently. For example, the strong constructive or destructive interference of emitted light enables arrays to function as nearly perfect mirrors, support topological edge states, and allow for exponentially better quantum memories. In these proposals, the assumed atomic structure was simple, consisting of a unique electronic ground state. Within linear optics, the system is then equivalent to a periodic array of classical dielectric particles, whose periodicity supports the emergence of guided modes. However, it has not been known whether such phenomena persist in the presence of hyperfine structure, as exhibited by most quantum emitters. Here, we show that waveguiding can arise from rich atomic entanglement as a quantum many-body effect and elucidate the necessary conditions. Our work represents a significant step forward in understanding collective effects in arrays of atoms with realistic electronic structure.
Mathematical tools and concepts initially developed to study topological properties of geometrical objects have allowed for better understanding and interpretation of a number of phenomena in condensed matter physics, from the quantum Hall effect to topological insulators. It would be interesting to realize analogs of these phenomena with light scattered by cold atoms because atomic systems are simpler and allow for better control than complex solid-state compounds in which electrons interact with each other and with phonons, and where disorder is omnipresent. At the same time, mastering topological photonics of cold atoms may lead to interesting applications in quantum information science, for example. We study the opening of topological band gaps in two-dimensional honeycomb lattices of two-level atoms [1], the impact of disorder on their properties [2], as well as the constructive role that disorder can play by inducing a topologically nontrivial phase known as “topological Anderson insulator” [2,3]. Modifying the structure of the atomic lattice in an appropriate way allows for constructing a synthetic spin degree of freedom and thus for exploring the physics of spinful particles, such as the quantum spin Hall effect, for example. The analogy between topological phenomena in solid-state physics and in optics of cold atoms is not complete: atomic systems exhibit a number of new features due to the vector nature of light and to the differences in the impact of disorder on their properties.1. P. Wulles and S.E. Skipetrov, Topological photonic band gaps in honeycomb atomic arrays, arXiv:2308.134232. S.E. Skipetrov and P. Wulles, Topological transitions and Anderson localization of light in disordered atomic arrays, Phys. Rev. A 105, 043514 (2022)3. S.E. Skipetrov and P. Wulles, Photonic topological Anderson insulator in a two-dimensional atomic lattice, Comptes Rendus. Physique 24(S3), 39–54 (2023)
The present thesis studies a variety of cold atomic systems in artificial gauge fields. In the first part we focus on fractional quantum Hall effects, asking whether interesting topological states can be realized with cold atoms. We start by making a close connection to solid-state systems and first consider fermionic atoms with dipolar interactions. Assuming the system to be in the Laughlin state, we evaluate the energy gap in the thermodynamic limit as a measure for the robustness of the state. We show that it can be increased by additionally applying a non-Abelian gauge field squeezing the Landau levels. We then switch to bosonic systems with repulsive contact interactions. Artificial magnetic fields for cold bosons have extensively been discussed before in the context of rotating Bose gases. We follow a different approach where the gauge field is due to an atom-laser coupling. Thus, transitions between different dressed states have to be included. They are shown to break the cylindrical symmetry of the system. Modifying the Laughlin state and the Moore-Read state accordingly, we determine the parameter regimes where they are good representations for the ground state of the system obtained via exact diagonalization. One of the most interesting feature of fractional quantum Hall states is the anyonic behavior of their excitations. We therefore also study quasiholes in the Laughlin state and the modified Laughlin state. They are shown to posses anyonic properties, which become manifest even in small systems. Moreover, the dynamics of a single quasihole causes visible traces in the density of the system which allow to clearly distinguish the Laughlin regime from less correlated phases. In the latter, a sequence of collapses and revivals of the quasihole can be observed, which is absent in the Laughlin regime. Extending our study to bosonic systems with a pesudospin-1/2 degree of freedom, we discuss the formation of strongly correlated spin singlets. Strikingly, at filling v=4/3, the system is described by a state with non-Abelian excitations, which is constructed as the zero-energy ground state of repulsive three-body contact interactions. Systems with internal degrees of freedom also allow for implementing artificial spin-orbit coupling. It is shown to give rise to a variety of incompressible states. In the second part of the thesis, we concentrate on condensed system. Bose-Einstein condensates with spin-orbit coupling are shown to have a degeneracy on the mean-field level, which is lifted by quantum and thermal fluctuations. The system becomes experimentally feasible in three dimensions, where the condensate depletion remains finite, and thus allow for an experimental observation of this order-by-disorder mechanism. Finally, we study the influence of Abelian and non-Abelian gauge fields on the quantum phase transitions of bosons in a square optical lattice. Re-entrant superfluid phases and superfluids at finite momenta are interesting properties featured by such systems.
When quantum emitters couple indistinguishably to light, they can synchronize into a collective light matter system with radiative properties profoundly different from those of independent particles. To date, the resulting collective effects have largely been confined to point like or homogeneous ensembles. Here, we open access to a qualitatively new collective regime by realizing geometrically ordered, spatially extended atom arrays with subwavelength spacing. This establishes a fundamentally new platform in which collective emission is no longer confined to a single Dicke mode but instead emerges from an ordered network of photon mediated interactions. We find that 2D atom arrays undergo strong super and subradiant emission. Despite subwavelength spacing, we achieve site resolved imaging and directly observe the buildup of spatial correlations, demonstrating the transformation of cooperative decay into a strongly correlated many-body process. We observe extensive scaling of superradiance, uncover superradiant revivals, and reveal the ferromagnetic nature of superradiance and the antiferromagnetic nature of subradiance. Our results realize a novel programmable platform for exploring and utilizing dissipative many-body quantum physics, opening new possibilities for photon capture, storage, and atom photon entanglement.
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.