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.
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.
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.
We demonstrate single-site and single-atom-resolved fluorescence imaging of a bosonic Mott insulator of 7Li atoms in an optical lattice. The fluorescence images are obtained by implementing Raman sideband cooling on a deep two-dimensional square lattice, where we collect scattered photons with a high numerical aperture objective lens. The square lattice is created by a folded retroreflected beam configuration that can reach a 2.5 mK lattice depth from a single laser source. The lattice beam is elliptically focused to have a large area with deep potential. On average, 4000 photons are collected per atom during 1 s of Raman sideband cooling and the imaging fidelity is over 95 in the central $80\ifmmode\times\else\texttimes\fi{}80$ lattice sites. As a first step to study correlated quantum phases, we present the site-resolved imaging of a Mott insulator. By tuning the magnetic field near the Feshbach resonance, the scattering length can be increased to 680aB and we are able to produce a large-sized unity filling Mott insulator with 2000 atoms at low temperature. Our work provides a stepping stone to further in-depth investigations of intriguing quantum many-body phases in optical lattices.
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 the microscopic investigation of antiferromagnetic order in Hubbard chains, realized with ultracold repulsively interacting fermions in an optical lattice. Extending a quantum gas microscope on spin resolution opened the possibility to Access the full charge and spin statistics of a strongly correlated fermionic many body system. Using this technique, we measured antiferromagnetic correlations over distances up to three lattice sites. Starting with a repulsive degenerate two component mixture of 6Li atoms trapped in a single plane of a vertical lattice, we loaded the Atoms into one-dimensional tubes of a transverse optical superlattice. By adiabatically ramping up the lattice potential along the tubes, we isentropically entered the strongly correlated regime of the one-dimensional Fermi-Hubbard Hamiltonian. We spatially separated the two spin states into opposite sites of local double wells orthogonal to the direction of the lattice before single atom and site sensitive imaging. In this way we extracted the spin information of every single lattice site and were able to evaluate spin-spin correlations. The two component degenerate gases were produced with sub-Poissonian atom number fluctuations by magnetically driven evaporative cooling in vicinity of a Feshbach resonance, used to set the scattering length. The dependence of antiferromagnetic correlations on the driving superexchange coupling was experimentally investigated by varying the interparticle scattering length before loading the atoms into the optical lattice. Taking advantage of the underlying trapping potential of the optical lattice, which shaped the filling and the entropy of the gases, the influence of density excitations and different entropies on spin correlations was observed. By post-selecting the Hubbard chains based on their average filling and local atom number fluctuations, spin correlations corresponding to 58% of the zero temperature predictions in the Heisenberg regime were measured. By comparing the obtained antiferromagnetic correlations to Quantum-Monte-Carlo predictions for our System the lowest measured entropy per particle could be stated as s = 0.51(4)kB, clearly below the critical value of s = ln(2)kB, which is required to form longer ranged correlations. Below this critical entropy, in contrast to local density fluctuations, these spin correlations strongly depend on the entropy of the system. In the future, such a spin thermometer can be used to benchmark novel cooling techniques, which are required to enter the temperature regime of d-wave superconducting states. The access to the full particle and spin statistics will enable us to read out multi-point correlation functions, which characterize such exotic states of matter.
This thesis describes the methods used to achieve single-atom and single-site resolved fluorescence imaging of a quantum gas of fermionic atoms held in an optical lattice. This kind of quantum gas microscopy has been previously applied to bosonic atoms in two experiments, and has allowed for extensive studies of many-body quantum systems. Here we detail methods to extend the techniques of quantum gas microscopy to fermionic species of atoms, opening the door to quantum simulation of electronic models of condensed matter physics. We prepare quantum degenerate gases of fermionic 40K through sympathetic cooling with a gas of \Rb. The gas prepared is trapped less than 1 mm away from a thin vacuum window, an experimental geometry which permits interrogation with a large Numerical Aperture microscope objective. The cloud is loaded into a 527 nm-period cubic optical lattice, ideal for quantum simulation of many-body models of fermionic particles such as the Hubbard model. The optical lattice is designed to allow for potential depths up to V/kB = 250 microKelvin, sufficient to strongly confine 40K atoms into individual lattice sites. EIT cooling --- a technique previously demonstrated in ion-trapping experiments --- is used to cool the fermionic atoms deeply towards the ground motional state of the lattice wells. We collect the photons scattered during continuous application of EIT cooling, while atoms are kept pinned in the lattice for many seconds. We strongly suppress all other sources of light with the use of a modulated cooling scheme and a spinning chopper wheel. Collecting the scattered light produced during 2 s of EIT cooling allows us to resolve single atoms in a fluorescence image. We demonstrate that the high resolution of our imaging apparatus also permits atom positions to be precisely identified on the length scale of the optical lattice. Thus we demonstrate the realisation of a quantum gas microscope for fermionic atoms, allowing for precise investigation of the ground states and dynamics of correlated quantum states of fermionic particles.
The imaging of neutral atoms confined in an optical lattice has been demonstrated by a number of groups, resolving single fluorescing atoms in samples of hundreds of atoms. To obtain a high signal the atoms remain confined in the wells of a deep optical lattice whilst fluorescence excitation light is applied for high resolution imaging. In most cases, the excitation light frequency is chosen so that there is a concomitant laser cooling effect. In existing implementations of an imaging lattice the preceding manipulation stage has used optical trapping and manipulation. In this thesis I describe work towards applying this imaging lattice technique on a magnetic trapping apparatus, in particular for carrying out quantum simulation experiments. An introduction to the specific challenge of performing a quantum simulation of the fractional quantum Hall effect is given, with the link to and nature of the imaging lattice technique explained. The existing quantum-gas machine that has been developed to produce Bose-Einstein condensates of 87Rb in this work is then described, including the new optical lattice subsystem and the associated diode laser system. An auxiliary project to develop a servo-control system for frequencies that are several GHz away from an atomic reference is presented. We implement an optical lattice using laser light with a frequency detuning of -20 GHz below the D1-resonance line. The construction and geometry of the individual dipole trapping beams in combination with our existing apparatus is discussed as well as the alignment methods used. We confirm the presence of three independent 1D lattices through diffraction, and observe the decay of a BEC loaded into a lattice using absorption imaging. We observe good long-term alignment and operational stability of the optical lattice. This system will enable us to ultimately detect single fluorescing atoms in the optical lattice, following the application of excitation light co-propogating with lattice beams, via an imaging system with a moderate numerical aperture of 0:27.