Electron shelving of a superconducting artificial atom

Efficiently interfacing long-lived qubits with propagating photons is a significant challenge in building scalable quantum technologies. Current circuit quantum electrodynamics (cQED) architectures typically rely on off-resonant cavities to prevent qubit emission and enable quantum non-demolition (QND) dispersive readout. However, this approach requires an additional cavity mode, increasing complexity and resource consumption. A different strategy, inspired by atomic physics, utilizes three-level systems with a metastable qubit transition and a bright cycling transition, leveraging the electron shelving effect. This method eliminates the need for an intermediary cavity mode, allowing for a more direct and efficient qubit-photon interface. This work explores the feasibility of implementing electron shelving in a superconducting artificial atom – specifically, the fluxonium qubit – and demonstrates its potential for simplifying and improving quantum computing architectures. The advantages of a direct qubit-photon interface include simplified circuit design, reduced chip area, and potentially enhanced quantum communication capabilities.

Previous work has demonstrated strong interactions between artificial circuit atoms and radiation, including nearly unit efficiency single-photon scattering using superconducting flux qubits and transmission lines, and resonant fluorescence studies with transmon qubits. However, limitations in transition frequency diversity and selection rules in these systems necessitate the use of an extra cavity mode for full quantum control. In contrast, many optical quantum technologies utilize atoms possessing both dark (long coherence time) and bright (fluorescent) transitions. This electron shelving effect allows a direct interface between high-coherence qubits and propagating photons. The use of cavity resonators in cQED has been the prevailing method to achieve both long coherence times and QND readout. This study seeks to show that a direct interface can be achieved without the need for a cavity by adopting a three-level circuit atom with carefully designed transitions. This could potentially reduce the on-chip space occupied by readout resonators in quantum processors, a significant consideration for scaling up quantum computing systems.

The experiment uses a fluxonium qubit, a superconducting circuit comprising a Josephson junction shunted by a high-value inductance and a capacitance, configured as a bow-tie antenna. At a half-integer magnetic flux, the fluxonium exhibits a double-well potential, with the lowest two energy levels defining the qubit states |0⟩ and |1⟩. Higher-energy states, |2⟩, |3⟩, etc., are used for the cycling transition. The specific transition |0⟩ ↔ |3⟩ is selected due to its high frequency and suitability for fluorescence readout. The fluxonium is placed inside a copper enclosure (not a cavity resonator) with a specially designed input/output port. The port transforms the transverse-electromagnetic (TEM) field of the coaxial cable into a transverse electric (TE) field, coupling to the qubit antenna. This design introduces a low-frequency cutoff near ω03, leading to a much shorter radiative lifetime for state |3⟩ compared to state |1⟩. The radiative decay |3⟩ → |2⟩ is suppressed due to the TE-mode cutoff, and the direct decay |3⟩ → |1⟩ is dipole-forbidden. The readout is performed using a phase-sensitive (homodyne) scheme, monitoring fluorescence from the |0⟩ ↔ |3⟩ transition. The reflection coefficient, r, is measured as a function of drive frequency and amplitude, and a theoretical model is developed to relate r to the ground state population ρ0. The model considers the effects of radiative decay, thermal occupation of states, and the driving strength. Qubit manipulations (Rabi oscillations, relaxation, and spin-echo) are performed using drives at the qubit and cycling transition frequencies, and the resulting population dynamics are measured using the conditional fluorescence readout. A detailed relaxation model, incorporating radiative decay, dielectric loss, and quasiparticle tunneling, is developed and used to fit experimental data on population transients during readout. This model incorporates parameters such as dielectric loss quality factor, quasiparticle density, and transition rates between states to accurately capture the non-ideal QND behavior observed in the experiments.

The experimental results show excellent agreement with the theoretical model, confirming the efficient coupling of the |0⟩ ↔ |3⟩ transition to the waveguide. The qubit coherence time (T1 = T2 = 52 µs) is significantly longer than the radiative lifetime of the cycling transition (∼91 ns), indicating that the readout process does not significantly affect qubit coherence. The measured thermal equilibrium ground state population is consistent with the effective temperature of the system. Rabi oscillations between states |0⟩ and |1⟩ and states |0⟩ and |2⟩ are successfully demonstrated, showing good control over qubit state manipulation. The optical pumping model accurately describes the population transients during readout, revealing a gradual leakage of population from the cycling manifold {|0⟩, |3⟩} to states |1⟩ and |2⟩ with a characteristic timescale (Tcyc ≈ 9.6 µs). The dominant readout error is attributed to the |3⟩ → |2⟩ decay due to dielectric loss, whereas the direct parity-breaking decay |3⟩ → |1⟩ due to quasiparticle tunneling plays a minor role. This indicates the importance of reducing dielectric loss in future experiments to improve the readout fidelity. The average number of fluorescence cycles (Ncyc ≈ 105) provides a quantitative measure of the deviation from the ideal QND behaviour.

The successful demonstration of electron shelving in a fluxonium qubit provides a significant advancement in superconducting qubit technology. This cavityless approach simplifies the architecture and potentially increases the scalability of quantum processors. The long qubit coherence time, even with direct coupling to a waveguide, highlights the robustness of the fluxonium qubit design. The optical pumping model offers a detailed understanding of the readout process and the limitations in QND behavior, thereby guiding the optimization of future experiments. The observation that the dominant error mechanism is dielectric loss suggests that improvements in material quality can further improve the performance of the readout scheme. The use of a different cycling transition, for example |1⟩ ↔ |2⟩, might extend the fluorescence lifetime, approaching the T1 limit, further improving QND measurements. Furthermore, the integration of a parametric amplifier could enable single-shot readout, enhancing the sensitivity and speed of the technique.

This research demonstrates a cavityless approach to controlling superconducting qubits using the electron shelving effect in a fluxonium circuit atom. The high-fidelity QND readout, achieved with long qubit coherence time, offers a resource-efficient alternative to traditional cQED architectures. Future work could focus on implementing this approach with other types of qubits or using different cycling transitions to further enhance performance and improve QND fidelity. Furthermore, integrating single microwave photon counters could facilitate the exploration of various quantum optics phenomena and enhance quantum networking applications.

The current implementation suffers from some limitations, primarily the readout fidelity. The main source of readout error arises from dielectric loss, leading to transitions out of the cycling manifold. While the optical pumping model provides a good fit to the experimental data, there are other sources of decoherence that may not be fully captured, such as fluctuations in the environment. Improving material quality and reducing dielectric loss are critical for improving readout fidelity. Furthermore, the current readout scheme operates at the microwave power levels, limiting the detection efficiency; single-shot readout using a parametric amplifier would greatly enhance the speed and sensitivity of the method.