Many-particle interference in symmetric scattering scenarios

The project entitled Many-particle interference in symmetric scattering scenarios is focused on the collective behaviour of identical particles, which do not interact with each other (such as photons, the quanta of light, with identical colour and polarisation). When such particles are impinging on a scattering object (e.g., a beam splitter or a ground glass), they get spatially redistributed in a manner which depends on both, the structure of the scattering object as well as the type of the particle. Usually, the particles do not scatter individually, but exhibit a collective dynamics, called many- particle interference, which arises from the laws of quantum mechanics for identical particles. Calculating the probabilities for all possible outcomes becomes highly non-trivial for an increasing number of particles and scattering directions, as all possibilities of which particle took which path have to be taken into account. This project investigates for which symmetries of the scattering material the calculation can be simplified and a so-called suppression law can be derived. These are relatively simple formulas predicting which output configurations of the particles are ruled out by the symmetry, regardless of other details of the structure or the particle number. There are only four special cases of such suppression laws, which are already known, and only two of them have been demonstrated in an experiment. Our aims are to: 1. Find by theoretical calculations a generalised suppression law to unify all known cases in the framework of a more general symmetry 2. Experimentally demonstrate the suppression law for two known scenarios, which have so far been unobserved, via scattering of four photons in an optical waveguide chip 3. Improve the precision and accuracy of these experiments by building a brighter photon source using the latest semiconductor technology. Our work will substantially improve researchers understanding of the impact of symmetries on many-particle interference. This is, first of all, very interesting on a fundamental level. Moreover, these results may be useful in the long term for verifying the correct operation of quantum computers or provide tools for improving the quality and efficiency of information or energy transfer in artificial structures. In order to reach our goal number two, we will also require a new technological development in polarisation control in optical waveguides, which may lead to new applications in imaging, information processing or sensing in compact optical chips. Four our third goal, we will develop artificial atoms, called quantum dots, made from gallium arsenide (a semiconductor material), which can produce single photons with properties compatible to existing technology and with unprecedented brightness. Such devices could be used in the future as light sources for quantum communication, quantum metrology and optical quantum computing.

In this project we investigated the influence of symmetries on the collective behaviour of identical photons. The laws of quantum physics dictate that when several photons are identical, i.e., they cannot be distinguished by any internal property, such as colour or polarisation, their joint propagation characteristics can no longer be understood from their individual dynamics alone. Instead, an effect called multi-particle interference arises, which leads to complex mutual dependencies of the photons' propagation patterns. This rich multi-photon dynamics lies at the heart of several recent breakthroughs in photonic quantum computing. In our project, we aimed for simplification rather than complexity. That is, we investigated the conditions, which are needed to obtain fully-destructive interference scenarios, where certain output patterns disappear completely. Out theory work was successful in linking these so-called suppressions with symmetries in the material through which the photons are propagating. Specifically, we have unified some previously known cases by formulating a generalised suppression law. In experiments with up to four photons we could then demonstrate some intricate consequences of the generalised suppression law: As it turns out, not all photons need to be indistinguishable in order for a suppression to occur, but only those, which are linked by the symmetry. This has important consequences in the certification of multi-photon quantum interference protocols. In another work, we developed a tailored optical waveguide structure, which connects the spatial and polarisation degrees of freedom of light, to investigate the interference condition in highly symmetric hypercubes. This first generation of multi-photon interference experiments was carried out with an established photon source technique known as spontaneous parametric down-conversion. This technique has the drawback of a not sharply defined number of emitted photons, as the brightness is increased. We aimed to overcome this drawback by instead using semiconductor quantum dots as photon sources, which can only emit one photon at a time due to their internal structure, thus overcoming the photon number uncertainty. One complication with quantum dots is that the emitters are residing in high refractive index material, which strongly limits their outcoupling efficiency. We developed some cavity and antenna structures, which helped to boost the efficiency, yet more work needs to be done along these lines to reach sufficient brightness for the effective use of these sources in multi-photon interference experiments. A second issue with these sources is that the photons are emitted one after another, while for multi-photon interference one requires these photons in separate spatial channels. We succeeded in solving this problem, by setting up a fast and efficient demultiplexing stage, which sends up to four subsequently emitted photons in separate spatial channels, such that they can be readily used for interference.