Parametric Drive of a Double Quantum Dot in a Cavity

TL;DR

This work demonstrates that parametric modulation of the detuning in a double quantum dot coupled to a cavity can markedly boost readout by inducing intra-cavity field displacement via dipole radiation, even when the bare coupling remains transverse. By carefully tuning the phase and amplitude of a direct cavity drive and exploiting interference between multiple drive channels, the authors achieve a near-π phase shift between dipole states and an order-of-magnitude to sixty-fold improvement in SNR compared with conventional dispersive readout, without invoking true longitudinal coupling. The approach is validated in a CNT-based DQD with a Nb cavity, revealing that the intra-cavity displacement is dominated by the dipole-radiation pathway (via the lever arm $\beta_L$) and that adiabatic dynamics are maintained ($\eta \approx 0.04$). While this achieves substantial readout improvements and enables rapid, potentially single-shot readout, it does not realize true photon-number–dephasing elimination or two-qubit gates associated with genuine longitudinal coupling; nonetheless, it offers a powerful, adaptable tool for probing exotic electronic states in mesoscopic circuits and for high-fidelity readout of DQD-based qubits in cQED architectures.

Abstract

We demonstrate the parametric modulation of a double quantum dot charge dipole coupled to a cavity, at the cavity frequency, achieving an amplified readout signal compared to conventional dispersive protocols. Our findings show that the observed cavity field displacement originates from dipole radiation within the cavity, rather than from a longitudinal coupling mechanism, yet exhibits the same signatures while relying on a transverse coupling. By carefully tuning the phase and amplitude of the intra-cavity field, we achieve a $π$-phase shift between two dipole states, resulting in a substantial enhancement of the signal-to-noise ratio. In addition to its applications in quantum dot based qubits in cQED architectures, this protocol could serve as a new promising tool for probing exotic electronic states in mesoscopic circuits embedded in cavities.

Figures (13)

• Figure 1: Principle of the experiment. (a) Cavity field state-dependent trajectories for $\Delta_{cd}=0$ and cases $\sigma_z=\pm 1$ and $\chi=0$. The pure transverse coupling is in pink, the pure parametric longitudinal coupling is in green and the combination of both is in dark blue. The steady states are shown as dots at the end of the trajectories and the reference states for $\chi=0$ are shown as crosses. (b) Top: optical image of the device showing the Nb resonator (yellow) and the parametric drive line (red). The scale bar is 1mm. Bottom: SEM image of a typical DQD device with a transferred CNT. The scale bar is 500nm.
• Figure 1: Characterization of the cavity. Normalized transmitted amplitude $A/A_0$ (a) and phase of the transmitted signal(b) through the cavity when driving from the input port of the cavity (purple circles) and from the parasitic port via the DQD gates (blue circles). The orange line is a fit.
• Figure 2: Dipole radiation in the cavity. (a) Normalized output cavity field amplitude $A_d/A_0$, for $\chi=0$ ($\epsilon_\delta \gg t_{\rm c}$) and $r\approx 1$, as a function of the phase difference $\delta \phi$ between the input ($A_{in})$ and parasitic ($A_g$) drives. Inset: phase $\phi_d$ of $A_d$ around $\delta \phi=\pi$. (b) Phase variation $\Delta \varphi$ of the cavity field probed at $f_c$ across an interdot transition, as a function of the left and right plunger gate voltages. Insets: cuts along the detuning axis (black arrow) of $\Delta \varphi$ (left) and $\Delta A / A_{\rm off}$ (right). Normalized output field amplitude as a function of detuning $\epsilon_\delta$ and drive frequency $f_d$ in the standard dispersive readout regime (c) and with parametric modulation of $\epsilon_\delta$ at $f_d$ for $r=0.995$ and $\delta \phi=\pi$ (d).
• Figure 2: Characterization of the first interdot transition discussed in the main text. Relative amplitude variation $\Delta A / A$ (a) and phase variation $\Delta \varphi$ (b) as a function of the plunger gate voltage $V_{PL}$ along the detuning axis indicated by a black arrow in Fig. 2(b) of the main text and for different MC temperatures. (c) $\Delta \varphi(\epsilon_\delta=0)$ as a function of MC temperature $T$ (blue circles) and fit to the formula discussed in the text in orange. (d) Two-tone spectroscopy showing $\Delta \varphi$ as a function of detuning $\epsilon_\delta$ and second tone drive frequency $f_d$.
• Figure 3: Dynamical readout of the interdot transition. (a) Relative field amplitude variation $\Delta A / A_0$ of the interdot transition taken along the detuning axis (black arrow in Fig. \ref{['fig2:dipole_radiation']}(b)) and varying the drives interference phase $\delta \phi$ at constant $r\approx 1$. Experimental data (left side) and theory (right side) are displayed on the same plot. (b) Same as (a) but for the quantity $\Delta \varphi$. Respective cuts along $\delta \phi$ at zero detuning are shown in (c,e) and cuts along $\epsilon_\delta$ at $\delta \phi\approx0.99 \pi$ are shown in (d,f). Data are shown by blue circles and simulations by orange lines. (g) IQ plane trajectories as a function of readout time for the dispersive (light pink) and dynamic (dark blue) readout. Corresponding reference states are shown as crosses. The solid and dashed lines are theory for the $\langle \sigma_z \rangle=-1$ and $+1$ respectively. (h) Corresponding phase contrast $\Delta \varphi$ and (i) their ratio for the two readout schemes.