Asymptotic Expressions for Charge Matrix Elements of the Fluxonium Circuit

Abstract

In charge-coupled circuit QED systems, transition amplitudes and dispersive shifts are governed by the matrix elements of the charge operator. For the fluxonium circuit, these matrix elements are not limited to nearest-neighbor energy levels and are conveniently tunable by magnetic flux. Previously, their values were largely obtained numerically. Here, we present analytical expressions for the fluxonium charge matrix elements. We show that new selection rules emerge in the asymptotic limit of large Josephson energy and small inductive energy. We illustrate the usefulness of our expressions for the qualitative understanding of charge matrix elements in the parameter regime probed by previous experiments.

References in corpus (5)

• Charge insensitive qubit design derived from the Cooper pair box
• Coupling Superconducting Qubits via a Cavity Bus
• Suppressing Charge Noise Decoherence in Superconducting Charge Qubits
• Circuit QED with fluxonium qubits: theory of the dispersive regime
• Symmetries and collective excitations in large superconducting circuits

Cited by in corpus (9)

• Measurement of many-body chaos using a quantum clock
• Realization of a $\Lambda$ system with metastable states of a capacitively-shunted fluxonium
• Protecting a superconducting qubit from energy decay by selection rule engineering
• Microwave-Activated Controlled-Z Gate for Fixed-Frequency Fluxonium Qubits
• Fast high-fidelity gates for galvanically-coupled fluxonium qubits using strong flux modulation
• Proposal for entangling gates on fluxonium qubits via a two-photon transition
• Hardware-efficient fermionic simulation with a cavity-QED system
• Logical measurement-based quantum computation in circuit-QED
• Deterministic amplification of Schroedinger cat states in circuit quantum electrodynamics