Ultracold atoms in optical lattices have proven to provide an extremely clean and controlled setting to explore strongly interacting quantum many-body phases of matter. Imaging of atoms in such lattice structures has reached the level of single-atom sensitive detection combined with the highest resolution down to the level of individual lattice sites. This has opened up fundamentally new opportunities for the characterization and the control of quantum many-body systems including quantum magnetism. These lecture notes cover selected parts of the course given at the Varenna Summer School on Quantum Matter at Ultralow Temperatures.
Ultracold atoms in optical lattices have proven to provide an extremely clean and controlled setting to explore strongly interacting quantum many-body phases of matter. Imaging of atoms in such lattice structures has reached the level of single-atom sensitive detection combined with the highest resolution down to the level of individual lattice sites. This has opened up fundamentally new opportunities for the characterization and the control of quantum many-body systems including quantum magnetism. These lecture notes cover selected parts of the course given at the Varenna Summer School on Quantum Matter at Ultralow Temperatures.
Ultracold atoms in optical lattices have proven to provide an extremely clean and controlled setting to explore quantum many-body phases of matter. Now, imaging of atoms in such lattice structures has reached the level of single-atom sensitive detection combined with the highest resolution down to the level of individual lattice sites. This has opened up fundamentally new opportunities for the characterization and the control of quantum many-body systems. Here we give a brief overview of this field and explore the opportunities offered for future research.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
Summary form only given. Over the past years, ultracold quantum gases have offered remarkable opportunities to investigate quantum matter through new probing techniques and in previously unexplored regimes. They can in fact be seen as one of the first realizations of Richard Feynman's visionary concept of a quantum simulator offering far-reaching possibilities to engineer new phases of matter.In my talk, I will give an overview over some of the recent scientific highlights in the field. For example, I will explain how atoms can be imaged in optical lattices with single-site and single-atom resolution thereby allowing one to obtain single snapshots of a quantum many-body systems, where every individual atom of the system can be detected. Such high-resolution imaging has enabled our group to directly probe quantum fluctuations and reveal hidden order in a many-body setting. Having such high resolution at hand, it has also been possible to address and coherently control individual atoms, thereby allowing one to realize single atom impurities that can be tracked in a time resolved way during their propagation through a complex correlated quantum system. By making use of adiabatic state evolution in quantum mechanics or laser induced hopping in optical lattices, it has now also become possible to realize artificial magnetic fields for neutral particles. The field strengths that can be achieved for such systems can by far surpass even the strongest fields from the most powerful magnets on earth and allow one to probe quantum matter under the most extreme conditions.
Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom-based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.
High-resolution in situ imaging and manipulation of ultracold fermionic atoms in optical lattices are achieved experimentally for 40K with single-atom sensitivity. The tomographic imaging technique provides a promising tool to explore the physics of intriguing quantum many-body quantum phenomena in fermionic systems, such as unconventional superfluidity, transport and nonequilibrium dynamics, and the formation of magnetic domains.
One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.