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.
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.
Trapping photons in a dye high-Q microcavity comprising two dielectric mirrors allows for studying Bose-Einstein condensation (BEC) of the two-dimensional photon gas under ambient conditions. Adding polymer nanostructures on the surface of the mirrors by direct laser writing provides additional trapping potentials for the photon gas. As the dimensionality of a system profoundly influences its physical behavior, trapping potentials with different effective dimensionality allow to study the modifications of the behavior for the 2d-1d transition. Here, we experimentally study the properties of a harmonically trapped photon gas undergoing Bose-Einstein condensation along this dimensional crossover. By varying the aspect ratio of the harmonic trap, we tune from an isotropic two-dimensional confinement to an anisotropic, highly elongated one-dimensional trapping potential. We discuss the fabrication of the micro potential on the highly reflective dielectric mirrors and determine the caloric properties of the photon gas and discuss prospects of our polymer-based potential landscapes.
Abstract Photon Bose–Einstein condensates are characterised by a quite weak interaction, so they behave nearly as an ideal Bose gas. Moreover, since the current experiments are conducted in a microcavity, the longitudinal motion is frozen out and the photon gas represents effectively a two-dimensional trapped gas of massive bosons. In this paper we focus on a harmonically confined ideal Bose gas in two dimensions, where the anisotropy of the confinement allows for a dimensional crossover. If the confinement in one direction is strong enough so that this squeezed direction is frozen out, then only one degree of freedom survives and the system can be considered to be quasi-one dimensional. In view of an experimental set-up we work out analytically the thermodynamic properties for such a system with a finite number of photons. In particular, we focus on examining the dimensional information which is contained in the respective thermodynamic quantities.
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 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.
The equilibrium properties of a weakly interacting atomic Bose gas across the Berezinskii-Kosterlitz-Thouless (BKT) and Bose-Einstein condensation (BEC) phase transitions are numerically investigated through a dimensionality crossover from two to three dimensions. The crossover is realized by confining the gas in an experimentally feasible hybridized trap which provides homogeneity along the planar xy directions through a box potential in tandem with a harmonic transverse potential along the transverse z direction. The dimensionality is modified by varying the frequency of the harmonic trap from tight to loose transverse trapping. Our findings, based on a stochastic (projected) Gross-Pitaevskii equation, showcase a continuous shift in the character of the phase transition from BKT to BEC, and a monotonic increase of the identified critical temperature as a function of dimensionality, with the strongest variation exhibited for small chemical potential values up to approximately twice the transverse confining potential.
Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow the quantification of the degree of order and the classification of different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at and above the critical particle number for Bose-Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity. For the uncondensed gas, the transverse coherence decays on a length scale determined by the thermal de Broglie wavelength of the photons, which shows the expected scaling with temperature. At the onset of Bose-Einstein condensation, true long-range order emerges, and we observe quantum statistical effects as the thermal wave packets overlap. The excellent agreement with equilibrium Bose gas theory prompts microcavity photons as promising candidates for studies of critical scaling and universality in optical quantum gases.Phase transitions in quantum matter are related to correlation effects and they can change the ordering of material. Here the authors measure the first-order spatial correlation and the de Broglie wavelength for both thermal and condensed form of a photonic Bose gas in a dye-filled optical microcavity.