Tensor Berry connections and their topological invariants

The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector potential defined in momentum space. Inspired by developments in mathematical physics, where higher-form (Kalb-Ramond) gauge fields were introduced, we hereby explore the existence of "tensor Berry connections" in quantum matter. Our approach consists in a general construction of effective gauge fields, which we ultimately relate to the components of Bloch states. We apply this formalism to various models of topological matter, and we investigate the topological invariants that result from generalized Berry connections. For instance, we introduce the 2D Zak phase of a tensor Berry connection, which we then relate to the more conventional first Chern number; we also reinterpret the winding number characterizing 3D topological insulators to a Dixmier-Douady invariant, which is associated with the curvature of a tensor connection. Besides, our approach identifies the Berry connection of tensor monopoles, which are found in 4D Weyl-type systems [Palumbo and Goldman, Phys. Rev. Lett. 121, 170401 (2018)]. Our work sheds light on the emergence of gauge fields in condensed-matter physics, with direct consequences on the search for novel topological states in solid-state and quantum-engineered systems.Comment: 10 pages, 1 table. Published versio

Revealing tensor monopoles through quantum-metric measurements

Monopoles are intriguing topological objects, which play a central role in gauge theories and topological states of matter. While conventional monopoles are found in odd-dimensional flat spaces, such as the Dirac monopole in three dimensions and the non-Abelian Yang monopole in five dimensions, more exotic objects were predicted to exist in even dimensions. This is the case of "tensor monopoles", which are associated with generalized (tensor) gauge fields, and which can be defined in four dimensional flat spaces. In this work, we investigate the possibility of creating and measuring such a tensor monopole, by introducing a realistic three-band model defined over a four-dimensional parameter space. Our probing method is based on the observation that the topological charge of this tensor monopole, which we relate to a generalized Berry curvature, can be directly extracted from the quantum metric. We propose a realistic three-level atomic system, where tensor monopoles could be generated and revealed through quantum-metric measurements.Comment: 4+4 pages, 2 figures, Revised version containing new appendice

Non-Abelian Bloch oscillations in higher-order topological insulators

Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to an external force. Observed in a wide range of synthetic lattice systems, BOs are intrinsically related to the geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift that is synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties in synthetic matter through the measurement of Berry phases and center-of-mass displacements.Comment: 13 pages, 6 figure

Hybrid metal oxide cycle water splitting

Hybrid thermochemical water splitting cycles are provided in which thermally reduced metal oxides particles are used to displace some but not all of the electrical requirements in a water splitting electrolytic cell. In these hybrid cycles, the thermal reduction temperature is significantly reduced compared to two-step metal-oxide thermochemical cycles in which only thermal energy is required to produce hydrogen from water. Also, unlike the conventional higher temperature cycles where the reduction step must be carried out under reduced oxygen pressure, the reduction step in the proposed hybrid cycles can be carried out in air, allowing for thermal input by a solar power tower with a windowless, cavity receiver

Hybrid metal oxide cycle water splitting

Hybrid thermochemical water splitting systems are disclosed that thermally reduces metal oxides particles to displace some but not all of the electrical requirements in a water splitting electrolytic cell. In these hybrid systems, the thermal reduction temperature is significantly reduced compared to two-step metal-oxide thermochemical cycles in which only thermal energy is required to produce hydrogen from water. Also, unlike conventional higher temperature systems where the reduction step must be carried out under reduced oxygen pressure, the reduction step in the proposed hybrid systems can be carried out in air, allowing for thermal input by a solar power tower with a windowless, cavity receiver

Experimental characterization of the 4D tensor monopole and topological nodal rings

Quantum mechanics predicts the existence of the Dirac and the Yang monopoles. Although their direct experimental observation in high-energy physics is still lacking, these monopoles, together with their associated vector gauge fields, have been demonstrated in synthetic matter. On the other hand, monopoles in even-dimensional spaces have proven more elusive. A potential unifying framework--string theory--that encompasses quantum mechanics promotes the vector gauge fields to tensor gauge fields, and predicts the existence of more exotic tensor monopole in 4D space. Here we report the first experimental observation of a tensor monopole in a 4D parameter space synthesized by the spin degrees of freedom of a single solid-state defect in diamond. Using two complementary methods, we reveal the existence of the tensor monopole through measurements of its quantized topological invariant. By introducing a fictitious external field that breaks chiral symmetry, we further observe a novel phase transition to a topological nodal ring semimetal phase that is protected by mirror symmetries.Comment: main: 10 pages, 4 figures + SI: 22 pages, 27 figure

Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons

Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine interaction-induced geometric and topological effects can be realized in quantum-engineered systems. Our approach builds on the design of effective lattices for the center-of-mass motion of two-body bound states (\emph{doublons}), which can be created through long-range interactions. This general scenario is illustrated on several examples, where flat-band localization, topological pumps and higher-order topological corner modes emerge from genuine interaction effects. Our results pave the way for the exploration of interaction-induced topological effects in a variety of platforms, ranging from ultracold gases to interacting photonic devices.Comment: 10 pages,7 figure

Exploring Parity Magnetic Effects through Experimental Simulation with Superconducting Qubits

We present the successful realization of four-dimensional (4D) semimetal bands featuring tensor monopoles, achieved using superconducting quantum circuits. Our experiment involves the creation of a highly tunable diamond energy diagram with four coupled transmons, and the parametric modulation of their tunable couplers, effectively mapping momentum space to parameter space. This approach enables us to establish a 4D Dirac-like Hamiltonian with fourfold degenerate points. Moreover, we manipulate the energy of tensor monopoles by introducing an additional pump microwave field, generating effective magnetic and pseudo-electric fields and simulating topological parity magnetic effects emerging from the parity anomaly. Utilizing non-adiabatic response methods, we measure the fractional second Chern number for a Dirac valley with a varying mass term, signifying a nontrivial topological phase transition connected to a 5D Yang monopole. Our work lays the foundation for further investigations into higher-dimensional topological states of matter and enriches our comprehension of topological phenomena