Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands.

Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.

Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game.

Device-independent quantum key distribution (DIQKD) is information-theoretically secure against adversaries who possess a scalable quantum computer and who have supplied malicious key-establishment systems; however, the DIQKD key rate is currently too low. Consequently, we devise a DIQKD scheme based on the quantum nonlocal Mermin-Peres magic square game: our scheme asymptotically delivers DIQKD against collective attacks, even with noise. Our scheme outperforms DIQKD using the Clauser-Horne-Shimony-Holt game with respect to the number of game rounds, albeit not number of entangled pairs, provided that both state visibility and detection efficiency are high enough.

Observation of dark edge states in parity-time-symmetric quantum dynamics.

Topological edge states arise in non-Hermitian parity-time ([Formula: see text])-symmetric systems, and manifest themselves as bright or dark edge states, depending on the imaginary components of their eigenenergies. As the spatial probabilities of dark edge states are suppressed during the non-unitary dynamics, it is a challenge to observe them experimentally. Here we report the experimental detection of dark edge states in photonic quantum walks with spontaneously broken [Formula: see text] symmetry, thus providing a complete description of the topological phenomena therein. We experimentally confirm that the global Berry phase in [Formula: see text]-symmetric quantum-walk dynamics unambiguously defines topological invariants of the system in both the [Formula: see text]-symmetry-unbroken and -broken regimes. Our results establish a unified framework for characterizing topology in [Formula: see text]-symmetric quantum-walk dynamics, and provide a useful method to observe topological phenomena in [Formula: see text]-symmetric non-Hermitian systems in general.

Covariant influences for finite discrete dynamical systems.

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be stated as follows: If we evolve the dynamical system for n time steps and then disturb it, then it is the same as first disturbing the system with the same influence and then letting the system evolve for n time steps. Applying the powerful machinery of resource theories, we develop a theory of covariant influences both when there is a purely deterministic evolution and when randomness is involved. Subsequently, we provide necessary and sufficient conditions for the transition between states under deterministic covariant influences and necessary conditions in the presence of stochastic covariant influences, predicting which transitions between states are forbidden. Our approach, for the first time, employs the framework of resource theories, borrowed from quantum information theory, to the study of finite discrete dynamical systems. The laws we articulate unify the behavior of different types of finite discrete dynamical systems, and their mathematical flavor makes them rigorous and checkable.

Topological Spin Texture of Chiral Edge States in Photonic Two-Dimensional Quantum Walks.

Topological insulators host topology-linked boundary states, whose spin and charge degrees of freedom could be exploited to design topological devices with enhanced functionality. We experimentally observe that dissipationless chiral edge states in a spin-orbit coupled anomalous Floquet topological phase exhibit topological spin texture on boundaries, realized via a two-dimensional quantum walk. Our experiment shows that, for a walker traveling around a closed loop along the boundary in real space, its spin evolves and winds through a great circle on the Bloch sphere, which implies that edge-spin texture has nontrivial winding. This topological spin winding is protected by a chiral-like symmetry emerging for the low-energy Hamiltonian. Our experiment confirms that two-dimensional anomalous Floquet topological systems exhibit topological spin texture on the boundary, which could inspire novel topology-based spintronic phenomena and devices.

Microwave-driven generation and group delay control of optical pulses from an ultra-dilute atomic ensemble.

A cyclic atomic level scheme interacting with an optical and a microwave field is proposed for the generation and group-delay control of few-photon optical pulses. Our analysis exploits a hybrid second order-nonlinearity under conditions of electromagnetically induced transparency to generate an optical pulse. The generated pulse can be delayed or advanced through microwave intensity control of the absolute phase of the second-order-nonlinearity. Importantly, this handle on group delay of the generated pulse is number density-independent. Our scheme is thus ideally suited for the generation and control of few-photon optical pulses using ultra-dilute atomic samples. Our results will enable microscopic atomic interface systems that serve as controllable delay channels for both classical and quantum signal processing.

Cloning of Quantum Entanglement.

Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement-a highly nonclassical correlation-remained unexplored. Based on a multiphoton linear optics platform, we demonstrate quantum cloning of two-photon entangled states for the first time. Remarkably our results show that one maximally entangled photon pair can be broadcast into two entangled pairs, both with state fidelities above 50%. Our results are a key step towards cloning of complex quantum systems, and are likely to provide new insights into quantum entanglement.

