Ground-state quantum geometry in superconductor-quantum dot chains

Abstract

Multiterminal Josephson junctions constitute engineered topological systems in arbitrary synthetic dimensions defined by the superconducting phases. Microwave spectroscopy enables the measurement of the quantum geometric tensor, a fundamental quantity describing both the quantum geometry and the topology of the emergent Andreev bound states in a unified manner. In this work we propose an experimentally feasible multiterminal setup of $N$ quantum dots connected to $N+1$ superconducting leads to study nontrivial topology in terms of the many-body Chern number of the ground state. Moreover, we generalize the microwave spectroscopy scheme to the multiband case and show that the elements of the quantum geometric tensor of the noninteracting ground state can be experimentally accessed from the measurable oscillator strengths at low temperature.

arXiv comment13 pages, 4 figures, added and updated references, corrected typos, changed title; content corresponds to the published version

References in corpus (92)

• Topological Insulators
• Fault-tolerant quantum computation by anyons
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Photonics
• Topological superconductors: a review
• Colloquium: Topological Band Theory
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Symmetry and Topology in Non-Hermitian Physics
• Superfluidity in topologically nontrivial flat bands
• A Four Dimensional Generalization of the Quantum Hall Effect
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Carbon Nanotubes as Cooper Pair Beam Splitters
• Revealing the electronic structure of a carbon nanotube carrying a supercurrent
• Geometric origin of superfluidity in the Lieb lattice flat band
• Geometry and non-adiabatic response in quantum and classical systems
• Band geometry, Berry curvature and superfluid weight
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Coherent manipulation of Andreev states in superconducting atomic contacts
• Experimental Measurement of the Berry Curvature from Anomalous Transport
• Multi-terminal Josephson junctions as topological materials
• Observation of topological transitions in interacting quantum circuits
• Exciting Andreev pairs in a superconducting atomic contact
• Andreev Level Qubit
• Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Direct microwave measurement of Andreev-bound-state dynamics in a proximitized semiconducting nanowire
• Andreev quantum dots for spin manipulation
• Resonant tunneling through a small quantum dot coupled to superconducting leads
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Measuring a topological transition in an artificial spin 1/2 system
• Measuring quantized circular dichroism in ultracold topological matter
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Classifying and measuring the geometry of the quantum ground state manifold
• Geometric orbital susceptibility: quantum metric without Berry curvature
• Topological Maxwell Metal Bands in a Superconducting Qutrit
• Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions
• Extracting the quantum metric tensor through periodic driving
• Topological one-way fiber of second Chern number
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• How to Measure the Quantum Geometry of Bloch Bands
• Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
• Evidence for long-lived quasiparticles trapped in superconducting point contacts
• The $\omega$-SQUIPT: phase-engineering of Josephson topological materials
• Topological transconductance quantization in a four-terminal Josephson junction
• The multi-terminal Josephson effect
• Topological Andreev bands in three-terminal Josephson junctions
• Supercurrent Flow in Multi-Terminal Graphene Josephson Junctions
• Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter
• The 6D quantum Hall effect and 3D topological pumps
• Observation of topological Uhlmann phases with superconducting qubits
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• Revealing tensor monopoles through quantum-metric measurements
• Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
• Non-trivial Chern numbers in three-terminal Josephson junctions
• Singularities of Andreev spectrum in multi-terminal Josephson junction
• Magnetic field tuning and quantum interference in a Cooper pair splitter
• Andreev scattering and cotunneling between two superconductor-normal metal interfaces : the dirty limit
• Supercurrent Spectroscopy of Andreev States
• Adiabatic transport of Cooper pairs in arrays of Josephson junctions
• Weyl nodes in Andreev spectra of multiterminal Josephson junctions: Chern numbers, conductances and supercurrents
• Weyl Josephson Circuits
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• Quantum metric and wavepackets at exceptional points in non-Hermitian systems
• Majorana-Weyl crossings in topological multi-terminal junctions
• Connecting Berry's phase and the pumped charge in a Cooper pair pump
• Tensor Berry connections and their topological invariants
• Topological phase diagram of a three-terminal Josephson junction: From the conventional to the Majorana regime
• Topological properties of multi-terminal superconducting nanostructures: effect of a continuous spectrum
• Closing the proximity gap in a metallic Josephson junction between three superconductors
• Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra
• Non-Abelian Majorana modes protected by an emergent second Chern number
• Nodal Andreev Spectra in Multi-Majorana Three-Terminal Josephson Junctions
• Fast and accurate Cooper pair pump
• Evidence of Majorana Zero Modes in Josephson Trijunctions
• Topological quantization by controlled paths: application to Cooper pairs pumps
• Berry curvature tomography and realization of topological Haldane model in driven three-terminal Josephson junctions
• Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multi-terminal superconducting device
• Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction
• Spin-Weyl quantum unit: theoretical proposal
• Nonadiabatic Josephson current pumping by microwave irradiation
• Dynamics of a Majorana trijunction in a microwave cavity

Cited by in corpus (22)

• Relations between topology and the quantum metric for Chern insulators
• Nontrivial quantum geometry of degenerate flat bands
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Surrogate model solver for impurity-induced superconducting subgap states
• Cooper-pair transistor as a minimal topological quantum circuit
• Multi-terminal Josephson junctions: a road to topological flux networks
• From Classical to Quantum Information Geometry: A Guide for Physicists
• Tensor Monopoles in superconducting systems
• Non-hermitian topology in multiterminal superconducting junctions
• Quantum circuits with multiterminal Josephson-Andreev junctions
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Weyl singularities in polaritonic multi-terminal Josephson junctions
• Ground state topology of a four-terminal superconducting double quantum dot
• Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Charge quantization and detector resolution
• Quasiperiodic circuit quantum electrodynamics
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Fractional transconductance via non-adiabatic topological Cooper pair pumping
• Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids
• Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography
• Multiterminal Josephson junctions with tunable topological properties
• Evolution of quantum geometric tensor of 1D periodic systems after a quench