Abstract We show that ultracold fermions in an artificial magnetic field open up a new window to the physics of the spinful fractional quantum Hall (FQH) effect. We numerically study the lowest energy states of strongly interacting few-fermion systems in rapidly rotating optical microtraps. We find that skyrmion-like ground states with locally ferromagnetic, long-range spin textures emerge. To realize such states experimentally, rotating microtraps with higher-order angular momentum components may be used to prepare fermionic particles in a lowest Landau level. We find parameter regimes in which skyrmion-like ground states should be accessible in current experiments and demonstrate an adiabatic pathway for their preparation in a rapidly rotating harmonic trap. The addition of long range interactions will lead to an even richer interplay between spin textures and FQH physics.
Abstract We show that ultracold fermions in an artificial magnetic field open up a new window to the physics of the spinful fractional quantum Hall (FQH) effect. We numerically study the lowest energy states of strongly interacting few-fermion systems in rapidly rotating optical microtraps. We find that skyrmion-like ground states with locally ferromagnetic, long-range spin textures emerge. To realize such states experimentally, rotating microtraps with higher-order angular momentum components may be used to prepare fermionic particles in a lowest Landau level. We find parameter regimes in which skyrmion-like ground states should be accessible in current experiments and demonstrate an adiabatic pathway for their preparation in a rapidly rotating harmonic trap. The addition of long range interactions will lead to an even richer interplay between spin textures and FQH physics.
The fractional quantum Hall effect (FQHE) is theoretically investigated, with numerical and algebraic approaches, in assemblies of a few spinful ultracold neutral fermionic atoms, interacting via repulsive contact potentials and confined in a single rapidly rotating two-dimensional harmonic trap. Going beyond the commonly used second-order correlations in the real configuration space, the methodology in this paper will assist the analysis of experimental observations by providing benchmark results for N-body spin-unresolved, as well as spin-resolved, momentum correlations measurable in time-of-flight experiments with individual particle detection. Our analysis shows that the few-body lowest-Landau-level (LLL) states with good magic angular momenta exhibit inherent ordered quantum structures in the N-body correlations, similar to those associated with rotating Wigner molecules (WMs), familiar from the field of semiconductor quantum dots under high magnetic fields. The application of a small perturbing stirring potential induces, at the ensuing avoided crossings, formation of symmetry-broken states exhibiting ordered polygonal-ring structures, explicitly manifest in the single-particle density profile of the trapped particles. Away from the crossings, an LLL state obtained from exact diagonalization of the microscopic Hamiltonian, found to be well described by a (1,1,1) Halperin two-component variational wave function, represents also a spinful rotating WM. Analysis of the calculated LLL wave function enables a two-dimensional generalization of the Girardeau one-dimensional ``fermionization'' scheme, originally invoked for mapping of bosonic-type wave functions to those of spinless fermions.
We study ultracold Rydberg-dressed Bose gases subject to artificial gauge fields in the fractional quantum Hall (FQH) regime. The characteristics of the Rydberg interaction gives rise to interesting many-body ground states different from standard FQH physics in the lowest Landau level (LLL). The non-local but rapidly decreasing interaction potential favors crystalline ground states for very dilute systems. While a simple Wigner crystal becomes energetically favorable compared to the Laughlin liquid for filling fractions ν<1/12, a correlated crystal of composite particles emerges already for ν≤1/6 with a large energy gap to the simple Wigner crystal. The presence of a new length scale, the Rydberg blockade radius aB, gives rise to a bubble crystal phase for ν≲1/4 when the average particle distance becomes less than aB, which describes the region of saturated, almost constant interaction potential. For larger fillings indications for strongly correlated cluster liquids are found.
Realizing fractional quantum Hall (FQH) states in ultracold atomic systems remains a major goal despite numerous experimental advances in the last few decades. Recent progress in trap anisotropy control under rapid rotation has renewed interest in ultracold atomic FQH physics, enabling experiments that impart much larger angular momentum per particle and offer in situ imaging with resolution finer than the cyclotron orbit size. In this paper, we present a theoretical investigation of a rapidly rotating anisotropic Bose gas. By projecting the full Hamiltonian, including both kinetic and interaction terms, onto the lowest Landau level, we derive a compact two-parameter model that captures the effects of interaction strength, rotation rate, and anisotropy. Using exact diagonalization and density matrix renormalization group, we obtain a phase diagram that features broken-symmetry phases and topologically ordered quantum Hall states, while also highlighting the distinctive physics arising from the system's edges. Our results demonstrate the potential for future theoretical and experimental exploration of anisotropic quantum fluids, offering a unified framework for weakly interacting Bose condensates, vortex matter, and strongly correlated topological phases.
We study the physics of a rapidly rotating gas of ultracold atomic bosons, with an internal degree of freedom. We show that in the limit of rapid rotation of the trap the problem exactly maps onto that of noninteracting fermions with spin in the lowest Landau level. The spectrum of the real bosonic system is identical to the one of the effective fermions, with the same eigenvalues and the same density of states. When the ratio of the number of atoms to the spin degeneracy is an integer number, the ground state for the effective fermions is an integer quantum Hall state. The corresponding bosonic state is a fractional quantum Hall liquid whose filling factor ranges in the sequence $\ensuremath{\nu}=1/2,2/3,3/4,\dots{},$ as the spin degeneracy increases. Anyons with 1/2,1/3,1/4,… statistics can be created by inserting lasers with the appropriate polarizations. A special situation appears when the spin degeneracy equals the number of atoms in the gas. The ground state is then the product of a completely antisymmetric spin state and a $\ensuremath{\nu}=1$ Laughlin state. In this case the system exhibits fermionic excitations with fermionic statistics although the real components are bosonic atoms.
The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall states and their lattice analogs—fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations and, for spinful systems, are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group simulations, we demonstrate the emergence of a spin-polarized 1 / 3 -Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at ν = 1 and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around ν = 1 , whereas we do not find such textures around ν = 1 / 3 . The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.
Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement, and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light, preparing fractional quantum Hall states in engineered systems remains elusive. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic ν=1/2 Laughlin state with two particles on sixteen sites. This minimal system already captures many hallmark features of Laughlin-type FQH states: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations, and we measure a fractional Hall conductivity of σH/σ0=0.6(2) via the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field we map out the transition point between the normal and the FQH regime through a spectroscopic probe of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms.