High-resolution in situ imaging and manipulation of ultracold fermionic atoms in optical lattices are achieved experimentally for ${}^{40}$K 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.
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.
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].
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.
Our knowledge on ultracold quantum gases is strongly influenced by our ability to probe these objects. In situ imaging combined with single atom sensitivity is an especially appealing scenario as it can provide direct information on the structure and the correlations of such systems. For a precise characterization a high spatial resolution is mandatory. In particular, the perspective to study quantum gases in optical lattices makes a resolution well below one micrometer highly desirable. Here, we report on a novel microscopy technique which is based on scanning electron microscopy and allows for the detection of single atoms inside a quantum gas with a spatial resolution of better than 150 nm. Imaging a Bose-Einstein condensate in a one-dimensional optical lattice with 600 nm period we demonstrate single site addressability in a sub-um optical lattice. The technique offers exciting possibilities for the preparation, manipulation and analysis of quantum gases.
Strongly-correlated electron systems generate some of the richest phenomena and most challenging theoretical problems studied in physics. One approach to understanding these systems is with ultracold fermionic atoms in optical lattices, which can provide a level of control and ways of observing strongly-correlated fermionic systems that are not accessible with conventional materials. This thesis describes the development of an experimental technique where a quantum gas of fermionic 6Li atoms is prepared in a two-dimensional optical lattice and each atom can be frozen in place and imaged with single-site resolution. Combining a vacuum-compatible large numerical aperture microscope with Raman sideband cooling enables site-resolved fluorescence imaging with high fidelity. We observe several phases of the Hubbard model, including band and Mott insulators. The observed in-situ occupation distributions of atoms in the lattice are compared to theory with unprecedented detail and are used to determine the thermodynamic properties of the system. By combining site-resolved imaging with a spin-removal technique, we observe antiferromagnetic correlations in the Hubbard model with single-site resolution. We observe, for the first time in cold atom systems, beyond-nearest-neighbor magnetic correlations, which provide a direct measurement of the correlation length. We also present detailed measurements of the formation of correlations during lattice loading.
Recent advances in using microscopes in ultracold atom experiment have allowed experimenters for the first time to directly observe and manipulate individual atoms in individual lattice sites. This technique enhances our capability to simulate strongly correlated systems such as Mott insulator and high temperature superconductivity. Currently, all ultracold atom experiments with high resolution imaging capability use bosonic atoms. In this thesis, I present our progress towards creating the fermionic version of the microscope experiment which is more suitable for simulating real condensed matter systems. Lithium is ideal due to the existence of both fermionic and bosonic isotopes, its light mass, which means faster experiment time scales that suppresses many sources of technical noise, and also due to the existence of a broad Feshbach resonance, which can be used to tune the inter-particle interaction strength over a wide range from attractive, non-interacting, and repulsive interactions. A high numerical aperture objective will be used to image and manipulate the atoms with single lattice site resolution. This setup should allow us to implement the Hubbard hamiltonian which could describe interesting quantum phases such as antiferromagnetism, d-wave superfluidity, and high temperature superconductivity. I will also discuss the feasibility of the Raman sideband cooling method for cooling the atoms during the imaging process. We have also developed a new electronic control system to control the sequence of the experiment. This electronic system is very scalable in order to keep up with the increasing complexity of atomic physics experiments. Furthermore, the system is also designed to be more precise in order to keep up with the faster time scale of lithium experiment.
Ultracold quantum gases offer unique possibilities to study interacting many-body quantum systems. Probing and manipulating such systems with ever increasing degree of control requires novel experimental techniques. Scanning electron microscopy is a high resolution technique which can be used for in situ imaging, single site addressing in optical lattices and precision density engineering. Here, we review recent advances and achievements obtained with this technique and discuss future perspectives.