Nonlinear frequency conversions via weak surface polaritonic wave breaking in a hybrid plasmonic waveguide.

Material design and input field properties limit high-harmonic excitation efficiency of surface-plasmon polaritons (SPPs) in a nanoscopic device. We remedy these limitations by developing a concept for a plasmonic waveguide that exploits spatiotemporal control of a weak surface polaritonic field to create efficient four-wave mixing (FWM) and periodic phase singularities. Our configuration comprises four-level double Λ-type atomic medium (4Λ As) doped in a lossless dielectric situated above a negative-index metamaterial (NIMM) layer. We report the coherent excitation and propagation of the multiple surface polaritonic shock waves (SWs) and establish the highly efficient frequency combs by surface polaritonic wave (SPW) breaking. Consequently, multiple FWM and periodic plasmonic phase singularity patterns generate through nonlinear self-defocusing control commensurate with the plasmonic noise within the atomic electromagnetically induced transparency (EIT) window. Our work introduces SW formation within the subwavelength scale and generates efficient nonlinear frequency conversion, thereby opening prospects for designing fast optical modulators and nonlinear plasmonic gates.

Two-colour interferometry and switching through optomechanical dark mode excitation.

Efficient switching and routing of photons of different wavelengths is a requirement for realizing a quantum internet. Multimode optomechanical systems can solve this technological challenge and enable studies of fundamental science involving widely separated wavelengths that are inaccessible to single-mode optomechanical systems. To this end, we demonstrate interference between two optomechanically induced transparency processes in a diamond on-chip cavity. This system allows us to directly observe the dynamics of an optomechanical dark mode that interferes photons at different wavelengths via their mutual coupling to a common mechanical resonance. This dark mode does not transfer energy to the dissipative mechanical reservoir and is predicted to enable quantum information processing applications that are insensitive to mechanical decoherence. Control of the dark mode is also utilized to demonstrate all-optical, two-colour switching and interference with light separated by over 5 THz in frequency.

Phase-sensitive amplification of an optical field using microwaves.

We report phase-sensitive amplification (PSA) of a near-infrared electromagnetic field using room-temperature 85Rb atoms possessing ground-state coherence. Our novelty is in achieving significant optical PSA by manipulating the intensity and phase of a frequency-separated microwave field. PSA is obtained by inducing a three-wave mixing nonlinear process utilising a three-level cyclic scheme in the D1 manifold. We achieve a near-ideal PSA with a gain of 7 dB over a range of 500 kHz bandwidth with very low pump-field intensities and with low optical depths. Such a hybrid, ground-state-coherence-assisted PSA is the first such demonstration using atomic ensembles.

Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics.

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 [Formula: see text]-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 [Formula: see text] 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.

Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity.

Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication complexity. Recently, a novel quantum resource called the quantum switch-which creates a coherent superposition of the causal order of events, known as quantum causality-has been harnessed theoretically in a new protocol providing provable exponential separation. We experimentally demonstrate such an advantage by realizing a superposition of communication directions for a two-party distributed computation. Our photonic demonstration employs d-dimensional quantum systems, qudits, up to d=2^{13} dimensions and demonstrates a communication complexity advantage, requiring less than (0.696±0.006) times the communication of any causally ordered protocol. These results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.

Spectral singularities of a potential created by two coupled microring resonators.

Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, the coupling for each microring resonator yields two counter-propagating modes with equal frequencies. We show that such a system enables implementation of many types of scattering peculiarities. The spectral singularities, which are either the second or fourth order, separate parameter regions where the spectrum is either purely real or composed of complex eigenvalues; hence, they represent the points of the phase transition. By modifying the gain-loss relation for the resonators, such an optical scatterer can act as a laser, as a coherent perfect absorber, be unidirectionally reflectionless or transparent, and support bound states either growing or decaying in time. These characteristics are observed for a discrete series of the incident-radiation wavelengths.

Observation of Topologically Protected Edge States in a Photonic Two-Dimensional Quantum Walk.

Periodically driven systems have displayed a variety of fascinating phenomena without analogies in static systems, which enrich the classification of quantum phases of matter and stimulate a wide range of research interests. Here, we employ discrete-time quantum walks to investigate a nontrivial topological effect unique to a two-dimensional periodically driven system: chiral edge states can exist at the interface of Floquet insulators whose Chern numbers vanish. Thanks to a resource-saving and flexible fiber-loop architecture, we realize inhomogeneous two-dimensional quantum walks up to 25 steps, over an effective 51×51 lattice with tunable local parameters. Spin-polarized chiral edge states are observed at the boundary of two distinct quantum walk domains. Our results contribute to establishing a well-controlled platform for exploring nontrivial topological phases.

