Equilibrium And Non-equilibrium Phenomena In Photonic Quantum Walks

A quantum system can be in a equilibrium or non-equilibrium state.Because it will inevitably be affected by the environment and interact with each other,almost all quantum systems will be in a non-equilibrium state to a certain extent in practical quan-tum information processes.When a quantum system is close enough to equilibrium,it can be described exactly by current quantum statistical mechanics.After the discov-ery of integer quantum Hall effect in the year of nineteen eighty,although the study of quantum phase and topological phase in condensed matter physics have achieved great success,most of them are limited to such equilibrium and static systems,and their non-equilibrium dynamics has not drawn much attention.Because of the rapid development of artificial quantum simulations based on cold atoms,trapped ions and linear optics,as well as the advances in theoretical physics,they again become a focus of attention recently.Better understanding of non-equilibrium phenomena could lead to new meth-ods for generating light-induced topology and superconductivity and new insights into the quantum origin of thermodynamics.Quantum walks represent a promising versatile platform for quantum information processes,and can be used as an equilibrium and non-equilibrium quantum simula-tion.It was usually realized by the cold atoms in optical lattices and photonic systems.Many degrees of freedom of photons,such as polarization,path,time and orbital angu-lar momentum,can be well controlled to implement quantum walks.The linear optical schemes have a long coherent time and can be manipulation easily at room temper-ature.Furthermore,integration with optical fiber and waveguide technology is also feasible.Thus,photonic quantum walk plays an important role in quantum simulation and quantum computation.The main research works of my doctoral dissertation based on photonic quantum walks are as follows:??Using the time-multiplexed technique to develop a novel large-scale quan-tum walks with genuine single photonsWe implement experimentally a photonic quantum walk using the polarization and time degree of freedom of photons as the walker's coin and discrete position space.Fun-damentally,the spin-orbit coupling is implemented via a birefringent crystal collinearly cut based on a time-multiplexing scheme.Our protocol is compact and avoids extra loss,making it suitable for realizing genuine single-photon quantum walks at a large scale.By adopting a heralded single photon as the walker and with a high time resolution technology in single-photon detection,we carry out a fifty-step Hadamard discrete-time quantum walk with high fidelity up to 0.948 ± 0.007.??Equilibrium quantum simulation based on photonic quantum walks1.In general,the topology of system is characterized by the bulk topological in-variant defined in the ground state at equilibrium.Through the reconstruction of the complete wave function of walker in real space and a Fourier transform,we can obtain the eigenvectors of the system Hamiltonian in quasimomentum space and directly read out the winding numbers in different topological phases.By introducing two nonequiva-lent time frames,we can completely classify the topological phase in periodically driven system.2.The deep connection between the entanglement entropy and band topology can be used to real the equilibrium topology phase.We use the local quantum state tomog-raphy to reconstruct the reduced density matrix of the coin.And,based on its eigen-value spectrum,we then analyze the dynamics of entanglement between two degrees of freedom toward equilibrium under different quantum-walk scenarios.It is found exper-imentally that the robustness of entanglement at equilibrium can be used as a signature of detecting topological phases and their boundaries.??Non-equilibrium quantum simulation based on photonic quantum walks1.Because the practical quantum systems always interact with the environment to a certain extent,investigations of the non-equilibrium behaviours is a key problem in practical quantum information process.Through the wave-function reconstruction technique,we measure the dynamical topological order parameter(DTOP).Then,the quantum quenches in quantum walk can be classified by the qualitatively different tem-poral behavior of the DTOP.Upon identifying an equivalent many-body problem,we reveal an intriguing connection between the nonanalytic changes of the DTOP and the occurrence of dynamical quantum phase transitions.2.Generally,the topological invariants defined in equilibrium systems through their ground-state manifold cannot be directly applied to the topological systems far from equilibrium.We construct the momentum-time manifold and then measure the dynamical Chern number appearing in different quantum quenches of quantum walks.Moreover,our results demonstrate further its relation to equilibrium topological bulk in-variants associated with quenched quantum walks between different topological phases.While both of the integer-quantized numbers,i.e.,DTOP and dynamical Chern num-ber,can be used to classify the quantum quench,our results clearly show they are totally different.3.Understanding the dynamical equilibrium of isolated quantum systems driven out of equilibrium by quenches and its statistical ensemble predication is an important topic in non-equilibrium physics.Herein,in an isolated integrable quantum-walk sys-tem,we experimentally observed that the relaxation of the coin subsystem of interest always agrees with the prediction of the diagonal ensemble of the mutual eigenstates.Importantly,by applying the quantum state engineering and eigenvectors reconstruc-tion techniques,the generalized eigenstate thermalization hypothesis(GETH)has been verified.We further demonstrated that the combination of the GETH and the diagonal ensemble can be used to understand the generalized thermalization,i.e.,the local ob-servables in integrable systems can relax to the generalized Gibbs ensemble prediction.