Quantum Capacitance Advances Kitaev Chain Identification with Minimal 1-Dot Coupling

Researchers are increasingly exploring quantum-dot systems as viable platforms for realising topological quantum computation, and a new study delves into the crucial characteristics of these devices. Chun-Xiao Liu from Tsung-Dao Lee Institute, Shanghai Jiao Tong University, alongside colleagues, investigates the quantum capacitance and parity switching within a specifically designed Kitaev chain. Their theoretical work reveals how capacitance measurements can pinpoint optimal conditions for Kitaev chain operation, aligning with experimental tunnel spectroscopy results. Furthermore, the team demonstrates the interplay of external and internal mechanisms governing parity switching , a critical process for quantum information protection , offering valuable insights for advancing this promising avenue of quantum technology.

Their theoretical work reveals how capacitance measurements can pinpoint optimal conditions for Kitaev chain operation, aligning with experimental tunnel spectroscopy results. Furthermore, the team demonstrates the interplay of external and internal mechanisms governing parity switching, a critical process for quantum information protection, offering valuable insights for advancing this promising avenue of quantum technology.

Quantum capacitance identifies Kitaev chain sweet

This detailed analysis moves beyond simple observation, offering a deeper understanding of the underlying physics governing these nanoscale devices. The team’s model incorporates a normal-metal lead weakly coupled to the chain, allowing them to investigate the effects of varying the lead’s chemical potential and tunneling strength. This detailed modelling, utilising semiclassical rate equations to account for non-equilibrium conditions, provides a comprehensive picture of the system’s behaviour and its potential for manipulation. This breakthrough reveals that quantum capacitance is not merely a probe of nanoscale devices but a powerful tool for reading out joint fermion parity and the ground-state parity of a Majorana qubit, essential elements for measurement-based topological quantum computing. Recent demonstrations of single-shot readout of Majorana parity in two-site Kitaev chains, consistent with theoretical predictions, underscore the practical relevance of this research. The work opens new avenues for controlling and characterising Kitaev chains, bringing the realisation of robust topological quantum computing closer to reality, and builds upon significant experimental progress in creating and observing Majorana zero modes in coupled Quantum dots.

Capacitance modelling of a two-dot Kitaev chain reveals

Researchers engineered a model Hamiltonian, HK, encompassing dot and Andreev bound state (ABS) contributions, alongside tunnelling terms, to describe the system. This Hamiltonian, HD + HA + Htunn, detailed the energy landscape of the quantum dots, ABSs, and their interactions, with parameters including chemical potentials μi, Zeeman splitting EZi, Coulomb energy Ui, pairing potential ∆0, and tunnelling amplitudes tsc and tsf. To simulate the impact of an external normal lead, the team developed an extended Hamiltonian, Hext, incorporating lead electron occupancy and tunnelling strength, tc, controlled by a tunnel gate. The research employed a semiclassical rate equation, dPα/dt = Σβ (ΓαβPβ −ΓβαPα) = 0, to determine the steady-state probability distribution, {Pα}, accounting for transitions driven by single-electron tunnelling, quasiparticle poisoning, and relaxation processes.

Specifically, the team calculated rates Γβα for these mechanisms, incorporating Fermi-Dirac functions, nF, to reflect temperature-dependent electron distributions. Experiments employed a method to calculate stationary current, I, and differential conductance, G = dI/dV, based on the calculated probability distribution and transition rates. Furthermore, the study introduced a novel approach to determine the averaged quantum capacitance, ⟨Cq⟩, by evaluating the second derivative of eigenenergies with respect to the chemical potential of quantum dot one, effectively linking capacitance measurements to Hamiltonian parameters. This work provides a detailed theoretical framework for interpreting experimental observations in these complex quantum systems.

Capacitance maps reveal Kitaev chain configuration and localization

Scientists have demonstrated a new platform for creating Kitaev chains with Majorana zero modes using an array of dots coupled via superconductivity. Experiments revealed that in the open regime, these diagrams can identify the optimal configuration for a Kitaev chain. Results demonstrate that analytically derived expressions for quantum capacitance, Cq,eg and Cq,og, accurately model the system’s behaviour, with curves scaled by a constant factor of approximately 0.282. Data shows that state population of |eg⟩ and |og⟩ varies with μ1 for μA = 0.5, providing a detailed picture of the system’s quantum states.

The Cq peak extends along the μ1 = ±μ2 directions for odd- and even-parity ground states, consistent with numerical results. Measurements confirm that coupling to the normal lead relaxes the system to its global ground state, allowing both conductance and quantum capacitance to reflect the dominant coupling between quantum dots. Further analysis in the closed regime, where the normal lead is decoupled, indicates a combination of resonance lines in the averaged quantum capacitance along the μ1 = μ2 and μ1 = −μ2 directions. This signifies a finite population of both |og⟩ and |eg⟩ due to parity switching caused by quasiparticle poisoning. However, distinction between states exists only in the magnitude of the quantum capacitance for different values of μA. The height and width of these peaks vary with the chemical potential of the Andreev bound states.

Capacitance reveals Kitaev chain parity dynamics at chain

This work offers valuable physical insights into the behaviour of quantum-dot-based Kitaev chain devices, particularly concerning capacitance and parity dynamics. By examining the quantum capacitance at varying voltage biases, researchers proposed a method for estimating the rates at which the system switches between parity ground states. While the modelling of quasiparticle poisoning and relaxation processes was acknowledged as phenomenological, the results successfully captured key features observed in recent experimental investigations. The authors note that the robustness of their conclusions extends beyond the specific details of their modelling approach, provided certain key characteristics are maintained. The authors acknowledge limitations in their microscopic modelling of poisoning and relaxation processes, suggesting these areas for future research. They propose that further investigation into these processes could refine the understanding of device behaviour.