Understanding how classical and quantum descriptions of nature connect remains one of the central challenges in physics. Classical mechanics provides a deterministic picture for macroscopic systems, while quantum mechanics is governed by probabilistic behavior at microscopic scales. In the intermediate regime — where quantum effects clash with classical intuition, such as tunneling through forbidden regions or the appearance of chaos-like features in quantum systems — new experimental insight is essential. This thesis investigates two questions: How fast can a particle move within a classically forbidden region? and In what ways can classical chaos leave signatures in quantum systems? Both problems are explored experimentally using an optical microcavity filled with dye, in which confined photons behave as massive particles. This platform provides offers high-resolution spatial and temporal access to quantities that are difficult to measure in traditional quantum systems. In the first part of this thesis, we examine the kinematics of classically forbidden motion, where the particle energy is lower than the potential energy of a barrier or a potential step. While classical mechanics forbids such motion, quantum mechanics allows particles to explore these regions due to an effectively negative local kinetic energy, raising the long-standing question of tunneling time: How long does it take to traverse a barrier? We address this by engineering a system in which the speed associated with forbidden motion can be derived and directly measured. Different theoretical approaches to tunneling time are compared, and we discuss how our results relate to and challenge existing models, with particular attention to Bohmian mechanics. The second half of this thesis focuses on the emergence of classical chaos signatures in quantum systems. While the correspondence principle suggests that quantum behavior should resemble classical physics in certain limits, quantum systems are fundamentally linear and therefore cannot exhibit chaos in the classical sense. Nonetheless, under specific conditions – such as non-resonant optical pumping leading to lasing – we observe sensitivity to initial conditions in a billiard-shaped potential. By combining novel experimental techniques with foundational theoretical questions, this thesis contributes to the ongoing dialogue between classical and quantum physics.
Understanding how classical and quantum descriptions of nature connect remains one of the central challenges in physics. Classical mechanics provides a deterministic picture for macroscopic systems, while quantum mechanics is governed by probabilistic behavior at microscopic scales. In the intermediate regime — where quantum effects clash with classical intuition, such as tunneling through forbidden regions or the appearance of chaos-like features in quantum systems — new experimental insight is essential. This thesis investigates two questions: How fast can a particle move within a classically forbidden region? and In what ways can classical chaos leave signatures in quantum systems? Both problems are explored experimentally using an optical microcavity filled with dye, in which confined photons behave as massive particles. This platform provides offers high-resolution spatial and temporal access to quantities that are difficult to measure in traditional quantum systems. In the first part of this thesis, we examine the kinematics of classically forbidden motion, where the particle energy is lower than the potential energy of a barrier or a potential step. While classical mechanics forbids such motion, quantum mechanics allows particles to explore these regions due to an effectively negative local kinetic energy, raising the long-standing question of tunneling time: How long does it take to traverse a barrier? We address this by engineering a system in which the speed associated with forbidden motion can be derived and directly measured. Different theoretical approaches to tunneling time are compared, and we discuss how our results relate to and challenge existing models, with particular attention to Bohmian mechanics. The second half of this thesis focuses on the emergence of classical chaos signatures in quantum systems. While the correspondence principle suggests that quantum behavior should resemble classical physics in certain limits, quantum systems are fundamentally linear and therefore cannot exhibit chaos in the classical sense. Nonetheless, under specific conditions – such as non-resonant optical pumping leading to lasing – we observe sensitivity to initial conditions in a billiard-shaped potential. By combining novel experimental techniques with foundational theoretical questions, this thesis contributes to the ongoing dialogue between classical and quantum physics.
