The effect of boundary deformation on the non-separable entanglement which appears in the classical elec- tromagnetic field is considered. A quantum chaotic billiard geometry is used to explore the influence of a mechanical modification of the optical fiber cross-sectional geometry on the production of non-separable entan- glement within classical fields. For the experimental realization of our idea, we propose an optical fiber with a cross section that belongs to the family of Robnik chaotic billiards. Our results show that a modification of the fiber geometry from a regular to a chaotic regime can enhance the transverse mode entanglement. Our proposal can be realized in a very simple experimental set-up which consists of a specially designed optical fiber where non-entangled light enters at the input end and entangled light propagates out at the output end after interacting with a fiber boundary that is known to generate chaotic behavior.
The effect of boundary deformation on the non-separable entanglement which appears in the classical elec- tromagnetic field is considered. A quantum chaotic billiard geometry is used to explore the influence of a mechanical modification of the optical fiber cross-sectional geometry on the production of non-separable entan- glement within classical fields. For the experimental realization of our idea, we propose an optical fiber with a cross section that belongs to the family of Robnik chaotic billiards. Our results show that a modification of the fiber geometry from a regular to a chaotic regime can enhance the transverse mode entanglement. Our proposal can be realized in a very simple experimental set-up which consists of a specially designed optical fiber where non-entangled light enters at the input end and entangled light propagates out at the output end after interacting with a fiber boundary that is known to generate chaotic behavior.
This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. We begin by introducing the fundamental principles of chaotic ray dynamics in optical microcavities, where the transition from regular to fully chaotic dynamics fundamentally alters the underlying wavefunctions and lasing properties. A central focus is placed on "chaos-assisted light emission," which serves as a practical manifestation of "chaos-assisted tunneling" -- a hallmark phenomenon in the study of quantum chaos. We discuss both theoretical frameworks and experimental validations, demonstrating how chaotic orbits facilitate the coupling between evanescently localized modes and far-field emission. Furthermore, exploring how the presence of a gain medium influences established results from quantum chaos research remains a fundamental and intriguing problem in physics. To address this, we establish a rigorous and comprehensive derivation of the Maxwell-Bloch equations for two-dimensional microcavity lasers, specifically examining their application to fully chaotic, stadium-shaped billiard lasers. By bridging the gap between nonlinear lasing processes and chaotic wavefunctions, this chapter highlights the unique potential of chaotic billiards for controlling light-matter interactions and shaping the next generation of unconventional coherent light sources.
Summary form only given. One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a dosed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off the beams of light. These beams create the desired spatial pattern, forming an "optical billiard". The system is extremely flexible due to the high level of control of the billiards geometry, the initial atomic sample, and the available measurement techniques. We find an excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new experimental testing ground for classical and quantum chaos.
We report on the numerical simulation of the double-slit experiment, where the initial wave packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.
This paper explores the potential for controlling chaotic dynamics within dynamical systems by leveraging the principles of quantum entanglement. The core claim is that the inherent complexity of chaotic systems can be precisely manipulated through the utilization of quantum entanglement. We propose a mechanism whereby entanglement is used to target and modify key parameters governing the chaotic behavior. The theoretical framework presented outlines a methodology for achieving this control, focusing on the intricate relationship between classical chaos and quantum correlations. This work offers a novel approach to chaos control, potentially leading to advancements in areas such as secure communication, precision sensing, and advanced control systems. The paper details the mathematical formulation, focusing on the manipulation of the system's Hamiltonian and the corresponding evolution equations. The central equation governing the system's dynamics is presented, alongside methods for quantifying the degree of entanglement and its impact on the system's trajectory. Finally, we discuss the challenges and future directions of this research area.
A bstract We investigate how IR modifications of the bulk geometry reshape long-range multipartite entanglement on the boundary in holography. We modify the IR geometries in two opposite directions: spherical modifications that enhance long-range entanglement and hyperbolic modifications that suppress them. We utilize various multipartite entanglement measures/signals to analyze the multipartite entanglement structures. These measures/signals are combinations of entanglement entropy, multi-entropy, entanglement wedge cross sections (EWCS) and multi-EWCS. Our results reveal that in the extremal limits of these two geometric modifications, the multipartite entanglement structures exhibit starkly contrasting behaviors: various measures saturate either their theoretical upper or lower bounds in the respective geometries. This demonstrates that IR deformations provide a practical holographic framework for realizing extremal entanglement regimes. Moreover, it serves as an effective tool for studying quantum marginal problems in holography. Finally, by observing how different measures respond to these engineered geometries, we gain clarifying insights into the specific types of multipartite entanglement that each measure/signal is particularly sensitive to.
Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely simple model consisting of alternating one-dimensional walks along the two spatial coordinates in bidimensional closed domains (hard wall billiards). The chaotic or regular behavior induced by the boundary shape in the deterministic classical motion translates into chaotic signatures for the quantized problem, resulting in sharp differences in the spectral statistics and morphology of the eigenfunctions of the quantum walker. Indeed, we found, for the Bunimovich stadium—a chaotic billiard—level statistics described by a Brody distribution with parameter δ≃0.1. This indicates a weak level repulsion, and also enhanced eigenfunction localization, with an average participation ratio (PR)≃1150 compared to the rectangular billiard (regular) case, where the average PR≃1500. Furthermore, scarring on unstable periodic orbits is observed. The fact that our simple model exhibits such key signatures of quantum chaos, e.g., non-Poissonian level statistics and scarring, that are sensitive to the underlying classical dynamics in the free particle billiard system is utterly surprising, especially when taking into account that quantum walks are diffusive models, which are not direct quantizations of a Hamiltonian.