Quantum walks are the quantum mechanical analog to classical random walks. However, due to the wavelike nature of quantum particles, they reveal drastically different dynamics compared to their classical counterpart. These unique properties make quantum walks a new promising platform for quantum algorithms and a powerful tool to understand complex transport phenomena. This thesis presents three experiments specifically designed to send photons on a quantum walk. The experiments are based on a fiber network spreading the photonic wave packets over discrete time bins. With these Quantum Walks in Time we simulate the propagation of quantum particles in various different environments, revealing diverse dynamics such as a fast ballistic spread and an Anderson-like localization effect. Furthermore we use our concept to implement the first quantum walk on a two-dimensional lattice. The underlying topology allows for investigations of the intriguing dynamics of two strongly interacting quantum particles, which reveals unique effects such as the creation of bound states.
Quantum walks are the quantum mechanical analog to classical random walks. However, due to the wavelike nature of quantum particles, they reveal drastically different dynamics compared to their classical counterpart. These unique properties make quantum walks a new promising platform for quantum algorithms and a powerful tool to understand complex transport phenomena. This thesis presents three experiments specifically designed to send photons on a quantum walk. The experiments are based on a fiber network spreading the photonic wave packets over discrete time bins. With these Quantum Walks in Time we simulate the propagation of quantum particles in various different environments, revealing diverse dynamics such as a fast ballistic spread and an Anderson-like localization effect. Furthermore we use our concept to implement the first quantum walk on a two-dimensional lattice. The underlying topology allows for investigations of the intriguing dynamics of two strongly interacting quantum particles, which reveals unique effects such as the creation of bound states.
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.
Photonics provide an efficient way to implement quantum walks, the quantum analog of classical random walks, which demonstrate rich physics with potential applications. However, most photonic quantum walks do not involve photon interactions, which limits their potential to explore strongly correlated many-body physics of light. We propose a strongly interacting discrete-time photonic quantum walk using a network of single atom beamsplitters. We calculate output statistics of the quantum walk for the case of two photons, which reveals the strongly correlated transport of photons. Particularly, the walk can exhibit either bosonlike or fermionlike statistics which is tunable by postselecting the two-photon detection time interval. Also, the walk can sort different types of two-photon bound states into distinct pairs of output ports under certain conditions. These unique phenomena show that our quantum walk is an intriguing platform to explore strongly correlated quantum many-body states of light. Finally, we propose an experimental realization based on time-multiplexed synthetic dimensions. Published by the American Physical Society 2024
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
Multidimensional quantum walks can exhibit highly nontrivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a two-dimensional (2D) optical quantum walk on a lattice, demonstrating a scalable quantum walk on a nontrivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions by using an optical fiber network. With our broad spectrum of quantum coins, we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong nonlinearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems.
Random processes are ubiquitous in the natural world as well as in man-made environments. While classical random walks may behave highly complex or even chaotic, there outcome can, in principle, always be predicted from the parameters of the system and the initial conditions. In the realm of quantum mechanics, however, this is not possible as the underlying wave mechanics leads to intrinsically indeterministic outcomes. Moreover, if multiple indistinguishable particles are subjected to such a quantum random walk, their exchange symmetry causes quantum interference, thereby enriching the dynamics of the system even further. \nIn this work, quantum random walks of pairs of indistinguishable photons, the quanta of light, are investigated. Networks of coupled optical waveguides are chosen as the experimental platform of choice, offering a high degree of coherence and versatility. In these photonic lattices, light propagates along one spatial dimension, whereas the individual waveguides are connected by evanescent coupling in the transverse dimensions. \nIn particular, it is investigated how the various degrees of freedom, which are available in such photonic lattices, affect the trajectories in the quantum walks and their complexity. It is shown how the facilitation of both transverse dimensions allows for much richer quantum walks with properties unencountered in planar arrangements. But even if just a single transverse dimension is available, the coupling properties of the lattice along this dimension are a potent degree of freedom, which can be used to manipulate the quantum walk. Finally, an experimental technique is developed which enables a convenient characterisation of the expected quantum walk in an arbitrary waveguide lattice by classical light. \nThe thesis concludes with a summary of the results and an outlook onto further developments in the field.
Photonics provide an efficient way to implement quantum walks, the quantum analogue of classical random walk that demonstrates rich physics with potential applications. However, most photonic quantum walks do not involve photon interactions, which limits their potential to explore strongly-correlated many-body physics of light. We propose a strongly interacting discrete-time photonic quantum walk using a network of single atom beamsplitters. We calculate output statistics of the quantum walk for the case of two photons, which reveals the strongly-correlated transport of photons. Particularly, the walk can exhibit either boson-like or fermion-like statistics which is tunable by post-selecting the two-photon detection time interval. Also, the walk can sort different types of two-photon bound states into distinct pairs of output ports under certain conditions. These unique phenomena show that our quantum walk is an intriguing platform to explore strongly-correlated quantum many-body states of light. Finally, we propose an experimental realization based on time-multiplexed synthetic dimensions.