Quantum mechanics is considered the most fundamental theory for describing nature. Classical mechanics is thought to arise from quantum mechanics in the limit of high quantum numbers. Unlike quantum mechanics, classical mechanics allows for chaotic motion, characterized by sensitivity to initial conditions, a feature ambiguous for translation to quantum systems. Here, we investigate the onset of classical chaos in a non-Hermitian quantum system. We study photons in a microcavity, treated as two-dimensional quantum particles moving in the plane of the resonator. By nanostructuring the resonator's mirrors, we can confine the photons in arbitrary potential landscapes, particularly billiard-like potentials. Non-resonant optical pumping inside of these potentials creates gain in the optical medium. We anticipate that introducing latter will amplify modes with maximum overlap with the gain region, introducing sensitivity to initial conditions, specifically to the pumping spot position. This investigation is expected to shed light on the quantum-to-classical transition in a chaotic system.
For nearly a century, quantum tunneling has been a subject of sustained scientific interest. In a prior investigation [1], we introduced an unconventional method to explore evanescent phenomena at step potentials by examining particle motion within a system of coupled waveguides. In this system, the transfer of particles between waveguides serves as a clock, facilitating the determination of particle speeds even in classically forbidden regions. We implement this idea for photons in optical microcavity, which has full experimental access to the wave function. Using a novel nanostructuring method [2], we can guide photons in diverse potential landscapes, specifically within a coupled waveguiding structure. We measure particle speeds both in classically allowed and forbidden regions. Notably, our measurements show that classically forbidden regions speed up the motion of photons. Furthermore, our observations emphasize the significance of density gradients in wave functions for the motion of particles. We hope, these outcomes will provide valuable insights into the intricate dynamics of quantum tunneling phenomena, in particular make useful contribution to the tunneling time debate. Moreover, our findings can be viewed as a test of Bohmian trajectories in quantum mechanics. [1] Klaers, J., Sharoglazova, V., & Toebes, C. (2023). Physical Review A, 107(5), 052201. [2] Vretenar, M., Puplauskis, M., Klaers, J.. Adv. Optical Mater. 2023, 2202820.
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.
In quantum mechanics, regions of negative local kinetic energy can manifest. This occurs when the wave function's amplitude undergoes significant decay, typically associated with quantum tunneling. Here, we investigate the particles motion in a system of two coupled waveguide potentials, where the population transfer between the waveguides effectively acts as a clock, allowing particle speeds along the waveguide axis to be determined [1]. We implement this idea for photons in optical microcavity, using a novel nanostructuring method [2] to create waveguides. By applying this scheme to evanescent phenomena at a reflective potential step, we determine an energy-speed relationship for classically forbidden motion, which shows speed increase as energy decreases. Our findings contribute to the ongoing tunneling time debate, and separately, can be viewed as a test of Bohmian trajectories in quantum mechanics. [1] Klaers, J., Sharoglazova, V., & Toebes, C. (2023). Physical Review A, 107(5), 052201. [2] Vretenar, M., Puplauskis, M., Klaers, J.. Adv. Optical Mater. 2023, 2202820.
For nearly a century, quantum tunneling has been a subject of sustained scientific interest. In a prior investigation [1], we introduced an unconventional method to explore evanescent phenomena at step potentials by examining particle motion within a system of coupled waveguides. In this system, the transfer of particles between waveguides serves as a clock, facilitating the determination of particle speeds even in classically forbidden regions. We implement this idea for photons in optical microcavity, which has full experimental access to the wave function. Using a novel nanostructuring method [2], we can guide photons in diverse potential landscapes, specifically within a coupled waveguiding structure. We measure particle speeds both in classically allowed and forbidden regions. Our measurements show that classically forbidden regions speed up the motion of photons. Moreover, our findings emphasize the significance of density gradients in wave functions for the motion of particles. We hope, these outcomes will provide valuable insights into the intricate dynamics of quantum tunneling phenomena, in particular make useful contribution to the tunneling time debate. [1] Klaers, J., Sharoglazova, V., & Toebes, C. (2023). Physical Review A, 107(5), 052201. [2] Vretenar, M., Puplauskis, M., Klaers, J.. Adv. Optical Mater. 2023, 2202820.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.