Studying the dynamics of quantum many-body systems is often constrained by the limitations in probing relevant observables, especially in continuous systems. A powerful method to gain information about such systems is the reconstruction of local currents from the continuity equation. We show that this approach can be used to extract the total phase fluctuation of adjacent Bose gases. We validate our technique numerically and demonstrate its effectiveness by analyzing data from selected experiments simulating 1D quantum field theories through the phase difference of two parallel 1D Bose gases. This analysis reveals the previously hidden sector of the sum mode of the phase, which is important for studying long-time thermalization and out-of-equilibrium dynamics of the system. Our method is general and can be applied to other cold atom systems with spatial phase gradients, thereby expanding the scope and capabilities of cold-atomic quantum simulators.
Studying the dynamics of quantum many-body systems is often constrained by the limitations in probing relevant observables, especially in continuous systems. A powerful method to gain information about such systems is the reconstruction of local currents from the continuity equation. We show that this approach can be used to extract the total phase fluctuation of adjacent Bose gases. We validate our technique numerically and demonstrate its effectiveness by analyzing data from selected experiments simulating 1D quantum field theories through the phase difference of two parallel 1D Bose gases. This analysis reveals the previously hidden sector of the sum mode of the phase, which is important for studying long-time thermalization and out-of-equilibrium dynamics of the system. Our method is general and can be applied to other cold atom systems with spatial phase gradients, thereby expanding the scope and capabilities of cold-atomic quantum simulators.
Quantum state tomography provides a powerful and versatile framework for characterizing quantum states across diverse quantum systems. However, tomography is still largely restricted to systems with a few degrees of freedom, while for continuous systems, it is typically tailored to quantum-optical platforms. For other many-body systems described by continuous quantum fields such as ultracold atomic gases, tomographic technique is not as well-established. The present thesis addresses this gap by providing new approaches to measurement and tomography of ultracold Bose gases trapped in one (1D) and two dimensions (2D). These systems serve as analog quantum field theory (QFT) simulators and exhibit novel physics absent in higher dimensions. We begin by systematically assessing state-of-the-art method for extracting the relative phase field in parallel 1D Bose gases with matter-wave interference. In particular, we derive a formula for the systematic phase shift due to longitudinal dynamics, a factor that is often ignored in previous modeling of the measurement. We further examine how the single-shot readout error propagates to correlation and distribution functions of the relative phase. Then, we broaden the scope of experimentally accessible quantities by developing a new methodology to extract the common phase field---the sum of the phase fields of the two parallel gases---from the already available density ripple data. We rigorously benchmark this new readout with numerical simulations and experimental data in 1D systems and further generalize it to 2D systems. By combining the relative and common phases information, we improve Gaussian state tomography in parallel 1D Bose gases and apply it to probe new physical phenomena in quantum field simulators. Specifically, we focus on two applications: (i) field-space entanglement detection at finite temperatures and out of equilibrium, and (ii) probing non-linear relaxation in near-integrable quantum systems. This thesis bridges theory and experiment in the simulation of QFTs and reveals new opportunities for exploring many-body quantum effects in ultracold bosonic gases.
Interference upon free expansion gives access to the relative phase between two interfering matter waves. Such measurements can be used to reconstruct the spatially-resolved relative phase, which is a key observable in many quantum simulations of quantum field theory and non-equilibrium experiments. However, in 1D systems, longitudinal dynamics is typically ignored in the analysis of experimental data. In our work, we give a detailed account of various effects and corrections that occur in finite temperatures due to longitudinal expansion. We provide an analytical formula showing a correction to the readout of the relative phase due to longitudinal expansion and mixing with the common phase. Furthermore, we numerically assess the error propagation to the estimation of the gases’ physical quantities such as correlation functions and temperature. We also incorporate systematic errors arising from experimental imaging devices. Our work characterizes the reliability and robustness of interferometric measurements, directing us to the improvement of existing phase extraction methods necessary to observe new physical phenomena in cold-atomic quantum simulators.
Abstract Quantum simulators allow to explore static and dynamical properties of otherwise intractable quantum many-body systems. In many instances, however, the read-out limits such quantum simulations. In this work, we introduce an innovative experimental read-out exploiting coherent non-interacting dynamics. Specifically, we present a tomographic recovery method allowing to indirectly measure the second moments of the relative density fluctuations between two one-dimensional superfluids, which until now eluded direct measurements. Applying methods from signal processing, we show that we can reconstruct the relative density fluctuations from non-equilibrium data of the relative phase fluctuations. We employ the method to investigate equilibrium states, the dynamics of phonon occupation numbers and even to predict recurrences. The method opens a new window for quantum simulations with one-dimensional superfluids, enabling a deeper analysis of their equilibration and thermalization dynamics.
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.
Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with no further approximations. Simulations are of a set of stochastic equations that in the limit of many realizations correspond exactly to the full quantum evolution. These are obtained using the stochastic gauge method (derived here), an extension of the positive P phase-space representation. The systems investigated are: 1) Dynamics of spatial correlations in uniform 1D and 2D Bose gases after the rapid appearance of significant two-body collisions (e.g. after entering a Feshbach resonance). 2) Dynamics of stimulated Bose enhancement of scattered atom modes during the collision of two Bose-Einstein condensates with a mean of 150 000 atoms. 3) Dynamics of trapped bosons, where the size of the trap is of the same order as the range of the interparticle potential. 4) Grand canonical thermodynamics of uniform 1D Bose gases for a variety of temperatures and collision strengths. Observables calculated include 1st-3rd order spatial correlation functions (including finite separation) and momentum distributions. The stochastic gauge method is derived, and its application to interacting Bose gases investigated in detail. It is found to improve simulation effectiveness under many conditions, and to be capable of overcoming instability and boundary term problems. Additionally, conditions under which very generalized phase-space represntations can be used to obtain tractable many-body simulations are analysed.
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.