We realize a quantum-gas microscope for fermionic ^{40}K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.
We realize a quantum-gas microscope for fermionic ^{40}K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.
Quantum gas microscopes have expanded the capabilities of quantum simulation of Hubbard models by enabling the study of spatial spin and density correlations in square lattices.However, quantum gas microscopes have not been realized for fermionic atoms in frustrated geometries.Here, we demonstrate the single-atom resolved imaging of ultracold fermionic 6 Li atoms in a triangular optical lattice with a lattice constant of 1003 nm.The optical lattice is formed by a recycled narrow-linewidth, high-power laser combined with a light sheet to allow for Raman sideband cooling on the D 1 line.We optically resolve single atoms on individual lattice sites using a high-resolution objective to collect scattered photons while cooling them close to the two-dimensional ground vibrational level in each lattice site.By reconstructing the lattice occupation, we measure an imaging fidelity of approximately 98%.Our triangular lattice microscope platform for fermions clears the path for studying spin-spin correlations, entanglement, and dynamics of geometrically frustrated Hubbard systems which are expected to exhibit exotic emergent phenomena including spin liquids and kinetic frustration.
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.
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.
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.
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.
Cold atom experiments have traditionally employed bulk imaging techniques, such as absorption imaging, to measure atomic sample densities. However, in recent years, single-atom imaging methods have emerged as powerful tools to probe and manipulate quantum many-body systems at the level of individual particles. This work focuses specifically on quantum gas microscopy using Raman sideband cooling in an optical lattice. This technique, which has been used extensively in several cold atoms groups, has mostly been applied in the context of discrete systems, such as the celebrated Bose- and Fermi-Hubbard models and their generalization. In this thesis, we show how quantum gas microscopy can be extended beyond its original scope to probe continuous many-body systems in a quantitative manner. Our proposed protocol consists in a rapid ramp of the pinning lattice intensity, projecting atoms from the continuum onto discrete lattice sites, followed by a Raman sideband cooling stage that confines atoms near the motional ground state and prevents them from escaping during imaging. To validate the effectiveness of this new method, we characterize the pinning and imaging processes by using continuous quantum gas microscopy to reconstruct the wavefunction of a single-atom Gaussian wave packet during its free expansion. Under optimal conditions, we achieve an imaging fidelity in excess of 95%, defined as the probability of projecting an atom from the continuum to the nearest lattice site and successfully imaging it. We also apply this technique to a quasi-two-dimensional non-interacting Fermi gas, enabling us to extract two- and three-body correlation functions, g2 and g3, with unprecedented spatial resolution and finding an excellent agreement with the theoretical prediction. In particular, our measurements reveal a 90% reduction in the probability of finding two atoms in close proximity for the coldest samples, offering one of the most pristine in situ observations of the Pauli exclusion principle in a continuous system. Finally, we propose a thermometry method based on atom number fluctuations, which are readily obtained from our imaging procedure. Crucially, this thermometry technique could be generalized to strongly interacting systems, where temperature estimation is typically challenging. The quantum gas microscopy technique developed here opens new avenues for studying continuous many-body systems with unprecedented resolution, offering a powerful tool for future cold atom experiments.