This thesis presents a series of experimental studies that leverage atom-resolved imaging to probe fundamental properties of ultracold Fermi gases in continuous space. We demonstrate the viability of this continuum microscopy by reliably observing the expansion of a Gaussian wave packet and the Fermi hole of a two-dimensional ideal Fermi gas, measuring its second- and third-order correlation functions. Building upon this foundation, we introduce a novel local thermometer based on the relationship between fluctuations and correlations. This method enables accurate global and local temperature measurement without requiring trap calibration. Further investigations reveal sub-extensive fluctuations absent from the well-known fluctuation-dissipation theorem. We describe how these fluctuations are linked to entanglement entropy and observe a violation of the area law. Following this we connect the spatial organization of non-interacting fermions to random matrix theory via the Fredholm determinant. Measurements of the counting statistics and nearest-neighbor spacing are compared with numerical predictions, showing excellent agreement. Finally, we explore the physics of two-dimensional interacting fermions in the BEC-BCS crossover. Our measurements of two- and three-point correlation functions show significant discrepancies with mean-field BCS theory, but are corroborated by exact quantum Monte Carlo calculations. We also perform a precise measurement of Tan's contact. As a whole, this work provides a unique and unprecedented microscopic perspective on the fundamentals of Fermi gases, and establishes quantum gas microscopy as a powerful and versatile tool for exploring quantum gases in the continuum.
This thesis presents a series of experimental studies that leverage atom-resolved imaging to probe fundamental properties of ultracold Fermi gases in continuous space. We demonstrate the viability of this continuum microscopy by reliably observing the expansion of a Gaussian wave packet and the Fermi hole of a two-dimensional ideal Fermi gas, measuring its second- and third-order correlation functions. Building upon this foundation, we introduce a novel local thermometer based on the relationship between fluctuations and correlations. This method enables accurate global and local temperature measurement without requiring trap calibration. Further investigations reveal sub-extensive fluctuations absent from the well-known fluctuation-dissipation theorem. We describe how these fluctuations are linked to entanglement entropy and observe a violation of the area law. Following this we connect the spatial organization of non-interacting fermions to random matrix theory via the Fredholm determinant. Measurements of the counting statistics and nearest-neighbor spacing are compared with numerical predictions, showing excellent agreement. Finally, we explore the physics of two-dimensional interacting fermions in the BEC-BCS crossover. Our measurements of two- and three-point correlation functions show significant discrepancies with mean-field BCS theory, but are corroborated by exact quantum Monte Carlo calculations. We also perform a precise measurement of Tan's contact. As a whole, this work provides a unique and unprecedented microscopic perspective on the fundamentals of Fermi gases, and establishes quantum gas microscopy as a powerful and versatile tool for exploring quantum gases in the continuum.
Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in situ density profiles, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this Letter, we introduce a novel in situ thermometry for quantum gases, leveraging single-atom-resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes containing as little as one atom on average, we extract both global and local temperatures over a broad dynamic range. Our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering subextensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.
We demonstrate atom-resolved detection of itinerant bosonic ^{23}Na and fermionic ^{6}Li quantum gases, enabling the direct in situ measurement of interparticle correlations. In contrast to prior work on lattice-trapped gases, here we realize microscopy of quantum gases in the continuum. We reveal Bose-Einstein condensation with single-atom resolution, measure the enhancement of two-particle g^{(2)} correlations of thermal bosons, and observe the suppression of g^{(2)} for fermions; the Fermi or exchange hole. For strongly interacting Fermi gases confined to two dimensions, we directly observe nonlocal fermion pairs in the BEC-BCS crossover. We obtain the pair size and the short-range contact directly from the pair correlations. In situ thermometry is enabled via the fluctuation-dissipation theorem. Our technique opens the door to the atom-resolved study of strongly correlated quantum gases of bosons, fermions, and their mixtures.
In this Letter, we explore two-dimensional attractive Fermi gases at the microscopic level by probing spatial charge and spin correlations in situ. Using atom-resolved continuum quantum gas microscopy, we directly observe fermion pairing and study the evolution of two- and three-point correlation functions as interspin attraction is increased. The precision of our measurement allows us to reveal nonlocal anticorrelations in the pair correlation function, fundamentally forbidden by the mean-field result based on BCS theory but whose existence we confirm in exact auxiliary-field quantum Monte Carlo calculations. We demonstrate that the BCS prediction is critically deficient not only in the superfluid crossover regime but also deep in the weakly attractive side. Guided by our measurements, we find a remarkable relation between two- and three-point correlations that establishes the dominant role of pair correlations. Finally, leveraging local single-pair losses, we independently characterize the short-range behavior of pair correlations, via the measurement of Tan's contact, and find excellent agreement with numerical predictions. Our measurements provide a novel microscopic view into strongly correlated two-dimensional Fermi gases in the continuum.
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.
Since its initial use by Wigner in describing heavy atom spectra, random matrix theory (RMT) has found applications and revealed universal laws in diverse physical contexts, from quantum field theory to disordered systems and wireless communications. A particularly compelling application arises in the mathematical structure of the many-body wavefunction of non-interacting Fermi gases, which underpins a complex spatial organization driven by Pauli’s exclusion principle. However, experimental validation of the counting statistics predicted in such systems has remained elusive. Here, we probe at the single-atom level ultracold atomic Fermi gases made of two interacting spin states, obtaining direct access to their counting statistics in situ. We show that, while the system is strongly attractive, each spin component is described to a high accuracy by RMT predictions based on Fredholm determinants. Our results constitute an experimental validation of the Fermi-sphere point process through the lens of RMT, and establish its relevance for strongly-interacting systems. Random matrix theory (RMT) is used to describe non-interacting ultracold Fermi gases. Here, the authors directly probe the full counting statistics in a 2D system of 6Li atoms with two interacting spin states, by means of a continuum quantum gas microscopy technique. The measured number and spacing statistics agree well with predictions from RMT, also in the strongly interacting regime.
This thesis presents experiments probing the physics of strongly interacting fermionic atoms in the BCS-BEC crossover. Ultracold atom experiments bring the ability to arbitrarily tune interatomic interactions, which allows for unprecedented access to the regime of strongly interacting physics. The majority of cold atom experiments, however, are carried out in an atom trap that imprints an inhomogeneous density on the cloud of atoms. Many phenomena, especially the signatures of phase transitions, are significantly modified by this non-uniform density. In this thesis, I present a novel imaging technique that allows us to probe a region of nearly homogeneous density within a larger, inhomogenenous cloud. Using this technique, I present new results for strongly interacting fermionic atoms, including the first measurements of the contact and the occupied spectral function of a homogeneous Fermi gas, and the first direct observation of the "textbook" momentum distribution of an ideal Fermi gas.