Large-bandwidth Transduction Between an Optical Single Quantum Dot Molecule and a Superconducting Resonator

Quantum transduction between the microwave and optical domains is an outstanding challenge for long-distance quantum networks based on superconducting qubits. For all transducers realized to date, the generally weak light-matter coupling does not allow high transduction efficiency, large bandwidth, and low noise simultaneously. Here we show that a large electric dipole moment of an exciton in an optically active self-assembled quantum dot molecule (QDM) efficiently couples to a microwave resonator field at the single-photon level. This allows for transduction between microwave and optical photons without coherent optical pump fields to enhance the interaction. With an on-chip device, we demonstrate a sizeable single-photon coupling strength of 16 MHz. Thanks to the fast exciton decay in the QDM, the transduction bandwidth between an optical and microwave resonator photon reaches several 100 s of MHz. We also show that the transduction process via the QDM is fully coherent within the measurement error range.

Popular Summary

The realization of a quantum network requires quantum circuits that locally process quantum information to be connected via quantum channels that can faithfully transmit quantum information from one of these nodes to another. Great progress has been made in implementing local quantum processors, especially using superconducting quantum circuits. However, superconducting circuits are not suitable for transmitting quantum information over long distances. To this end, a transducer is required to convert the quantum information from the microwave domain—in which most state-of-the-art quantum processors operate—to optical photons, which can be easily sent through fibers over long distances without significant loss or decoherence. Implementing such a transducer, however, is challenging, particularly because the coupling strength between a single microwave quantum and a single optical photon is typically weak in transducers based on traditional nonlinear optical or optomechanical devices.

In order to address this issue, we demonstrate a novel physical platform consisting of a quantum dot molecule (QDM) integrated into a superconducting coplanar waveguide resonator. The electric dipole moment of an optically excited exciton in an InAs/GaAs QDM couples efficiently to the microwave field in the resonator. The large electric dipole moment of the molecular excitonic state in the QDM enables the realization of large single-photon coupling strength between the microwave resonator photon and the exciton. Mediated by such single-photon interaction, we demonstrate microwave-to-optical photon transduction. Furthermore, the fast optical recombination of the exciton implies that the transduction bandwidth can be very large.

Figure 1

(a) Optical microscope images of the transducer system and an enlarged image around QDMs. A λ/2 coplanar waveguide resonator electrically couples to $\mathrm{In}\mathrm{As}/\mathrm{Ga}\mathrm{As}$ QDMs embedded in the mesa structure at the field antinode. (b) Schematic cross section (not to scale). The top $\mathrm{Ti}/\mathrm{Au}$ gate and the bottom doped layer confines a vertical microwave field E, allowing for efficient microwave coupling to the vertical electric dipole moment μ = ed of an optically excited exciton inside the QDM. The bottom DBR mirror, together with the thin $\mathrm{Ti}/\mathrm{Au}$ top gate, ensures the optical coupling to free space. (c) Energy diagram of the transduction process. A QDM emits an optical photon upon absorption of a microwave and red-detuned optical photon (microwave-to-optical transduction highlighted by red arrows) or emits a microwave photon upon absorption of a blue-detuned optical photon (optical-to-microwave transduction highlighted by blue arrows).

Figure 2

(a) Bias voltage (V_bias) dependence of DR for a QDM measured by lock-in detection. The signal dx/R represents the ratio of the real part of the demodulated complex QD emission signal to the laser reflection intensity. (b) DR signal measured at the point A in (a) while driving the QDM with increasing microwave resonator photon number (n_m). (c) Relationship between the estimated single-photon coupling strengths (g₀) and the dipole sizes (|d|) for QDM1 (red dots) and QDM2 (blue dots) in the same device. The error bars represent the standard errors of the fits used for the estimation. The solid black line and shaded area show the theoretically estimated g₀ and its systematic error range.

Figure 3

(a) Microwave mean photon number (n_m) dependence of the internal transduction gain (G_int) for up- and down-conversion with the red- or blue-detuned optical drives, corresponding to the microwave-to-optical (M-O) or optical-to-microwave (O-M) transduction gain, respectively. The solid black line exhibits the fit for the linear regime. (b) Single-photon coupling strength (g₀) dependence of G_int for the M-O transduction measured with QDM1 and QDM2 at various n_m. (c) Normalized internal transduction gain G_int for up- (top panel) and down-conversion (bottom panel) measured as a function of the red- or blue-detuned laser frequency (ω_L = ω^± + Δω) at a fixed microwave drive frequency, power, and bias voltage. The data is normalized by the Lorentzian fits. The up- and down-conversion correspond to the M-O and O-M transduction, respectively. The dark and light red (blue) shaded areas show the 68% confidence band (CB) and prediction band (PB) of the fit shown as the solid red (blue) line. The signal-to-noise ratio of the down-converted photons is worse than that of the up-converted photons simply because the excitation laser power (P_o ∼ 3 nW) used particularly for this down-conversion experiment is an order of magnitude smaller.

Figure 4

Interference contrasts between the laser field and the transduced photon field [microwave to optical in (a) and optical to microwave in (b)] measured by DR spectroscopy. The contrasts are normalized by the amplitude A_m corresponding to perfectly coherent transduction. The experiment is performed on QDM1 with an applied dc bias voltage and resonant laser wavelength of 966.19 nm corresponding to point A in Fig. 2 while sweeping the phase ϕ_m of the EOM drive frequency. The dots and solid lines represent the experimental results and the sinusoidal fit. The vertical error bars on the measurement data points represent the standard deviation of the DR measurement. The horizontal error bars indicate the phase uncertainty. The red and blue shaded areas represent the 1σ error ranges that include the standard errors of the fits and the uncertainty of the normalization factor A_m. (c) shows the interference contrasts for the transduced photon field from the M-O transduction process over the entire exciton spectral range, obtained by shifting the QD exciton frequency with respect to the red-detuned laser frequency by tuning the dc bias voltage. ΔV_bias represents the amount of the detuning of the dc bias voltage.

Figure 5

(a) Dipole size (|d|) dependences of the single-photon cooperativity (C₀). We calculate the solid black line and points using the theoretically and experimentally estimated g₀ shown in Fig. 2, Γ_QD/2π = 300 MHz, and κ/2π = 138 MHz. The solid orange line shows the dependence when a QDM couples to a high-impedance superconducting resonator with κ ≪ Γ_QD. The dashed line indicates C₀= 1 at |d| = 2.6 nm. The inset shows η_int as a function of C₀. The solid brown line is the theoretically predicted result using Eq. (2) and C₀ shown in the main panel, and the black dots represent the experimentally estimated η_int from Fig. 3. The dashed line indicates η_int ∼ 10^-3 at C₀= 1. (b) Theoretically predicted detuning (δ = ω_m − Δ_ef) dependence of η_int at |d| = 2.6 nm. The dashed lines are far-detuned cases (|δ| ≫ ω_m) for the current device (black) and a QDM with a high-impedance resonator (orange). The solid lines are close-to-resonance cases (|δ| < ω_m) where state |f〉 plays a role. The black dot indicates the experimentally estimated η_int with the current device at |d| = 2.6 nm. The energy diagrams next to the graph show the M-O (red) and O-M (blue) transduction processes with the detuning |δ| < ω_m.

Figure 6

Schematic of the measurement setup. The sample is located at 4.2 K in a bath cryostat. The system comprises the setups for microwave drive and detection, photoluminescence measurement, DR measurement, transduction experiment, and coherence measurement.