Photon Bose-Einstein condensates (pBECs) are a platform of interest for both the study of fundamental phenomena in many-body physics and the implementation of next-generation analog simulators for solving optimization problems. In our physical system, the network of coupled pBECs in a microcavity setup is created by individually laser-pumping trap sites that are formed by permanent nanostructuring and connected via waveguides to their nearest neighbours. Due to the roughness and non-flat landscape of the microcavity mirrors, trap sites are excited at different frequencies, making the relative phases undefined. This is crucial for finding the ground state of a network of pBECs - a problem that is NP-complete, which makes this platform a promising candidate for analog optimization problem solver. We propose an approach for in-situ coherence tuning using a permanent nanostructuring technique with active feedback on excited trap site frequencies and report our preliminary results on the creation of an uncoupled coherent network of pBECs using this approach.
Photon Bose-Einstein condensates (pBECs) are a platform of interest for both the study of fundamental phenomena in many-body physics and the implementation of next-generation analog simulators for solving optimization problems. In our physical system, the network of coupled pBECs in a microcavity setup is created by individually laser-pumping trap sites that are formed by permanent nanostructuring and connected via waveguides to their nearest neighbours. Due to the roughness and non-flat landscape of the microcavity mirrors, trap sites are excited at different frequencies, making the relative phases undefined. This is crucial for finding the ground state of a network of pBECs - a problem that is NP-complete, which makes this platform a promising candidate for analog optimization problem solver. We propose an approach for in-situ coherence tuning using a permanent nanostructuring technique with active feedback on excited trap site frequencies and report our preliminary results on the creation of an uncoupled coherent network of pBECs using this approach.
A novel approach to tackling computationally challenging problems involves utilizing a physical system of coupled Bose-Einstein condensates (BEC). The problem of finding a ground state of a network of BECs can be mapped in polynomial time to any problem of the NP-Complete class. In our network, we use photonic BECs (pBECs) [1] which rapidly reach their lowest energy state, typically within a fraction of a nanosecond, after which they can be subjected to interference to extract relative phases. These phases are then interpreted as a solution to the original problem. In our setup, we employ a cavity formed by two highly reflective Bragg mirrors, a dye serving as a thermalizing agent, and a green laser acting as a photon source. Additionally, by nanostructuring [2] one of the mirrors, we achieve transverse confinement of the pBECs. We will present our latest findings on a system of negatively coupled triangular arrangement of pBECs exhibiting spin frustration. References [1] J. Klaers, Nature 468, 545-548 (2010). [2] M. Vretenar, Advanced Optical Materials 11, 2202820 (2023).
Bose-Einstein condensates (BECs), a quantum state of matter formed when bosonic atoms are cooled close to absolute zero, have become the premier platform for investigating fundamental physics with atomic vapours. Experiments on Bose-Einstein condensates now achieve exquisite control over many aspects of the system, including interactions, trapping potential, and dynamics. This has precipitated a new wave of research into many-body quantum phenomena and, in particular, solitons. These structures are fundamental excitations of an interacting non-linear medium, of interest to a multitude of scientific disciplines from non-linear optics to financial markets. The highly controllable environment of BECs form an attractive playground for the study of solitons allowing the non-linearity to be dynamically tuned, facilitating deeper investigations into these structures. Consistently generating and analysing solitons in BEC experiments continues to be problematic. In particular, the non-linear dynamics of BECs, though required for the generation of solitons, produce particularly challenging control and optimization problems. These control problems must be solved before further investigations into the fundamental physics of soliton dynamics can be answered. This thesis makes three important advances in the control and measurement of BECs that will lead to better generation and observation of solitons. (1) a theoretical model for a control scheme capable of highly precise wavefunction engineering, (2) the experimental implementation of a machine learning algorithm for online optimisation, and (3) a continuous non-destructive imaging system capable of directly observing soliton dynamics in real-time. Together, these advances provide a suite of tools for manipulating and exploiting solitons in Bose-Einstein condensates. A novel technique was developed theoretically, offering control of the macroscopic wavefunction of a Bose-Einstein condensate with unprecedented spatial resolution and speed. The ability to control the atomic wavefunction at the fundamental length scale is key to the advancement of many quantum technologies such as quantum simulators. The magnetic resonance control scheme is demonstrated through simulation of a 87Rb condensate with the exemplar model generating a single dark soliton with corresponding π phase kink. The soliton represents a structure at the fundamental length scale of the system, and demonstrates the potential of the scheme for precision state engineering. The scheme is extended to generate higher-order soliton modes which are yet to be experimentally realised. A machine learning algorithm based on Gaussian processes was developed and implemented on the evaporative cooling stage of the production of a 87Rb Bose-Einstein condensate, successfully demonstrating fast optimisation to condensation. The Gaussian process develops a statistical model based on the data that enables the characterisation of the relationship between the experimental controls and resultant quality of the BEC. This relationship is often obfuscated through technical details of the apparatus, frustrating the use of theoretical models to design optimal evaporation ramps. These models often only consider ergodic dynamics with two-body s-wave interactions and no other loss rates with better ramps likely exploiting more complex interactions. The internal model generated from the Gaussian process utilised uncertainty in measured data, making the optimisation more robust to experimental noise than alternate methods. The algorithm is shown to produce high quality Bose-Einstein condensates in 10 times fewer experimental iterations than previously used online optimisation techniques. By exploiting information on the sensitivity of each control, the model can be used to aid experimental design. The convergence of the optimisation is further improved by eliminating a superfluous parameter identified by the model. The general usefulness of machine learning compared with bespoke optimisation algorithms has seen machine learning approach ubiquity. Finally, an experimentally straightforward technique for continuous non-destructive imaging of matter-wave solitons was developed and implemented, facilitating measurements of stochastic phenomena. The technique is readily practicable on any ultracold atom experiment with an existing absorption imaging system, simply requiring the probe laser be far-detuned from resonance. With a signal-to-noise of ∼ 33 at 1.25 GHz detuning, the technique is capable of producing 100 images with no observable heating or atom loss. Coupled with a fast optical phase locked loop, the technique can be used in conjunction with absorption imaging to generate a series of non-destructive images followed by a final high signal-to-noise absorption image solely through moving the laser on resonance for the final image. The high performance and utility of this imaging setup make it a powerful tool for ultra-cold atom experiments.
