We experimentally study a pair of tunnel-coupled one-dimensional atomic superfluids, which realize the quantum sine-Gordon/massive Thirring models relevant for a wide variety of disciplines from particle to condensed-matter physics. From measured interference patterns we extract phase correlation functions and analyze if, and under which conditions, the higher-order correlation functions factorize into lower ones. This allows us to characterize the essential features of the model solely from our experimental measurements, detecting the relevant quasiparticles, their interactions and the topologically distinct vacua. Our method provides comprehensive insights into a non-trivial quantum field theory and establishes a general method to analyze quantum many-body systems through experiments.
We experimentally study a pair of tunnel-coupled one-dimensional atomic superfluids, which realize the quantum sine-Gordon/massive Thirring models relevant for a wide variety of disciplines from particle to condensed-matter physics. From measured interference patterns we extract phase correlation functions and analyze if, and under which conditions, the higher-order correlation functions factorize into lower ones. This allows us to characterize the essential features of the model solely from our experimental measurements, detecting the relevant quasiparticles, their interactions and the topologically distinct vacua. Our method provides comprehensive insights into a non-trivial quantum field theory and establishes a general method to analyze quantum many-body systems through experiments.
Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems.Here, we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data.This determination is accomplished by extracting the one-particle irreducible (1PI) correlation functions from which one can construct all physical observables.To match the capabilities of experimental techniques, our approach employs a formulation of quantum field theory based on equal-time correlation functions only.We illustrate the theoretical foundations of our procedure by applying it to the sine-Gordon model in thermal equilibrium and then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids.We extract all 1PI correlation functions up to the 1PI four-point function (interaction vertex) and their variation with momentum, encoding the "running" of the couplings.The measured 1PI correlation functions are compared to the theoretical estimates, verifying our procedure.Our work opens new ways of addressing complex many-body questions emerging in a large variety of settings from fundamental science to practical quantum technology.
We present a series of experiments performed with two ultracold one-dimensional Bose gases (rubidium atoms) in a double well potential. Employing matter-wave interference, we can measure the spatially resolved phase difference between the two gases and consequently investigate spatial correlations. By investigating whether higher order correlation functions can be factorized into correlations of lower order, we can investigate the interaction properties of the system. For a non-interacting system, all correlation functions with orders greater than two factorize and one observes Gaussian fluctuations. Here, we present the measurement of non-factorizing fourth-order correlation functions, leading to an experimental characterization of the interactions between the collective excitations of the quantum many-body system. The degree of non-factorizibility, i.e., the degree of non-Gaussianity of the phase fluctuations, depends on the tuneable tunneling strength between the wells. Starting from such a non-Gaussian state, we are able to observe the dynamical evolution towards a state with factorizing correlation functions (Gaussian fluctuations). We start in a double well with tunneling and then abruptly decouple the two subsystems. Subsequently, we observe how the initially non-Gaussian phase fluctuations become Gaussian. Moreover, we discuss the dynamical emergence of phase coherence in a double well potential with tunneling. We experimentally investigate the evolution starting from two different initial states. In one case, we split a cloud of atoms into two and trigger global oscillations in their relative phase. The oscillations subsequently damp and phase coherence sets in. In the other case, two independent clouds are suddenly coupled by tunneling. Again, phase coherence emerges between the two subsystems.
Quantum field theories (QFTs) as relevant for condensed-matter or high-energy physics are formulated in continuous space and time, and typically emerge as effective low-energy descriptions. In atomic physics, an example is given by tunnel-coupled superfluids, which realize the paradigmatic sine-Gordon model, and can act as quantum simulators of continuous QFTs. To quantitatively characterize QFT simulators, or to discover the Hamiltonian governing the dynamics of a continuous many-body quantum system, we discuss Hamiltonian learning as a method to systematically extract the operator content and the coupling constants of Hamiltonians from experimental data. In contrast to Hamiltonian learning for lattice models with a given lattice scale, we learn QFT Hamiltonians on a resolution scale set by the experiment. Varying the resolution scale gives access to QFTs at different energy scales, and allows to learn a flow of Hamiltonians reminiscent of the renormalization group. Applying these techniques to available experimental data from a tunnel-coupled quantum gas experiment allows a definite distinction between a free quadratic theory from an interacting sine-Gordon model, as the underlying QFT description of the system. Published by the American Physical Society 2024
Quantum Many-Body Physics: A Path Integral Approach offers a fresh perspective on quantum phenomena in condensed matter physics. This comprehensive book provides a powerful and versatile framework for understanding complex problems in systems such as ultracold atoms, superfluids, and superconductors. The text begins with a solid foundation in canonical quantum field theory before progressing to advanced topics, ensuring readers develop both deep conceptual understanding and practical skills. Features include: Concise yet thorough coverage of path integral methods Practical applications to real-world quantum systems Problem-solving techniques that bridge theory and experiment Designed for graduate students in physics and related disciplines, this book serves as an essential resource for those aiming to advance their studies in quantum mechanics. Researchers in condensed matter physics, quantum optics, and quantum information will also find valuable insights to support their work on the next breakthroughs in the field.
In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system-the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.
(English) In recent years, the evolution of quantum technologies has resulted in an unprecedented control over individual quantum particles and many-body systems. This remarkable progress has given rise to a new era, marked by the convergence of classical and quantum methodologies to investigate fundamental questions concerning the nature of quantum matter, improving our understanding of the role of entanglement in solid-state systems or the mechanisms behind high-energy physics. From analog quantum simulators to digital quantum computers, these advancements hold potential across diverse domains. This thesis explores the interplay between classical and quantum methods in understanding topological phases of matter. We concentrate on three distinct directions: non-conventional topological superconductors, interaction-induced topological phases in ultracold atom quantum simulators, and applications of variational quantum algorithms. Each trajectory relies on the combination of different techniques with the aim of understanding and characterizing topological phenomena in different settings. Exploring non-conventional topological superconductors involves extending the paradigmatic Kitaev chain model by incorporating additional terms in the Hamiltonian such as long-range interactions and quasi-periodic potentials. This investigation is relevant to better understand the impact of real-world conditions on the both the topological and localization properties of systems hosting non-local Majorana modes, which are promising candidates for topological quantum computation. In the realm of interacting systems, we explore the realization of interaction-induced topological phases in systems of ultracold atoms in optical lattices, both in one and two dimensions. The remarkable control and versatility of such platforms enable the simulation of both theoretical topological models and strongly correlated physics. Notably, the interplay between interactions and topology can give rise to intriguing phenomena, such as delocalized fractional charges and gapless topological phases,challenging existing intuition. We employ advanced numerical methods based on tensor networks to benchmark the experimental proposals that open the door to the realization and detection of novel many-body phases of matter, including topological quantum critical points and a higher-order topological Peierls insulator in Bose-Hubbard models with long-range interactions. Variational quantum algorithms, conversely, have the potential to efficiently tackle a wide range of problems, including ground state search, phase classification or accessing topological invariants. Despite current limitations in trainability and scalability, these hybrid classical-quantum algorithms provide practical insights into current quantum hardware capabilities and can inspire future architectures. We explore the application of variational quantum algorithms to shed light on topological phenomena, raising questions about their ability to discern topological phase transitions and compute topological invariants in situations where classical approaches fail. This thesis presents a comprehensive exploration of distinct approaches to topological quantum matter by leveraging quantum technologies and quantum-inspired classical algorithms. Our results not only advance our understanding of quantum systems but also pave the way for the realization and discovery of novel physics extending to quantum information processing, materials science, and beyond.