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.
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.
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.
Recently, Sharoglazova et al. [Nature 643, 67 (2025)] proposed a procedure for determining the speed of a quantum particle in the classically forbidden region of a potential step, and implemented it in a beautiful experiment. The inferred speeds disagree significantly with the Bohmian velocities, which the authors presented as an experimental challenge to Bohmian mechanics. This is puzzling because the speeds are inferred from particle populations in coupled waveguides for which Bohmian mechanics and standard quantum mechanics make identical predictions. We resolve the puzzle by a detailed theoretical analysis of the experimental setup. We show that the speed inference rests on an assumption that fails in the relevant (evanescent) regime according to both Bohmian mechanics and standard quantum mechanics -- namely that the inter-waveguide tunneling time is set by the transverse coupling and is not affected by entanglement with the longitudinal degree of freedom. We also consider a second speed estimate suggested by Sharoglazova et al., which is based on the Büttiker dwell time formula for particles in the forbidden region. We show that the authors applied the formula incorrectly, and that a correct application yields exact agreement with the predictions of Bohmian mechanics. Our analysis includes explicit calculations of Bohmian trajectories, dwell times, and longitudinal speeds in the two-dimensional waveguide model of the experiment.
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.
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.
This thesis provides a fundamental characterization of photon gases in nanostructured microcavities, investigating the underlying physics that may eventually support new forms of information processing. While the transition from electronic to photonic architectures is often motivated by the physical limits of semiconductors, such as the ’power wall’ and carrier scattering, realizing these systems requires a deep understanding of quantum dynamics. This work addresses these fundamental questions by examining collective dynamics in condensate networks, single-particle tunneling, and the thermodynamics of isolated quantum gases. The first part of this work explored the collective behavior of coupled photon Bose-Einstein condensates as a preliminary step toward building larger computational networks. By experimentally realizing a negatively coupled triplet of condensates, this study demonstrated that the system resides in a frustrated state. Although this represents only a fundamental building block, it serves as a necessary milestone for the potential scaling of these networks into larger Hamiltonian simulators. Future research in this direction will be required to implement reconfigurable coupling geometries and to determine if these analog systems can effectively compete with classical heuristic algorithms for complex optimization tasks. The second part of this research was the investigation of particle motion within classically forbidden regions. Understanding the transport mechanisms that govern phase coherence is essential for any platform where particles must move between defined sites. Using a measurement scheme based on two coupled waveguides, where population transfer acts as a clock to determine particle speed, evanescent states in a reflective potential step were analyzed. The results revealed an inverse relationship between energy and speed, where lower energy leads to higher speeds within the potential. These findings agree with the Büttiker and Landauer tunneling time framework, suggesting that the effective speed within the barrier is governed by the interaction between phase and amplitude gradients. Extending this waveguide clock methodology to more complex landscapes, such as periodic barriers or time-dependent potentials, will clarify the role of amplitude gradients in particle transport. This understanding directly supports the design of high-speed quantum electronic components, where evanescent states play a major role. The final section examined the emergence of thermodynamic behavior from an isolated quantum system. This was achieved by studying a photon gas within a gravitational wedge billiard. Experimental analysis of spatial autocorrelation functions showed that the microcanonical standard deviation decreases as the system approaches the semiclassical limit, which supports the Eigenstate Thermalization Hypothesis. Furthermore, thermodynamic phase transitions in the microcanonical density of states, surface entropy, and surface temperature were observed. Because the gas is two-dimensional, these transitions were driven entirely by the geometry of the billiard. The quantum virial theorem was also qualitatively confirmed. Future research can build on these results to investigate the transition from ergodicity to many-body localization within photon gases, and to study how dimensionality and boundary conditions dictate the macroscopic thermodynamic properties of a quantum system. In conclusion, the findings described in this thesis contribute to a broader scientific effort to understand and control light as a state of matter. By investigating the fundamental mechanisms of tunneling and thermalization, this work provides the physical insights necessary to move beyond the constraints of current electronic architectures. While the development of large-scale photonic simulators remains a long-term objective, the methodologies and theoretical frameworks established here offer a cohesive narrative on how the structural control of light can lead to the observation and utilization of complex quantum phenomena.
Quantum tunnelling, a hallmark phenomenon of quantum mechanics, allows particles to pass through the classically forbidden region. It underpins fundamental processes ranging from nuclear fusion and photosynthesis to the operation of superconducting qubits. Yet the underlying dynamics of particle motion during tunnelling remain subtle and are still the subject of active debate. Here, by analyzing the temporal evolution of the tunnelling process, we show that the particle velocity inside the barrier continuously relaxes from a large initial value toward a smaller one, and may even approach zero in the evanescent regime. Meanwhile, the probability density within the barrier gradually builds up before reaching its stationary profile, in contrast to existing inherently. In addition, starting from the steady-state equations, we derive an explicit relation between the particle velocity and the barrier width, and show that the velocity in evanescent states approaches zero when the barrier is sufficiently wide. These findings resolve the apparent paradox of a vanishing steady-state velocity coexisting with a finite particle density. We point out that defining an effective speed from the probability density, rather than from the probability current, can lead to spuriously nonzero "stationary speed," as appears to be the case in Ref. [Nature 643, 67 (2025)]. Our work establishes a clear dynamical picture for the formation of tunnelling flow and provides a theoretical foundation for testing time-resolved tunnelling phenomena.