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Register a new userTopological edge states of interacting photon pairs emulated in a topolectrical circuit
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Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities can be achieved by realizing topological states of quantum light. This area, however, remains largely uncharted due to the number of experimental challenges. Here, we take an alternative route and design a classical structure based on topolectrical circuits which serves as a simulator of a quantum-optical one-dimensional system featuring the topological state of two photons induced by the effective photon-photon interaction. Employing the correspondence between the eigenstates of the original problem and circuit modes, we use the designed simulator to extract the frequencies of bulk and edge two-photon bound states and evaluate the topological invariant directly from the measurements. Furthermore, we perform a reconstruction of the two-photon probability distribution for the topological state associated with one of the circuit eigenmodes.
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Electromagnetic signals are always composed of photons, though in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photons energy is usually not evident. However, by coupling a superconducting qubit to signals on a microwave transmission line, it is possible to construct an integrated circuit where the presence or absence of even a single photon can have a dramatic effect. This system is called circuit quantum electrodynamics (QED) because it is the circuit equivalent of the atom-photon interaction in cavity QED. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit can absorb and re-emit a single photon many times. Here, we report a circuit QED experiment which achieves the strong dispersive limit, a new regime of cavity QED in which a single photon has a large effect on the qubit or atom without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability to find the corresponding photon number in the cavity. This effect has been used to distinguish between coherent and thermal fields and could be used to create a photon statistics analyzer. Since no photons are absorbed by this process, one should be able to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.
Recent theoretical studies have extended the Berry phase framework to account for higher electric multipole moments, quadrupole and octupole topological phases have been proposed. Although the two-dimensional quantized quadrupole insulators have been demonstrated experimentally, octupole topological phases have not previously been observed experimentally. Here we report on the experimental realization of classical analog of octupole topological insulator in the electric circuit system. Three-dimensional topolectrical circuits for realizing such topological phases are constructed experimentally. We observe octupole topological states protected by the topology of the bulk, which are localized at the corners. Our results provide conclusive evidence of a form of robustness against disorder and deformation, which is characteristic of octupole topological insulators. Our study opens a new route toward higher-order topological phenomena in three-dimensions and paves the way for employing topolectrical circuitry to study complex topological phenomena.
We constructed an electrical circuit to realize a modified Haldane lattice exhibiting the unusual phenomenon of antichiral edge states. The circuit consists of a network of inductors and capacitors with interconnections reproducing the effects of a magnetic vector potential. The next nearest neighbor hoppings are configured differently from the standard Haldane model, and as predicted by earlier theoretical studies, this gives rise to antichiral edge states that propagate in the same direction on opposite edges and co-exist with bulk states at the same frequency. Using pickup coils to measure the voltage distributions in the circuit, we experimentally verify the key features of the modified Haldane lattice, including the group velocities of the antichiral edge states.
Recently, the theory of quantized dipole polarization has been extended to account for electric multipole moments, giving rise to the discovery of multipole topological insulators (TIs). Both two-dimensional (2D) quadrupole and three-dimensional (3D) octupole TIs with robust zero-dimensional (0D) corner states have been realized in various classical systems. However, due to the intrinsic 3D limitation, the higher dimensional multipole TIs, such as four-dimensional (4D) hexadecapole TIs, are supposed to be extremely hard to construct in real space, although some of their properties have been discussed through the synthetic dimensions. Here, we theoretically propose and experimentally demonstrate the realization of classical analog of 4D hexadecapole TI based on the electric circuits in fully real space. The explicit construction of 4D hexadecapole circuits, where the connection of nodes is allowed in any desired way free from constraints of locality and dimensionality, is provided. By direct circuit simulations and impedance measurements, the in-gap corner states protected by the quantized hexadecapole moment in the 4D circuit lattices are observed and the robustness of corner state is also demonstrated. Our work offers a new pathway to study the higher order/dimensional topological physics in real space.
A system is non-Hermitian when it exchanges energy with its environment and non-reciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.
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