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.
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.
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].
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 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.
Imagine a new generation of computers that dramatically surpasses the most powerful supercomputers, being able to tackle the most challenging of computational problems. These problems arise, for example, in quantum physics where the computational power required to model a many-particle system increases exponentially with the number of its constituents, and as a consequence the calculations become prohibitively time-consuming. Nobel laureate Richard Feynman proposed this new type of computer in the early 1980s: ‘Let the computer itself be built of quantum mechanical elements which obey quantum mechanical laws.’ Such a quantum simulator would allow researchers to tackle challenging problems in condensed-matter physics. In particular many-body fermionic quantum systems are very difficult to compute due to the antisymmetric nature of the wave function, and the resulting sign problem for quantum Monte Carlo methods. This is why a quantum simulator will be an excellent test bed to investigate phenomena and properties of strongly correlated fermionic quantum systems. A powerful experimental platform to realize a quantum simulator is laser-cooled atoms [1] held in an artificial crystal of light, generated by superimposing laser beams. The atoms are kept in this optical lattice similar to marbles in the hollows of an egg carton, and they can mimic the behaviour of electrons in a real crystal. These systems interface atomic physics with condensed matter physics in a new way, as the tools of atomic physics allow for exquisite control of many experimental parameters, which are often inaccessible in solid state experiments. In-situ imaging techniques [2] using ‘quantum-gas microscopes’ constitute a new approach to the study of many-body quantum systems in an optical lattice with unprecedented resolution at the single-particle and single-site level [3,4]. This new method is complementary to earlier optical lattice experiments measuring distributions in momentum space after a time-of-flight expansion. A quantum-gas microscope uses an optical imaging system (Fig. 1a) for collecting the fluorescence light of ultracold atoms in an optical lattice with high spatial resolution comparable to the lattice spacing of ≈ 500 nm. (a) Atoms in optical lattice atoms are imaged with a high-resolution microscope objective [4]. (b) Single-site addressing is achieved by focussing a laser beam through the microscope onto selected atoms, bringing them into resonance with microwave radiation which produces spin flips [12]. (c) and (d) Single-atom-resolved fluorescence images of bosonic Mottinsulators [4,9]. (e) Deterministically prepared atom distribution using single-site addressing [12]. (f) Direct observation of single-atom quantum walks [15]. Fluorescence imaging of atoms in a quantum-gas microscope has made it possible to directly observe bosonic Mott insulators with single-atom resolution [4–6], giving access to in-situ measurements of temperature and entropy distributions. Subsequently, ground-breaking experiments in many-body quantum dynamics have been performed, such as the first direct observation of correlation spreading after quenches of the system to lower lattice depths [7]. Other experiments include the quantum simulation of an antiferromagnetic spin-1/2 chain [8], the realization of algorithmic cooling [9], the direct measurement of correlations across the superfluid-to-Mott-insulator transition [10], or the observation of the ‘Higgs’ amplitude mode [11]. The high-resolution imaging system is also capable of optically addressing individual atoms with sub-diffraction-limited resolution. For this purpose, a laser beam is focussed though the microscope objective onto selected lattice sites, bringing the atoms into resonance with microwave radiation which produces spin flips [12,13]. The preparation of arbitrary atom distributions in the lattice not only opens perspectives for neutral-atom quantum information processing, but also allows the deterministic creation of specific out-of-equilibrium situations, and their ensuing system dynamics can be studied with single-atom resolution. Examples include the creation of spin impurities and the study of their dynamics in a many-body system [14], the observation of quantum walks [15] and magnon-bound states [16], and the measurement of entanglement entropy [17]. The technique used for single-site-resolved detection of individual atoms in the optical lattice is fluorescence imaging. It requires laser cooling of the atoms to sub-Doppler temperatures while detecting the fluorescence photons emitted during this process. A challenge is to achieve a low particle loss rate and to prevent the atoms from hopping between lattice sites. In the case of the first quantum-gas microscopes, this has been implemented with bosonic rubidium-87 atoms, and also recently for ytterbium-174. However, it has proven more challenging for fermionic alkaline species such as potassium-40 and lithium-6, as their low mass and small excited state hyperfine splitting-prevented standard sub-Doppler cooling from working. As a result, it took several years to extend the quantum-gas microscope technique to fermionic species, and in 2015 several groups have demonstrated single-atom-resolved imaging of fermions [18]. In these setups, the direct observation of band insulators [19], fermionic Mott insulators [20,21] and even antiferromagnetic correlations [22] has been reported most recently. These developments provide fascinating opportunities to study many-body fermionic quantum systems with single-particle access. The fermionic nature of the electron is vital to understanding a range of phenomena within solid-state physics, such as electron pairing in superconductivity, and quantum magnetism. In this context, the quantum simulator will allow, e.g. for direct measurement of ordered quantum phases and out-of-equilibrium dynamics, with access to quantities such as spin--spin correlation functions and the growth of many-body entanglement. The high-resolution imaging systems could also be used to project tailored time-varying light fields onto the atoms, allowing the removal of high-entropy regions by locally modifying the confining potential to attain very low-entropy states. Attaining these low-entropy many-particle states is one of the key challenges in our field. In summary, quantum-gas microscopes offer unprecedented access to many-body quantum systems, and they will allow us to gain an even deeper insight into the intriguing world of quantum physics that governs the properties of strongly correlated materials. Using a well-controlled quantum system to simulate other quantum systems could help resolve some of the most challenging problems scientists face in condensed matter physics and materials science, but it will also provide new insights in quantum chemistry, high-energy physics and biology. SK acknowledges funding from the EU (ERC FERMILATT, SIQS, QuProCs) and SUPA.
Since the first proposal of quantum simulation by Richard Feynman in 1982, multiple platforms have been explored to probe the behaviour of subatomic particles, exploiting the intrinsic nature of quantum systems. As one of the most promising candidates to realise large-scale simulation, quantum simulators with ultracold gases have attracted unprecedented attention. Featuring novel detection possibilities, a high degree of controllability and the extreme physical parameter regimes that can be reached in these ‘artificial solids’, quantum simulation with ultracold atoms has progressively matured to the point that it can be used to study exotic quantum phenomena. This review presents the theoretical fundamentals and recent advances in related technology and offers comment on future directions.
Seventy years after Einstein's prediction, the seminal achievement of Bose–Einstein condensation in dilute atomic gases in 1995 has provided us with a new form of quantum matter. Such quantum matter can be described as a single giant matter wave. By loading it into an artificial periodic potential formed by laser light—a so-called optical lattice—it has become possible to probe matter far beyond the wave-like description. In a review of a series of experiments with ultracold quantum gases in optical lattices, we show that the granularity of the matter wave field, caused by the discreteness of atoms, gives rise to effects going beyond the simple single matter wave description. Bose–Einstein condensates in optical lattices have thereby opened novel possibilities for investigating strongly correlated many-particle phenomena of condensed matter physics and have opened new opportunities for quantum information processing with neutral atoms