The Generalized Transmon Hamiltonian for Andreev Spin Qubits is a solution for an interacting quantum dot within a Josephson junction between two superconductors. Based on the Richardson model, this approach allows for exact diagonalization while retaining all necessary states to describe low-energy phenomena. It accounts for the physics of the quantum dot, the Josephson effect, and the Coulomb repulsion charging energy. This method can be applied for modeling Andreev spin qubits in transmon circuits, describing time-dependent processes, and calculating transition matrix elements for microwave-driven transmon spin-flip and mixed transitions.
What is the Generalized Transmon Hamiltonian for Andreev Spin Qubits?
The Generalized Transmon Hamiltonian for Andreev Spin Qubits is a solution to the problem of an interacting quantum dot embedded in a Josephson junction between two superconductors with finite charging energy. This solution is described by the transmon Cooper pair box Hamiltonian. The approach is based on the flatband approximation of the Richardson model, which reduces the Hilbert space to the point where exact diagonalisation is possible while retaining all states that are necessary to describe the low energy phenomena.
The method accounts for the physics of the quantum dot, the Josephson effect, and the Coulomb repulsion charging energy at the same level. In particular, it captures the quantum fluctuations of the superconducting phase as well as the coupling between the superconducting phase and the quantum dot spin degrees of freedom. The method can be directly applied for modelling Andreev spin qubits embedded in transmon circuits in all parameter regimes for describing time-dependent processes and for the calculation of transition matrix elements for microwave-driven transmon spin-flip and mixed transitions that involve coupling to charge or current degree of freedom.
How are Superconducting Circuits Utilized in Quantum Technology?
Superconducting circuits are one of the primary platforms for realizing various quantum technological applications. Most implementations of superconducting qubits are based on creating an anharmonic oscillator by replacing the inductor in an LC-circuit with a Josephson junction, which has nonlinear inductance. The realization where the charging energy due to capacitance is small compared to the Josephson energy is called the transmon qubit. These devices utilize the macroscopic coherence of superconducting states to encode and manipulate quantum information. Their popularity is due to their robustness with respect to charge fluctuations, which is one of the main decoherence mechanisms in superconducting qubits.
What is the Andreev Spin Qubit?
In pursuit of further enhancing these devices, a novel approach has emerged combining the robust coherence of superconductors with the controllability of spin qubits built out of semiconducting quantum dots. The idea consists of embedding a quantum dot into the Josephson junction and storing quantum information in the spin of the quasiparticle trapped in discrete sub-gap states that emerge in the few-channel regime of the junction. The architecture is called the Andreev spin qubit. The spin-orbit coupling permits manipulation of the spin degree of freedom using the supercurrent or the electric field as well as advanced readout based on circuit quantum electrodynamics techniques.
How is the Transmon Qubit Modelled?
Modelling of the transmon qubit typically relies on neglecting the superconducting quasiparticles and only accounting for the dynamics of Cooper pairs. However, the presence of an interacting quantum dot in the Josephson junction induces Cooper pair-breaking processes, and an accurate description of the physics requires solving the full electronic problem. This is particularly important for modeling the Andreev spin qubit, where a quantum dot with a large charging energy is favored as it ensures a ground state with a single localized spin trapped in the quantum dot.
What is the Quantum Dot-Josephson Junction?
In a conventional Josephson junction without an embedded quantum dot, quasiparticles play no role at temperatures much lower than the superconducting gap. An approximate description of Cooper pair hopping is adequate to capture the Josephson effect. Microscopically, it is shown to arise from the coherent transfer of electron pairs across the junction. This can be expressed by writing the Hamiltonian in the charge basis, with the difference in the number of Cooper pairs occupying the two superconductors.
These terms couple to the neighboring and the Hamiltonian in this basis is tridiagonal. As the different states are equivalent, this corresponds to a tight-binding chain in space. It is diagonalised by Fourier transforming into states labelled by the dual quantity, this is the emergent superconducting phase difference. The eigenstates are Bloch waves superpositions of states. Their dispersion is given by the Josephson energy, which is given by twice the hopping matrix element between and, i.e., the energy associated with transferring a single Cooper pair across the junction.
Generalized transmon Hamiltonian for Andreev spin qubits was published on February 3, 2024, by authors Luka Pavešić and Rok Žitko. The article was sourced from arXiv (Cornell University).