Non-classical and chaotic motion of two-dimensional light
Violetta Sharoglazova is a PhD student in the Department of Adaptive Quantum Optics. (Co)Promotors are prof.dr. P.W.H. Pinkse and dr. J.A. Klärs from the Faculty of Science & Technology.
Understanding how classical and quantum descriptions of nature connect remains one of the most fundamental challenges in physics. While classical mechanics provides a deterministic framework for macroscopic systems, quantum mechanics is governed by the probabilistic behavior of particles at microscopic scales. However, in the transition region between these regimes, particularly where quantum phenomena defy classical intuition, such as tunneling through classically forbidden regions or the emergence of behaviors reminiscent of classical chaos in quantum systems, even though quantum mechanics itself does not support classical chaos – new experimental insights are crucial.
This thesis investigates two questions: How fast can a particle move within a classically forbidden region?, and in what ways can classical chaos manifest in quantum systems? These problems are approached through direct experimental study using a canonical platform – an optical microcavity filled with dye, in which confined photons behave as if they were massive particles. This system offers a powerful analogy to quantum particles in a potential landscape, while allowing high-resolution spatial and temporal access to quantities that are otherwise challenging to measure.
In the first part of this thesis, we examine the kinematics of classically forbidden motion, where the total energy of a particle 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 for a quantum particle to traverse a potential barrier? We address this question by constructing a system where the speed of classically forbidden motion can be both derived and experimentally measured. Furthermore, we discuss different theoretical approaches to tunneling time and highlight how our results relate to and challenge existing models, particularly in the context of 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 same sense. Nonetheless, under specific conditions – such as non-resonant optical pumping leading to lasing – we observe evidence of chaos-like behavior. Using the same dye-filled microcavity platform, we explore a billiard-shaped potential and probe its dynamical stability. The results highlight how quantum systems can display behavior that structurally mirrors classical chaos, despite their fundamentally different underlying principles.
By combining novel experimental techniques with foundational theoretical questions, this thesis contributes to the ongoing dialogue between classical and quantum physics, offering both conceptual insights and empirical evidence at their intersection.
