Quantum simulation with controllable many-body platforms offers a powerful route to exploring complex phases and dynamics that are difficult to access in natural materials. Among these, topological spin textures such as skyrmions are central to modern condensed-matter physics and play a key role in chiral quantum many-body systems. Their controlled realisation in large, programmable quantum platforms, however, remains an outstanding challenge. Here, we report deterministic generation and site-resolved reconstruction of topological spin textures in a two-dimensional crystal of more than 150 trapped ions. Using globally applied spin-dependent forces, we generate skyrmion configurations and reconstruct the full vector spin field with single-ion resolution, obtaining a winding number of 0.99$\pm
0.02andameanlocalfidelityof0.87\pm$0.04. In addition, we implement single-ion-resolved control to deterministically prepare domain-wall states, extending our approach to a broader class of non-uniform spin textures. These results establish trapped-ion crystals as a platform for engineering complex spin textures and open the door to exploring topology-dependent nonequilibrium dynamics in long-range interacting quantum systems.
Chiral superfluidity in ultracold Fermi gases represents a fascinating frontier in condensed matter physics, offering a pristine platform for exploring exotic quantum phases with topological properties. This paper provides a comprehensive review of the theoretical underpinnings and potential experimental realizations of chiral superfluids when ultracold Fermi gases are subjected to artificial gauge fields. We begin by introducing the concept of artificial gauge fields, detailing how they can be engineered using laser-atom interactions to impart synthetic spin-orbit coupling and break time-reversal symmetry, thereby creating conditions conducive to chiral order. We then delve into the microscopic theory of chiral pairing, particularly focusing on p-wave and p+ip superfluid states, which are intrinsically chiral and support topologically protected edge modes, such as Majorana fermions. The methodology section outlines the theoretical tools employed, including mean-field BCS theory and Bogoliubov-de Gennes equations, to predict the phase diagrams and spectroscopic signatures of these exotic states. We discuss the effects of varying interaction strengths, gauge field parameters, and trapping potentials on the emergence and stability of chiral phases. The potential for experimental detection through rf spectroscopy, noise correlations, and direct imaging of vortex cores is also addressed. Our findings underscore the significant potential of ultracold atomic systems as quantum simulators for unraveling the mysteries of topological phases, with profound implications for fundamental physics and quantum information science.
Two-dimensional spin-orbit-coupled Fermi gases subject to
s-wave pairing can be driven into a topological phase by increasing the Zeeman spin splitting beyond a critical value. In the topological phase, the system exhibits the hallmarks of chiral
p-wave superfluidity, including exotic Majorana excitations. Previous theoretical studies of this realization of a two-dimensional topological Fermi superfluid have focused on the BCS regime where the
s-wave Cooper pairs are only weakly bound and, hence, the induced chiral
p-wave order parameter has a small magnitude. Motivated by the goal to identify potential new ways for the experimental realization of robust topological superfluids in ultracold-atom gases, we study the BCS-to-BEC crossover driven by increasing the Cooper-pair binding energy for this system. In particular, we obtain phase diagrams in the parameter space of two-particle bound-state energy and Zeeman spin-splitting energy. Ordinary characteristics of the BCS-to-BEC crossover, in particular the shrinking and eventual disappearance of the Fermi surface, are observed in the nontopological phase. In contrast, the topological phase retains all features of chiral
p-wave superfluidity, including a well-defined underlying Fermi surface, even for large
s-wave pair-binding energies. Compared to the BCS limit, the topological superfluid in the BEC regime turns out to be better realizable even for only moderate magnitude of spin-orbit coupling because the chiral
p-wave order parameter is generally larger and remnants of
s-wave pairing are suppressed. We identify optimal parameter ranges that can aid further experimental investigations and elucidate the underlying physical reason for the persistence of the chiral
p-wave superfluid.
Two-dimensional (2D) quantum magnetism is a paradigm in strongly correlated many-body physics. The understanding of 2D quantum magnetism can be expedited by employing a controllable quantum simulator that faithfully maps 2D-spin Hamiltonians. The 2D quantum simulators can exhibit exotic phenomena such as frustrated quantum magnetism and topological order and can be used to show quantum computational advantages. Many experimental platforms are being developed, including Rydberg atoms and superconducting annealers. However, with trapped-ion systems, which showed the most advanced controllability and quantum coherence, quantum magnetism was explored in one-dimensional chains. Here, we report simulations of frustrated quantum magnetism with 2D ion crystals. We create a variety of spin-spin interactions for quantum magnets, including those that exhibit frustration by driving different vibrational modes and adiabatically prepare the corresponding ground states. The experimentally measured ground states are consistent with the theoretical predictions and are highly degenerate for geometrically frustrated spin models in two dimensions. Quantum coherence of the ground states is probed by reversing the time evolution of the B-field to the initial value and then measuring the extent to which the remaining state coincides with the initial state. Our results open the door for quantum simulations with 2D ion crystals.
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.
A Majorana zero bound mode exists in the vortex core of a chiral
p+ip superconductor or superfluid, which can be driven from an
s-wave pairing state by two-dimensional spin-orbit coupling. We propose here a novel scheme based on realistic cold atom platforms to generate two-dimensional spin-orbit interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work may open a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems.