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.
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.
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.
For many-body quantum systems, dimensionality is known to exert a profound influence on the physical behaviour, allowing for the shaping of distinct phases of matter. In general, for lower dimensions, enhanced fluctuations serve to suppress long range order. For bosonic gases, for example, Bose-Einstein condensation in one dimension requires confinement that is stronger than linear in order to occur, in contrast to two-dimensional systems where harmonic confinement can suffice. In this thesis, the dimensional crossover between one and two dimensions in a harmonically trapped photon gas has been experimentally investigated. The photons were confined within a dye filled optical microcavity, where polymer nanostructures produced by direct laser writing defined the trapping potential. By systematically adjusting the aspect ratio of the harmonic trap, the confinement was varied from an isotropic two dimensional regime to a highly anisotropic one dimensional regime. The caloric properties of the photon gas were characterised across this transition, revealing that the sharp phase transition observed in two dimensions evolves into a smooth crossover in one dimension. This work enhances understanding of thermodynamic behaviour in photon Bose gases under confinement and demonstrates that here dimensionality can be used to tailor phase transition phenomena. Furthermore, polymer cavities fabricated via direct laser writing afforded precise control over the confinement geometry, enabling exploration of variable potential landscapes. Proof of concept studies of advanced geometries, previously inaccessible, are presented, opening new directions for research in driven dissipative Bose gases and photonic quantum simulation platforms.
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.
The study of second-order phase transitions is a broad research theme that provides fundamental insights into the physical nature of complex systems. A central aspect deals with the concept of universal behavior. Universality governs, for example, the diverging correlated fluctuations of an order parameter, characterized by a macroscopic correlation length ξ, as well as the divergence of other thermodynamic quantities near the critical point. Extracting the critical exponents associated with these diverging quantities shows that quite different physical systems can exhibit identical scaling behavior, placing them into common universality classes. Bose-Einstein condensation of an ideal (i.e., non-interacting) gas of bosons is a second-order phase transition, and thus provides a valuable platform to investigate universal critical behavior in the quantum gas regime, driven purely by quantum statistics rather than inter-particle interactions. While historically studied in ultracold atomic and molecular gases, Bose-Einstein condensation can now be realized in a two-dimensional photonic gas at room temperature using dye-filled microcavities. The microcavity imposes a low-energy cutoff, providing a non-vanishing ground state and an effective mass for the intracavity photons, which thermalize via repeated absorption and emission processes with the dye reservoir rather than inter-particle interactions. Consequently, this platform establishes an almost perfectly ideal, two-dimensional quantum gas of light. In combination with versatile trapping techniques, it provides a highly tunable platform to explore the thermodynamics of quantum gases. This thesis presents a quantitative study of spatial correlations in a uniformly trapped two-dimensional photon gas. The uniform confinement is achieved by a custom mirror-structuring technique, resulting in box-like trapping potentials. The temporal and spatial coherence properties of the gas are validated in both the thermal and condensed regimes using an interferometric measurement technique. Because the applicability of scanning interferometry limits measurements of critical scaling behavior, an alternative method is introduced to extract the first-order spatial coherence directly from the far-field angular distribution of the cavity emission in a single experimental shot. This technique enables the extraction of the spatial correlation length ξ and a precise evaluation of its scaling behavior in the vicinity of the critical point Nc. The measurements presented here demonstrate, for the first time, the determination of a critical exponent in the (ideal) Bose gas universality class. The obtained critical exponent of ν = 0.52 ± 0.04 for the two-dimensional ideal Bose gas is consistent with theoretical expectations. Crucially, this critical exponent is found to be robust and independent of the system size within experimental uncertainties, demonstrating the universality of the scaling behavior. Finally, the limits of this universal behavior are explored by demonstrating the breakdown of critical scaling when the thermalizing coupling between the photons and dye molecules in the cavity is reduced, driving the photon gas out of thermal equilibrium.
This thesis investigates two largely independent topics in many-body and quantum optical physics. The first concerns the thermalization of classical one-dimensional (1D) gases through three-body collisions, while the second explores collective light–matter interactions in atomic arrays and waveguide quantum electrodynamics, with an emphasis on subradiance, superradiance, and computational methods for many-body dynamics. The first part studies thermalization in dilute classical 1D gases, where conventional twobody collisions cannot establish thermal equilibrium. Using Monte Carlo calculations of the three-body collision kernel together with the Boltzmann equation and molecular dynamics simulations, we characterize the thermalization dynamics for particles interacting through inverse power-law and Lennard–Jones potentials. We show that the Boltzmann and molecular dynamics approaches agree in the dilute limit and derive the thermalization rate for inverse power-law interactions.The second part investigates realistic effects in collective light–matter systems. We first study the influence of finite trapping potentials on subradiant states in atomic arrays coupled through free space or a one-dimensional waveguide. We show that atomic motion fundamentally limits subradiant lifetimes through wavefunction delocalization, recoil heating, and dipole-force-induced motion, leading to decoherence and reduced quantum memory fidelity. These results identify optimal trapping and array configurations for long-lived collective excitations.The final chapters develop theoretical methods for describing photon emission in chiral and symmetric waveguide QED systems. Using higher-order mean-field approximations, we model collective emission in experimentally relevant chiral waveguides, obtaining agreement with recent experiments and deriving analytical expressions for photon statistics. We demonstrate that fourth-order correlations are required to capture the emergence of second-order coherence from a fully inverted state. Finally, in the thermodynamic limit of large atom number and fixed optical depth, we show that a second-order mean-field theory becomes exact, yielding analytical solutions for photon emission statistics in both chiral and symmetric waveguides. We characterize the crossover between enhanced superradiant and subradiant emission, establish the suppression of emission fluctuations in the large-system limit, and clarify the role of finite-size effects in generating nontrivial photon correlations.