Fundamental tests of quantum mechanics in optical waveguides

Quantum mechanics is one of the most successful theories in physics, governing practically all processes in the microscopic world and even affecting many phenomena on a mesoscopic scale. Its predictions have been in excellent agreement with all experimental observations made throughout what has been almost an entire century. Yet, as all theories, quantum mechanics relies on several axioms which cannot be theoretically proven. Hence, they can only and must be tested against experiments. One of these axioms is Born`s rule, relating the abstract concept of a wave function, a core feature of the theory, to the physically measurable quantity of probability. Another axiom postulates that states of physical systems are represented by complex vectors in configuration space, implying that their wave functions are complex functions. Both axioms can be tested in the domain of optics with one and the same experimental approach: multi-path interferometry with photons. In fact, this is the most advanced method for a test of Borns rule to date, mastered by the co-applicant Prof. Weihs and his group at the host institution, who are world leaders in this field. Their experiments in free-space interferometers have found no trace of a violation and confirmed it within certain bounds. These bounds depend on the experimental uncertainties and cannot be refined easily due to issues of stability in these setups. Moreover, a test of the axiom of complexity has so far been impossible due to the limited degree of coherence in free-space interferometers. The aim of this proposal is to transfer multi-path interferometry into the field of integrated optics which offers superior stability and coherence. To this end, laser-written optical waveguide multi- path-interferometers will be developed and utilised. This will allow an experimental test of Borns rule with substantially enhanced precision and accuracy and, thereby, a refinement of the violation bounds by at least two orders of magnitude. Moreover, due to the improved coherence of the waveguide interferometers the first ever experimental test of the complexity axiom against generalised models will come into reach. The outcome of the research will explore the boundaries of quantum mechanics and help to distinguish the theory against possible generalisations. The applicant, Dr. Keil, is a proven expert in integrated optics. His background knowledge and research experience will make the desired transfer possible and be a perfect match to the hosts group. Moreover, he will maintain a close connection to his previous group around Prof. Szameit, University of Jena, where the fabrication of the waveguide devices will take place. This will set up a new collaboration between the groups and provide the host with long-term access to advanced waveguide fabrication technology.

This project investigated the foundations of quantum physics. One goal was to determine with highest possible accuracy and precision whether the interference of light particles, termed photons, travelling along three or more beam lines in an interferometer follows the rules given by the established quantum theory or whether deviations from this theory, in form of so-called higher-order interferences, occur. In the latter case, these deviations would identify a weak point in the theory and could lead to new, more accurate descriptions of the microscopic world. Prior to this project, several experiments in this direction had been carried out by scientists around the world. All of them found the interference signals to be in accordance with the standard theory, the most precise one with a relative precision of about three parts in a thousand. Even without a violation of the standard theory, this precision is an important quantity, as it determines the largest possible values for key parameters in alternative, generalised quantum theories. In our work we also found no violation of quantum theory. However, we could improve the relative precision by a factor of 100 to 30 parts per million, setting the new record for this type of experiment. This has been achieved in a specially designed and stabilised optical interferometer with bulk optical elements, in particular holographic beam-splitters and lenses. For a similar experiment testing whether quantum physics should be better described by complex numbers or their more complicated higher-dimensional relatives (so-called quaternions), one needs interferometers with yet higher stability (especially on short time scales). Therefore, another goal of this project was to develop interferometers in optical waveguides, where the photons can travel only along hard-wired paths in a microchip, which promise potentially higher stabilities. The challenge in such waveguide interferometers, however, lies in the inherent difficulty to externally influence the propagation of light inside the chip, which is required to run either type of experiment. In the course of this project, we have subsequently developed two such interferometers and performed measurements testing their performance. We could show that their stability is high enough to avoid crucial undesired systematic errors, which arose from the limited short-term stability in bulk-optical interferometers. However, due to some not yet fully understood effects, other systematic errors influence our results, such that the test of complex numbers vs. quaternions cannot yet be performed. For the experimental test of higher-order interference we achieve a relative precision of 0.6 per mille, which lies in between the previously reported values and the precision of our bulk-optical device. We are currently working towards improving this precision further and we are investigating the origin of the systematic errors.