Exploring classically chaotic potentials with a matter wave quantum probe

Quantum Control beyond the Adiabatic Regime in 2D Curved Matter-Wave Guides

The propagation of matter waves in curved geometry is relevant for ion transport, atomtronics and electrons in nanowires. Curvature effects are usually addressed within the adiabatic limit and treated via an effective potential acting on the manifold to which the particles are strongly confined. However, the strength of the confinements that can be achieved experimentally are limited in practice, and the adiabatic approximation often appears too restrictive for realistic guides. Here, we work out a design method for 2D sharply bent waveguides beyond this approximation using an exact inverse-engineering technique. The efficiency of the method is confirmed by the resolution of the 2D nonlinear Schrödinger equation in curved geometry. In this way, we realize reflectionless and ultrarobust curved guides, even in the presence of interactions. Here, the transverse stability is improved by several orders of magnitude when compared to circular guides of similar size.

Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles

The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of noninteracting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wave packets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is, then, a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.

Testing for Basins of Wada

Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we say that the set of basins has theWada property and initial conditions near that boundary are even more unpredictable. Many physical systems of interest with this topological property appear in the literature. However, so far the only approach to study Wada basins has been restricted to two-dimensional phase spaces. Here we report a simple algorithm whose purpose is to look for the Wada property in a given dynamical system. Another benefit of this procedure is the possibility to classify and study intermediate situations known as partially Wada boundaries.

Observation of quantized conductance in neutral matter

In transport experiments, the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. Observations of quantized steps in electrical conductance have provided important insights into the physics of mesoscopic systems and have allowed the development of quantum electronic devices. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles. In its most fundamental form, it requires a quantum-degenerate Fermi gas, a ballistic and adiabatic transport channel, and a constriction with dimensions comparable to the Fermi wavelength. Here we report the observation of quantized conductance in the transport of neutral atoms driven by a chemical potential bias. The atoms are in an ultraballistic regime, where their mean free path exceeds not only the size of the transport channel, but also the size of the entire system, including the atom reservoirs. We use high-resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi-two-dimensional ballistic channel connecting the reservoirs. By varying either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaux in the atom conductance. The conductance in the first plateau is found to be equal to the universal conductance quantum, 1/h. We use Landauer's formula to model our results and find good agreement for low gate potentials, with all parameters determined a priori. Our experiment lets us investigate quantum conductors with wide control not only over the channel geometry, but also over the reservoir properties, such as interaction strength, size and thermalization rate.

New developments in classical chaotic scattering

Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described.

Optically guided beam splitter for propagating matter waves

We study experimentally and theoretically a beam splitter setup for guided atomic matter waves. The matter wave is a guided atom laser that can be tuned from quasimonomode to a regime where many transverse modes are populated, and propagates in a horizontal dipole beam until it crosses another horizontal beam at 45°. We show that depending on the parameters of this X configuration, the atoms can all end up in one of the two beams (the system behaves as a perfect guide switch), or be split between the four available channels (the system behaves as a beam splitter). The splitting regime results from a chaotic scattering dynamics. The existence of these different regimes turns out to be robust against small variations of the parameters of the system. From numerical studies, we also propose a scheme that provides a robust and controlled beam splitter in two channels only.