Abstract Exploring many-body interactions in an inquiry-based environment can enhance undergraduate and graduate student understanding of quantum physics. Specific classroom examples are provided in increasing complexity of content and maturity of comprehension. The simplest example of a purely quantum system (without using a classical potential) involves the many-body treatment of two quantum objects reflecting from each other via hard-sphere scattering in one dimensional motion. This example is extended to a particle confined in an infinite square well or interacting with a finite barrier and finite well where each of the objects generating the potentials now recoils due to reflection of the particle. These simple systems introduce concepts of entanglement, quantum correlated interference, and measurements made on a subset of the bodies. Completely inelastic scattering that involves the fusing (or destruction) of two bodies into the creation of a third is also discussed. In addition to this content, guided inquiry-based pedagogy is illustrated using two examples: collective recoil when a particle reflects from two scatterers and measurements on each body made asynchronously. The examples provided explore potential methods to verify quantum effects on a macroscopic scale and address measurement in a quantum system.
Abstract Exploring many-body interactions in an inquiry-based environment can enhance undergraduate and graduate student understanding of quantum physics. Specific classroom examples are provided in increasing complexity of content and maturity of comprehension. The simplest example of a purely quantum system (without using a classical potential) involves the many-body treatment of two quantum objects reflecting from each other via hard-sphere scattering in one dimensional motion. This example is extended to a particle confined in an infinite square well or interacting with a finite barrier and finite well where each of the objects generating the potentials now recoils due to reflection of the particle. These simple systems introduce concepts of entanglement, quantum correlated interference, and measurements made on a subset of the bodies. Completely inelastic scattering that involves the fusing (or destruction) of two bodies into the creation of a third is also discussed. In addition to this content, guided inquiry-based pedagogy is illustrated using two examples: collective recoil when a particle reflects from two scatterers and measurements on each body made asynchronously. The examples provided explore potential methods to verify quantum effects on a macroscopic scale and address measurement in a quantum system.
Abstract An interferometer in which all of its components are treated as quantum bodies is examined with the standard interpretation and with a model in which its uncoupled spatially separated components act collectively. These models utilize superposition principles that differ when applied to systems composed of three or more bodies. Interferometric discrepancies between these models that involve frequency shifts and recoil are shown to be difficult to measure. More pronounced differences involve quantum correlated interference. The collective model provides a missing connection between quantum and semiclassical theories. Scattering from an entangled state, which cannot be divided into disjoint parts, is proposed to involve such collective recoil. Collective scattering offers a viable supplement to the standard model, thereby providing insight into constructing tests of the superposition principle in systems with three or more bodies.
The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.
Experimental progress in the miniaturization of electronic devices has made routinely available in the laboratory small electronic systems, on the micrometre or sub-micrometre scale, which at low temperature are sufficiently well isolated from their environment to be considered as fully coherent. Some of their most important properties are dominated by the interaction between electrons. Understanding their behaviour therefore requires a description of the interplay between interference effects and interactions. The goal of this review is to address this relatively broad issue and more specifically to address it from the perspective of the quantum chaos community. I will therefore present some of the concepts developed in the field of quantum chaos which may be applied to the study of many-body effects in mesoscopic and nanoscopic systems. Their implementation is illustrated in a few examples of experimental relevance such as persistent currents, mesoscopic fluctuations of Kondo properties or Coulomb blockade. I will furthermore try to bring out, from the various physical illustrations, some of the specific advantages on more general grounds of the quantum chaos based approach.
We review methods that allow one to detect and characterize quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without requiring a number of measurements or computational resources to analyze the data that scale exponentially with the system size. We begin with introducing the concepts of quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in the bipartite scenario, to then present their multipartite generalization. We review recent progress on characterizing these quantum correlations from partial information on the system state, such as through data-driven methods or witnesses based on low-order moments of collective observables. We then review state-of-the-art experiments that demonstrate the preparation, manipulation and detection of highly-entangled many-body systems. For each platform (e.g. atoms, ions, photons, superconducting circuits) we illustrate the available toolbox for state preparation and measurement, emphasizing the challenges that each system poses. To conclude, we present a list of timely open problems in the field.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.