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Bulletin of the American Physical Society

Two-photon Rabi oscillations in a superconducting transmon qubit

Dong-Gwang Ha, Jung Hwan Park, Seung‐Bo Shim, Woon Young Song, Yonuk Chong

Published Mar 3, 2014• 0 citations
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Application of the Schwinger Oscillator Construct of Angular Momentum to an Interpretation of the Superconducting Transmon Qubit

Erickson, R. P.

The Schwinger oscillator construct of angular momentum, applied to the superconducting transmon and its transmission-line readout, modeled as capacitvely coupled quantum oscillators, provides a natural and robust description of a qubit. The construct defines quantum-entangled, two-photon states that form an angular-momentum-like basis, with symmetry corresponding to physical conservation of total photon number, with respect to the combined transmon and readout. This basis provides a convenient starting point from which to study error-inducing effects of transmon anharmonicity, surrounding-environment decoherence, and random stray fields on qubit state and gate operations. Employing a Lindblad master equation to model dissipation to the surrounding environment, and incorporating the effect of weak transmon anharmonicity, we present examples of the utility of the construct. First, we calculate the frequency response associated with exciting the ground state to a Rabi resonance with the lowest-lying spin-1/2 moment, via a driving external voltage. Second, we calculate the frequency response between the three lowest two-photon states, within a ladder-type excitation scheme. The generality of the Schwinger angular-momentum construct allows it to be applied to other superconducting charge qubits.

arXiv:2401.09573•Jan 17, 2024•0 citations
Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using nonlinear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large-bandwidth, nearly quantum-limited amplifier as is the case with linear readout resonators.
We demonstrate control and readout of a superconducting artificial atom based on a transmon qubit using a compact lumped-element resonator. The resonator consists of a parallel-plate capacitor with a wire geometric inductor. The footprint of the resonators is about 200 × 200 μm2, which is similar to the standard transmon size and one or two orders of magnitude more compact in the occupied area compared to coplanar waveguide resonators. We observe coherent Rabi oscillations and obtain time-domain properties of the transmon. The work opens a door to miniaturize essential components of superconducting circuits and to further scale up quantum systems with superconducting transmons.
The Schwinger oscillator construct of angular momentum, applied to the superconducting transmon and its transmission-line readout, modeled as capacitvely coupled quantum oscillators, provides a natural and robust description of a qubit. The construct defines quantum-entangled, two-photon states that form an angular-momentum-like basis, with symmetry corresponding to physical conservation of total photon number, with respect to the combined transmon and readout. This basis provides a convenient starting point from which to study error-inducing effects of transmon anharmonicity, surrounding-environment decoherence, and random stray fields on qubit state and gate operations. Employing a Lindblad master equation to model dissipation to the surrounding environment, and incorporating the effect of weak transmon anharmonicity, we present examples of the utility of the construct. First, we calculate the frequency response associated with exciting the ground state to a Rabi resonance with the lowest-lying spin-1/2 moment, via a driving external voltage. Second, we calculate the frequency response between the three lowest two-photon states, within a ladder-type excitation scheme. The generality of the Schwinger angular-momentum construct allows it to be applied to other superconducting charge qubits.