No abstract

Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.

Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic topological order parameters (DTOPs). In this work, we report the experimental study of DQPTs using discrete-time quantum walks of single photons. We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics, and experimentally characterize DQPTs and the underlying DTOPs through interferencebased measurements. The versatile photonic quantum-walk platform further allows us to experimentally investigate DQPTs for mixed states and in parity-time-symmetric non-unitary dynamics for the first time. Our experiment directly confirms the relation between DQPTs and DTOPs in quench dynamics of a topological system, and opens up the avenue of simulating emergent topological phenomena using discrete-time quantum-walk dynamics.

We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.

We experimentally simulate non-unitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time (PT )-symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT -symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT -unbroken andbroken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in PT -symmetric non-unitary quantum dynamics.

We show that a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flips and extend this method to the distribution of an arbitrary unknown multiqubit entangled state between every pair of sites in the multidimensional network. Furthermore, we study the routing of quantum information on this network in a quantum-walk architecture, which can be used as quantum information processors to communicate between separated qubits.

We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two periodic revivals of the walker distribution. In our beam-displacer interferometer, the walk corresponds to movement between discretely separated transverse modes of the field serving as lattice sites, and the time-dependent coin flip is effected by implementing a different angle between the optical axis of half-wave plate and the light propagation at each step. Each of the quantum-walk steps required to realize a revival comprises two sequential orthogonal coin-flip operators, with one coin having constant bias and the other coin having a time-dependent ramped coin bias, followed by a conditional translation of the walker. [4][5][6] plus the fundamental interest of being a natural quantized version of the ubiquitous random walk that appears in statistics, computer science, finance, physics, and chemistry. QW research has focused on evolution due to repeated applications of a time-independent unitary step operator U , but a QW with time-dependent unitary steps U (t), with discrete time t ∈ N := {0, 1, 2, . . . }, opens a much richer array of phenomena including localization and quasiperiodicity [7,8]. Here we demonstrate a time-dependent QW and use this technique to demonstrate a revival of the walker's position distribution.Rather than employing direct time-dependent control, we simulate time-dependent coin control by setting different coin parameters for different steps, which are effected in different locations along the longitudinal axis within our photonic beam-displacer interferometer (BDI) [9]. The quantum walker within the BDI is a single heralded photon produced by spontaneous parametric down conversion, and its walking degree of freedom is the set of discretely spaced transverse beam modes. The coin flip is effected by employing quarter-and half-wave plates.Our method for realizing the first time-dependent QW demonstrates the phenomenon of revivals and also opens the door to realizing a multitude of time-dependent QWs experimentally. Compared to prior work employing position-dependent control [10][11][12], our new technique decreases experimental complexity by relaxing the requirement of optical compensation. Our QW revival displays a different characteristic than typical QW properties such as ballistic spreading and localization of the walker distribution.The QW with a coin proceeds as a sequence of coin flips and then walker-coin entangling operations whereby the walker's position is displaced according to the coin state. We explain the QW now in full generality so the coin operator admits both spatial and temporal dependence. Spatially-dependent coin operations have dramatically demonstrated the realization of topological phases by QWs [4][5][6], but the time-dependent QW is, until now, only a theoretical construct and not yet explored experimentally.We employ a two...

Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we theoretically characterize and experimentally detect momentum-time skyrmions in parity-time -symmetric non-unitary quench dynamics in single-photon discrete-time quantum walks. The emergent skyrmion structures are protected by dynamic Chern numbers defined for the emergent two-dimensional momentum-time submanifolds, and are revealed through our experimental scheme enabling the construction of time-dependent non-Hermitian density matrices via direct measurements in position space. Our work experimentally reveals the interplay of symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.