Josephson junctions are the basis for the most sensitive magnetic flux detectors, the definition of the unit volt by the Josephson voltage standard, and superconducting digital and quantum computing.They result from the coupling of two coherent quantum states, as they occur in superconductors, superfluids, atomic Bose Einstein Condensates (BECs), and exciton-polariton condensates.In their ground state, Josephson junctions are characterized by an intrinsic phase jump.Controlling this phase jump is fundamental for applications in computing.Here, we experimentally demonstrate controllable phase relations between photon BECs resulting from particle exchange in a thermo-optically tunable potential landscape.Our experiment realizes an optical analog of a controllable 0,π -Josephson junction.By connecting several junctions, we can study a reconfigurable 4-condensate system demonstrating the potential of our approach for analog spin-glass simulation.More generally, the combination of static and dynamic nanostructuring techniques introduced in our work offers a powerful platform for the implementation of adaptive optical systems for paraxial light in and outside of thermal equilibrium.
Josephson junctions are the basis for many important fields, such as ultrafast electronics with magnetic flux quanta and superconducting quantum computing. The physical predictions of Josephson junctions are highly universal and can be observed in systems as diverse as coupled superconductors, atomic Bose-Einstein condensates, and others. We experimentally demonstrate tunable tunneling between two photon Bose-Einstein condensates by a targeted shaping of the potential landscape acting on the photons during the tunneling process. The investigated device realizes an optical analogue of a 0,π-Josephson junction, which can act as a building block for an ultrafast all-optical spin glass simulator. The potential landscape in our photon Bose-Einstein condensate Josephson junctions is realized by a combination of direct laser writing for permanent mirror nanostructuring, and heating a thermosensitive polymer for runtime fine tuning of couplings.
Bose-Einstein condensation is a state of matter for which massive bosons develop a macroscopic occupation of the ground state. After the theoretical discovery by Bose and Einstein, it took approximately 70 years to be experimentally realized using Rubidium-87 atoms. Ever since, many different species have been shown to Bose condense. The key in these experiments is cooling down atoms temperatures below 200 nK, while maintaining a large density. Despite all these species, it was thought that photons could not Bose condense. This changed in 2010 when the first Bose-Einstein condensate of photons (phBEC) was achieved. In a table top experiment photons are confined to a dye-filled microcavity where under the right conditions a thermalized photon gas is achieved. Using our setup, we quantitatively show from both the spectral and spatial distribution of photons in the microcavity that a macroscopic occupation of the ground state is achieved, i.e. a condensate of photons. The achievement of phBEC in a dye-filled microcavity has led to a renewed interest in the density distribution of the ideal Bose gas in a two-dimensional harmonic oscillator. We present measurements of the radial profile of photons inside the microcavity below and above the critical point for phBEC with a large signal-to-noise ratio. We obtain good agreement with theoretical profiles obtained using exact summation of eigenstates. An interesting open question is, whether the photons in the condensate are interacting or non-interacting and as a consequence, whether the condensate is also a superfluid or only forms a macroscopically occupied ground state, as predicted by Einstein. When increasing the photon density, we observe an increase in the radius of the condensate which we attribute to effective repulsive interactions. For several dye concentrations we accurately determine the radius of the condensate as a function of the number of condensate photons, and derive from the measurements an effective interaction strength. In many systems ranging from condensed matter physics and particle physics to cosmology, phase transitions and spontaneous symmetry breaking play a crucial role. The information of a polarized condensate from an unpolarized thermal cloud constitutes a directly observable prototype of spontaneous symmetry breaking. For every single-shot of the pump laser, we determine the Stokes parameters of the photons inside the microcavity which fully characterizes the polarization state of the sample. By varying experimental parameters, we investigate if the polarization is randomly chosen from shot-to-shot of the experiment. The dye-filled microcavity is a beautiful tool to achieve phBEC. However, it cannot provide the periodic potential required to achieve quantum phase transitions, such as the Mott insulator that have been so successfully exploited in the field of ultra-cold atoms. We use a local density approach to simulate large-area photonic crystal cavities. Clever interplay with both the electronic and photonic bandgap of these cavities has the potential of achieving phBEC in a periodic potential. We show that when the hole radius varies quadratically as a function of position, the eigenmodes of the photonic crystal can be described by the corresponding eigenmodes of the quantum harmonic oscillator.
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.