Non-classical and chaotic motion of two-dimensional light

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.