Experimental study of modified Tavis-Cummings model with directly-coupled superconducting artificial atoms.

The Tavis-Cummings model is intensively investigated in quantum optics and has important applications in generation of multi-atom entanglement. Here, we employ a superconducting circuit quantum electrodynamic system to study a modified Tavis-Cummings model with directly-coupled atoms. In our device, three superconducting artificial atoms are arranged in a chain with direct coupling through fixed capacitors and strongly coupled to a transmission line resonator. By performing transmission spectrum measurements, we observe different anticrossing structures when one or two qubits are resonantly coupled to the resonator. In the case of the two-qubit Tavis-Cummings model without qubit-qubit interaction, we observe two dips at the resonance point of the anticrossing. The splitting of these dips is determined by Δ λ=2g12+g32, where g1 and g3 are the coupling strengths between Qubit 1 and the resonator, and Qubit 3 and the resonator, respectively. The direct coupling J12 between the two qubits results in three dressed states in the two-qubit Tavis-Cummings model at the frequency resonance point, leading to three dips in the transmission spectrum. In this case, the distance between the two farthest and asymmetrical dips, arising from the energy level splitting, is larger than in the previous case. The frequency interval between these two dips is determined by the difference in eigenvalues (Δ λ=ε 1+-ε 1-), obtained through numerical calculations. What we believe as novel and intriguing experimental results may potentially advance quantum optics experiments, providing valuable insights for future research.

Simulating Chern insulators on a superconducting quantum processor.

The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions on a programable 30-qubit-ladder superconducting processor. We directly measure the band structures of the 2D Chern insulator along synthetic dimensions with various configurations of Aubry-André-Harper chains and observe dynamical localisation of edge excitations. With these two signatures of topology, our experiments implement the bulk-edge correspondence in the synthetic 2D Chern insulator. Moreover, we simulate two different bilayer Chern insulators on the ladder-type superconducting processor. With the same and opposite periodically modulated on-site potentials for two coupled chains, we simulate topologically nontrivial edge states with zero Hall conductivity and a Chern insulator with higher Chern numbers, respectively. Our work shows the potential of using superconducting qubits for investigating different intriguing topological phases of quantum matter.

Quantum Simulation of Topological Zero Modes on a 41-Qubit Superconducting Processor.

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-André-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.

Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole.

Hawking radiation is one of the quantum features of a black hole that can be understood as a quantum tunneling across the event horizon of the black hole, but it is quite difficult to directly observe the Hawking radiation of an astrophysical black hole. Here, we report a fermionic lattice-model-type realization of an analogue black hole by using a chain of 10 superconducting transmon qubits with interactions mediated by 9 transmon-type tunable couplers. The quantum walks of quasi-particle in the curved spacetime reflect the gravitational effect near the black hole, resulting in the behaviour of stimulated Hawking radiation, which is verified by the state tomography measurement of all 7 qubits outside the horizon. In addition, the dynamics of entanglement in the curved spacetime is directly measured. Our results would stimulate more interests to explore the related features of black holes using the programmable superconducting processor with tunable couplers.

Observation of entanglement transition of pseudo-random mixed states.

Random quantum states serve as a powerful tool in various scientific fields, including quantum supremacy and black hole physics. It has been theoretically predicted that entanglement transitions may happen for different partitions of multipartite random quantum states; however, the experimental observation of these transitions is still absent. Here, we experimentally demonstrate the entanglement transitions witnessed by negativity on a fully connected superconducting processor. We apply parallel entangling operations, that significantly decrease the depth of the pseudo-random circuits, to generate pseudo-random pure states of up to 15 qubits. By quantum state tomography of the reduced density matrix of six qubits, we measure the negativity spectra. Then, by changing the sizes of the environment and subsystems, we observe the entanglement transitions that are directly identified by logarithmic entanglement negativities based on the negativity spectra. In addition, we characterize the randomness of our circuits by measuring the distance between the distribution of output bit-string probabilities and the Porter-Thomas distribution. Our results show that superconducting processors with all-to-all connectivity constitute a promising platform for generating random states and understanding the entanglement structure of multipartite quantum systems.

Probing Operator Spreading via Floquet Engineering in a Superconducting Circuit.

Operator spreading, often characterized by out-of-time-order correlators (OTOCs), is one of the central concepts in quantum many-body physics. However, measuring OTOCs is experimentally challenging due to the requirement of reversing the time evolution of systems. Here we apply Floquet engineering to investigate operator spreading in a superconducting 10-qubit chain. Floquet engineering provides an effective way to tune the coupling strength between nearby qubits, which is used to demonstrate quantum walks with tunable couplings, reversed time evolution, and the measurement of OTOCs. A clear light-cone-like operator propagation is observed in the system with multiple excitations, and has a nearly equal velocity as the single-particle quantum walk. For the butterfly operator that is nonlocal (local) under the Jordan-Wigner transformation, the OTOCs show distinct behaviors with (without) a signature of information scrambling in the near integrable system.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits.

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Hierarchical FeCo2 S4 @FeNi2 S4 Core/Shell Nanostructures on Ni Foam for High-Performance Supercapacitors.

