We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6Li gas at magnetic fields above a Feshbach resonance, where no stable 6Li2 molecules would exist in vacuum. We accurately determined the position of the resonance to be 822+/-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.

Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance

From Superfluid to Mott Insulator One of the most attractive characteristics of cold atomic gases in optical lattices is their ability to simulate condensed-matter systems. The results of these quantum simulations are usually averaged over the atomic ensemble, or course-grained over several lattice sites. Now, Bakr et al. (p. 547, published online 17 June; see the Perspective by DeMarco) provide a single lattice site view onto the transition of a Bose gas of Rb-87 from the superfluid to the Mott-insulating state. Characteristic concentric shells of uniform number density were observed deep in the Mott insulator regime, and probing the local quantum dynamics revealed unexpectedly short time scales. The low-defect Mott structures identified may provide a starting point for quantum magnetism experiments. Imaging of atoms that were optically trapped in lattice sites reveals local dynamics of a quantum phase transition. Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We used single atom–single lattice site imaging to investigate the Bose-Hubbard model on a microscopic level. Our technique enables space- and time-resolved characterization of the number statistics across the superfluid–Mott insulator quantum phase transition. Site-resolved probing of fluctuations provides us with a sensitive local thermometer, allows us to identify microscopic heterostructures of low-entropy Mott domains, and enables us to measure local quantum dynamics, revealing surprisingly fast transition time scales. Our results may serve as a benchmark for theoretical studies of quantum dynamics, and may guide the engineering of low-entropy phases in a lattice.

Probing the Superfluid to Mott Insulator Transition at the Single Atom Level

After many years of development of the basic tools, quantum simulation with ultracold atoms has now reached the level of maturity at which it can be used to investigate complex quantum processes. Planning of new experiments and upgrading of existing set-ups requires a broad overview of the available techniques, their specific advantages and limitations. This Technical Review aims to provide a comprehensive compendium of the state of the art. We discuss the basic principles, the available techniques and their current range of applications. Focusing on the simulation of various phenomena in solid-state physics through optical lattice experiments, we review their basics, the necessary techniques and the accessible physical parameters. We outline how to control and use interactions with external potentials and interactions between the atoms, and how to design new synthetic gauge fields and spin–orbit coupling. We discuss the latest progress in site-resolved techniques that use quantum gas microscopes, and describe the unique features of quantum simulation experiments with two-electron atomic species. Quantum simulation with ultracold atomic gases is an established platform for investigating complex quantum processes. Focusing on optical lattice experiments, this Technical Review overviews the available tools and their applications to the simulation of solid-state physics problems.

Tools for quantum simulation with ultracold atoms in optical lattices

Spin-orbit interactions in ultracold quantum gases are synthesized via clock transitions between two energy levels, which act like pseudospin states.

/pdf/synthetic-dimensions-and-spin-orbit-coupling-with-an-optical-4bg7upyiwd.pdf

Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition.

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of nondiagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.

Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction.

Ultracold alkaline-earth atoms are used in precision measurements and quantum simulation. Because of their unique atomic structure, they could enable the study of problems in quantum many-body systems, such as the simulation of synthetic gauge fields, Kondo and SU(N) physics. But to fully exploit this potential, the capability to tune the interatomic interaction to the strongly interacting regime is needed. Several theoretical proposals and experimental demonstrations have shown that both the spin-independent and spin-exchange interaction can be tuned to resonance in the alkaline-earth atoms. In this Perspective, we review these advances and discuss the opportunities brought by these interaction-control tools for future quantum simulation studies. Due to their atomic structure, ultracold alkaline-earth atoms are well suited for quantum simulation and the study of quantum many-body physics. This Perspective overviews the ways to control the interactions between atoms and discusses the new physics that could be uncovered.

Controlling the interaction of ultracold alkaline-earth atoms

Ultracold alkaline-earth atoms have now been widely explored for precision measurements and quantum simulation. Because of its unique atomic structure, alkaline earth atoms possess great advantages for quantum simulation and studying quantum many-body matters, such as simulating synthetic gauge field, Kondo physics and $SU(N)$ physics. To fully explore the potential of ultracold alkaline-earth atoms, these systems also need to be equipped with the capability of tuning the inter-atomic interaction to the strongly interacting regime. Recently several theoretical proposals and experimental demonstrations have shown that both spin-independent and spin-exchanging interaction can be tuned to resonance. In this perspective, we will review these progress and discuss the new opportunities brought by these interaction control tools for future quantum simulation studies with ultracold alkaline-earth atoms.

Interaction Control of Ultracold Alkaline-Earth Atoms.

In this work we study the many-body dynamics of Bose-Einstein condensates subject to an arbitrary time-varying scattering length. By employing a variational ansatz which assumes the majority of the particles are condensed, we derive an effective Bogoliubov-like Hamiltonian that governs the dynamics of thermal particles. Crucially, we show that there exists a hidden symmetry in this Hamiltonian that can map the many-body dynamics to the precession of an SU(1,1) ``spin'' and also allows an exact dynamical solution for this precession in an arbitrary ``magnetic field.'' As a demonstration, we calculate the situation where the scattering length is sinusoidally modulated. We show that the noncompactness of the SU(1,1) group naturally leads to solutions with exponentially growth of Bogoliubov modes and causes instabilities.

Many-body dynamics with time-dependent interaction

The topological $\theta$-angle is central to the understanding of a plethora of phenomena in condensed matter and high-energy physics such as the strong CP problem, dynamical quantum topological phase transitions, and the confinement--deconfinement transition. Difficulties arise when probing the effects of the topological $\theta$-angle using classical methods, in particular through the appearance of a sign problem in numerical simulations. Quantum simulators offer a powerful alternate venue for realizing the $\theta$-angle, which has hitherto remained an outstanding challenge due to the difficulty of introducing a dynamical electric field in the experiment. Here, we report on the experimental realization of a tunable topological $\theta$-angle in a Bose--Hubbard gauge-theory quantum simulator, implemented through a tilted superlattice potential that induces an effective background electric field. We demonstrate the rich physics due to this angle by the direct observation of the confinement--deconfinement transition of $(1+1)$-dimensional quantum electrodynamics. Using an atomic-precision quantum gas microscope, we distinguish between the confined and deconfined phases by monitoring the real-time evolution of particle--antiparticle pairs, which exhibit constrained (ballistic) propagation for a finite (vanishing) deviation of the $\theta$-angle from $\pi$. Our work provides a major step forward in the realization of topological terms on modern quantum simulators, and the exploration of rich physics they have been theorized to entail.

Observation of microscopic confinement dynamics by a tunable topological $\theta$-angle

Enhancing Kondo Coupling in Alkaline-Earth Atomic Gases with Confinement-induced Resonances in Mixed Dimensions

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