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.
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.
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.
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.
This thesis presents theoretical research on microscopic measuring devices and thermal machines constructed from single trapped atoms. We study several variants on this theme, with a particular emphasis on their application to ultracold atom physics. The first part of the thesis is about quantum refrigerators powered by thermal absorption rather than by external work. We propose and detail how such a machine may be practically constructed with a trapped atom placed inside an optical cavity, and employed to cool the atom close to absolute zero temperature using only collimated sunlight as an energy source. We then show that quantum absorption refrigerators in the strong-coupling regime exhibit coherent oscillations, thus enabling one to outperform a typical classical refrigerator by reaching lower temperatures than the steady state in a finite time using quantum coherence. The second part of the thesis studies the use of impurity atoms as probes of ultracold atomic gases. We discuss two different thermometry methods using impurities which are sensitive to temperature differences on the order of nanokelvin or less. We characterise the precision of the proposed thermometers by explicit calculations in the context of both weakly and strongly interacting atomic Bose gases. Finally, we study impurities immersed in a cold atomic Fermi gas realising a superfluid. We show that the impurities' energy dissipation rate probes the spectrum of density fluctuations in the gas, providing nondestructive access to various properties of the superfluid order parameter along the crossover from a Bardeen-Cooper-Schrieffer (BCS) state to a Bose-Einstein condensate (BEC).
The precise measurement of low temperatures is a challenging, important, and fundamental task for quantum science. In particular, in situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here, we demonstrate that the temperature of a noninteracting Fermi gas can be accurately inferred from the nonequilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precision in the relevant temperature regime for degenerate Fermi gases in current experiments. We also discover an intriguing trade-off between measurement time and thermometric precision that is controlled by the impurity-gas coupling, with weak coupling leading to the greatest sensitivities. This is explained as a consequence of the slow decoherence associated with the onset of the Anderson orthogonality catastrophe, which dominates the gas dynamics following its local interaction with the immersed impurity.
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.
Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattices to simulate models for unsolved strongly correlated systems, so as to deduce their properties directly from experimental data. An important step in this effort is to determine the temperature of the system, which is essential for deducing all thermodynamic functions. This step, however, remains difficult for lattice systems at the moment. Here, we propose a method based on a generalized fluctuation-dissipation theorem. It does not rely on numerical simulations and gives a universal thermometry scheme for quantum gas systems including mixtures and spinor gases, provided that the local density approximation is valid.