Dispersive detection of a charge qubit with a broadband high-impedance quantum-Hall plasmon resonator

Cavity quantum electrodynamics (cQED) provides strong light-matter interactions that can be used for manipulating and detecting quantum states. The interaction can be enhanced by increasing the resonator’s impedance, while approaching the quantum impedance ($h/e^2$) remains challenging. Edge plasmons emergent as chiral bosonic modes in the quantum Hall channels provide high quantized impedance of $h/ νe^2$ that can exceed 10 k$Ω$ for the Landau-level filling factor $ν\leq 2$, well beyond the impedance of free space. Here, we apply such a high-impedance plasmon mode in a quantum-Hall plasmon resonator to demonstrate dispersive detection of a nearby charge qubit formed in a double quantum dot. The phase shift in microwave transmission through the plasmon resonator follows the dispersive shift associated with the qubit state in agreement with the cQED theory. The high impedance allows us to perform dispersive detection of qubit spectroscopy with a plasmon resonator having a broad bandwidth. Leveraging these topological edge modes, our results establish two-dimensional topological insulators as a new platform of cQED.

💡 Research Summary

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This paper demonstrates a dispersive readout of a charge qubit using a high‑impedance quantum‑Hall (QH) plasmon resonator. In the QH regime, edge channels support chiral plasmon modes whose characteristic impedance is quantized as (Z = h/(\nu e^{2})). For filling factors (\nu \le 2) this impedance exceeds 10 kΩ, far larger than the 377 Ω free‑space impedance and the few‑kΩ values typical of Josephson‑junction resonators. The authors fabricate a GaAs/AlGaAs heterostructure containing a two‑dimensional electron gas (2DEG) 100 nm below the surface. By applying negative voltages to top and bottom gates they close the edge channel around a circular mesa (perimeter (L = 113 µ)m), forming a plasmon resonator whose length equals one plasmon wavelength. The resonator is capacitively coupled to two metal pads (G_inj and G_det) that serve as input and output ports for microwave transmission measurements.

At a magnetic field of 3.6 T (ν≈2) the resonator exhibits a fundamental mode at (f_{r}=2.45) GHz with a decay rate (\kappa \approx 0.6) GHz, giving a quality factor (Q \approx 4). The high impedance (≈13 kΩ) enhances the electric‑field amplitude for a given microwave power, enabling strong interaction with a nearby double‑quantum‑dot (DQD) charge qubit. The DQD is defined by gate electrodes that control the electron occupation ((N_{1},N_{2})) and the inter‑dot detuning (\varepsilon). The qubit transition frequency is (hf_{q}= \sqrt{\varepsilon^{2}+4t^{2}}), where (t) is the tunnel coupling. The capacitive coupling between the plasmon voltage (V_{ch}) and the DQD is characterized by a dimensionless factor (\eta \approx 0.032).

In the dispersive regime ((|\Delta_{q-r}| \gg g), where (\Delta_{q-r}=hf_{q}-hf_{r}) and (g) is the qubit‑plasmon coupling) the resonator frequency shifts by (\Delta f_{0}\simeq -g^{2}/\Delta_{q-r}). This shift translates into a phase change (\phi = \arg(S_{21}) \approx 2Q\Delta f_{0}/f_{0}). Because the phase scales with the product (QZ), a high‑impedance, low‑Q resonator can produce a sizable signal despite its broad bandwidth. The authors map (\phi) as a function of the gate voltages that tune (\varepsilon) and (t). When (\varepsilon) is swept across zero at fixed (t), a single negative phase dip appears if (2t > hf_{r}). By reducing (t) via a gate (V_c), the dip splits into a characteristic “W‑shaped” profile, and for sufficiently small (t) the central region becomes positive, indicating that the qubit is now resonant with the plasmon mode ((\Delta_{q-r}=0)). These observations are fully reproduced by a quantum master‑equation model that includes resonator decay (\kappa), qubit relaxation (\gamma_{1}), and pure dephasing (\gamma_{\phi}). The fitting yields a maximum coupling strength (g/2\pi \approx 55) MHz and decoherence rates (\gamma) ranging from 0.07 to 0.34 GHz, confirming that the device operates in the weak‑coupling regime ((g < \kappa, \gamma)).

The authors also investigate the effect of increasing the drive power. As the average plasmon number (n) grows, the qubit ground‑state population (P_{g}) decreases and the excited‑state population (P_{e}) rises, leading to partial depolarization. By measuring the power dependence of both phase and amplitude, they infer that the dispersive readout performed at (-87.5) dBm corresponds to an average plasmon number well below one, ensuring that the qubit remains essentially in its ground state during measurement.

Finally, the paper outlines pathways toward the strong‑coupling regime. Reducing the filling factor to ν=1 or fractional values would raise the impedance further. Optimizing the geometry to increase (\eta) (e.g., adding screening electrodes or improving capacitive overlap) could boost the coupling proportionally to (\sqrt{Z}). Improvements in material quality and device design could lower both (\kappa) and (\gamma) to the few‑MHz range, as demonstrated in recent high‑mobility 2DEG resonators. Achieving (g/f_{0} > 0.1) would place the system in the ultra‑strong coupling regime, opening opportunities for fast, broadband qubit control, quantum‑limited amplification, and exploration of novel light‑matter physics in topological platforms.

In summary, the work establishes that chiral edge plasmons in a quantum‑Hall system provide a robust, high‑impedance, broadband resonator suitable for dispersive qubit readout. It validates the applicability of standard cavity‑QED theory to plasmonic modes and points to a clear roadmap for leveraging two‑dimensional topological insulators as a new platform for quantum electrodynamics and quantum information processing.