Ab initio characterization of coupling strength for all types of dangling-bond pairs on the hydrogen-terminated Si(100)-2 × 1 surface.

Recent work has suggested that coupled silicon dangling bonds sharing an excess electron may serve as building blocks for quantum-cellular-automata cells and quantum computing schemes when constructed on hydrogen-terminated silicon surfaces. In this work, we employ ab initio density-functional theory to examine the details associated with the coupling between two dangling bonds sharing one excess electron and arranged in various configurations on models of phosphorous-doped hydrogen-terminated silicon (100) surfaces. Our results show that the coupling strength depends strongly on the relative orientation of the dangling bonds on the surface and on the separation between them. The orientation of dangling bonds is determined by the anisotropy of the silicon (100) surface, so this feature of the surface is a significant contributing factor to variations in the strength of coupling between dangling bonds. The results demonstrate that simple models for approximating tunneling, such as the Wentzel-Kramer-Brillouin method, which do not incorporate the details of surface structure, are incapable of providing reasonable estimates of tunneling rates between dangling bonds. The results provide guidance to efforts related to the development of dangling-bond based computing elements.

Uncover Topology by Quantum Quench Dynamics.

Topological quantum states are characterized by nonlocal invariants. We present a new dynamical approach for ultracold-atom systems to uncover their band topology, and we provide solid evidence to demonstrate its experimental advantages. After quenching a two-dimensional (2D) Chern band, realized in an ultracold ^{87}Rb gas from a trivial to a topological parameter regime, we observe an emerging ring structure in the spin dynamics during the unitary evolution, which uniquely corresponds to the Chern number for the postquench band. By extracting 2D bulk topology from the 1D ring pattern, our scheme displays simplicity and is insensitive to perturbations. This insensitivity enables a high-precision determination of the full phase diagram for the system's band topology.

Detecting Topological Transitions in Two Dimensions by Hamiltonian Evolution.

We show that the evolution of two-component particles governed by a two-dimensional spin-orbit lattice Hamiltonian can reveal transitions between topological phases. A kink in the mean width of the particle distribution signals the closing of the band gap, a prerequisite for a quantum phase transition between topological phases. Furthermore, for realistic and experimentally motivated Hamiltonians, the density profile in topologically nontrivial phases displays characteristic rings in the vicinity of the origin that are absent in trivial phases. The results are expected to have an immediate application to systems of ultracold atoms and photonic lattices.

Experimental Blind Quantum Computing for a Classical Client.

To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.

Strong Coherent Light Amplification with Double Electromagnetically Induced Transparency Coherences.

We experimentally demonstrate coherent amplification of probe field in a tripod-type atoms driven by strong coupling, signal and weak probe fields. We suppress linear and nonlinear atomic absorptions for resonant and near resonant probe via double electromagnetically induced transparency (DEIT). Combining these advantages of suppressed absorption along with temperature- or atomic-density-controlled transfer of population(ToP) between hyperfine ground states, we can induce near-resonant amplification of probe through stimulated Raman scattering(SRS) pumped by low-intensity signal field. The increased population difference of initial and final states of SRS due to increased ToP rate, together with reduced absorption at the second EIT window in an optically thick Cesium vapor, gives rise to highly effective coherent amplification.

Unity-Efficiency Parametric Down-Conversion via Amplitude Amplification.

We propose an optical scheme, employing optical parametric down-converters interlaced with nonlinear sign gates (NSGs), that completely converts an n-photon Fock-state pump to n signal-idler photon pairs when the down-converters' crystal lengths are chosen appropriately. The proof of this assertion relies on amplitude amplification, analogous to that employed in Grover search, applied to the full quantum dynamics of single-mode parametric down-conversion. When we require that all Grover iterations use the same crystal, and account for potential experimental limitations on crystal-length precision, our optimized conversion efficiencies reach unity for 1≤n≤5, after which they decrease monotonically for n values up to 50, which is the upper limit of our numerical dynamics evaluations. Nevertheless, our conversion efficiencies remain higher than those for a conventional (no NSGs) down-converter.