The design of electrode materials with rational core/shell structures is promising for improving the electrochemical properties of supercapacitors. Hence, hierarchical FeCo2 S4 @FeNi2 S4 core/shell nanostructures on Ni foam were fabricated by a simple hydrothermal method. Owing to their structure and synergistic effect, they deliver an excellent specific capacitance of 2393 F g-1 at 1 A g-1 and long cycle lifespan as positive electrode materials. An asymmetric supercapacitor device with FeCo2 S4 @FeNi2 S4 as positive electrode and graphene as negative electrode exhibited a specific capacitance of 133.2 F g-1 at 1 A g-1 and a high energy density of 47.37 W h kg-1 at a power density of 800 W kg-1 . Moreover, the device showed remarkable cycling stability with 87.0 % specific-capacitance retention after 5000 cycles at 2 A g-1 . These results demonstrate that the hierarchical FeCo2 S4 @FeNi2 S4 core/shell structures have great potential in the field of electrochemical energy storage.

Reset Voltage-Dependent Multilevel Resistive Switching Behavior in CsPb1- xBi xI3 Perovskite-Based Memory Device.

All-inorganic CsPb1- xBi xI3 perovskite film was successfully fabricated by incorporating Bi3+ in CsPbI3 to stabilize the cubic lattice. Furthermore, the perovskite film was applied to manufacture a simple Ag/CsPb1- xBi xI3/indium tin oxide (ITO) memory device with a bipolar resistive switching behavior. Nonvolatile, reliable, and reproducible switching properties are demonstrated through retention and endurance test under fully open-air conditions. The memory device also presents highly uniform and long-term stable characteristics. Importantly, by modulating the reset stop voltages, multilevel high-resistance states are observed for the first time in lead halide perovskite memory device. The resistive switching behavior is proposed to explain the formation and partial rupture of conductive multifilament that are dominated by the migration of iodine ions and their corresponding vacancies in perovskite film. This study suggests Ag/CsPb1- xBi xI3/ITO device potential application for multilevel data storage in a nonvolatile memory device.

Intrinsic structural distortion and exchange interactions in SmFe x Cr1-x O3 compounds.

The effect of substituting different amounts of magnetic metal Fe on the magnetic properties of SmFe x Cr1-x O3 (0 < x < 0.5) is reported here in order to probe the relation between the structural distortion and magnetism in these materials. The structural properties of the samples were characterized using X-ray diffraction with Rietveld refinements, and Raman spectroscopy carried out at ambient temperature. Magnetization data reveals the Neel temperature (T N, where the Cr(Fe) ions order) increases with an increase in the average B-site ionic radius, and average Cr(Fe)-O-Cr(Fe) bond angle. By fitting the temperature dependence of the magnetic susceptibility to the Curie-Weiss law modified by the Dzyaloshinskii-Moriya (DM) interaction, the strengths of the symmetric and antisymmetric Cr(Fe)-Cr(Fe) exchange interactions (J and D) were determined. It was found that the strength of the symmetric interaction J (reflected in the changes in the Neel temperature) increases with the replacement of Cr3+ with Fe3+, which is ascribed to the changes in the average Cr(Fe)-O-Cr(Fe) bond angle and bond lengths. Meanwhile, the antisymmetric interaction D a slightly decreases, which may be ascribed to the displacement of oxygen ions (dO) away from their "original" middle point.

Facile synthesis of NiCo2S4/CNTs nanocomposites for high-performance supercapacitors.

Herein, porous NiCo2S4/CNTs nanocomposites were synthesized via a simple hydrothermal method followed by the sulphurization process using different sulfide sources. By comparing two different sulfur sources, the samples using thioacetamide as sulfide source delivered more remarkable electrochemical performance with a high specific capacitance of 1765 F g-1 at 1 A g-1 and an admirable cycling stability with capacitance retention of 71.7% at a high current density of 10 A g-1 after 5000 cycles in 2 M KOH aqueous electrolyte. Furthermore, an asymmetric supercapacitor (ASC) device was successfully fabricated with the NiCo2S4/CNTs electrode as the positive electrode and graphene as the negative electrode. The device provided a maximum energy density of 29.44 W h kg-1 at a power density of 812 W kg-1. Even at a high power density of 8006 W kg-1, the energy density still reaches 16.68 W h kg-1. Moreover, the ASC presents 89.8% specific capacitance retention after 5000 cycles at 5 A g-1. These results reveal its great potential for supercapacitors in electrochemical energy storage field.

Room-temperature ferromagnetism in Co doped MoS2 sheets.

Via the hydrothermal method, we synthesized MoS2 nanosheets with varying Co dopant concentrations of 0%, 3%, 7%, using cobaltous acetate as a promoter, and marked as A, B, and C, respectively. We found that the thickness and flatness of the nanosheets increased with the increase of the Co dopant concentrations. Meanwhile, the BET surface area of samples (A, B, and C) decreased with the increase of the Co dopant concentrations. Optical absorption spectroscopy showed that, compared to sample A, the A1 and B1 excitons of samples B and C were 10 and 23 meV redshifted, respectively. Then, we performed magnetization measurement to investigate the effect of Co-doping; the unique result implied that the values of the magnetic moment decreased with the increase of the Co dopant concentrations. We performed DFT computations to address the above magnetic result. The computational result indicated that the value of the magnetic moment decreased with the increase of the Co dopant concentrations, which is in agreement with the results of the experiments described above.