Terahertz-mediated microwave-to-optical transduction

Transduction of quantum signals between the microwave and the optical ranges will unlock powerful hybrid quantum systems enabling information processing with superconducting qubits and low-noise quantum networking through optical photons. Most microwave-to-optical quantum transducers suffer from thermal noise due to pump absorption. We analyze the coupled thermal and wave dynamics in electro-optic transducers that use a two-step scheme based on an intermediate frequency state in the THz range. Our analysis, supported by numerical simulations, shows that the two-step scheme operating with a continuous pump offers near-unity external efficiency with a multiorder noise suppression compared to single-step transduction. As a result, two-step electro-optic transducers may enable quantum-noise-limited interfacing of superconducting quantum processors with optical channels at MHz-scale bit rates.

Figure 1

(a) Single-step EO quantum transduction in the frequency domain. (b) Schematic of an EO transducer model consisting of a LN optical resonator with coupling parameter 1−$R$, cross-section diameter $w$, and length $L$, integrated with a superconducting NbN resonator. The heating $\mathrm{\Delta }{T}_{\mathrm{EO}}$ is caused by optical pump absorption in LN. The thermal transport is assumed to be radial. (c) The microwave mode occupancy and (d) the external conversion efficiency as a function of $w$ and $L$ for ${\omega }_{\mu }=2\pi \times 8$ GHz, $1-R={10}^{-3}$, and base temperature $T_{\mathrm{EO}}=10$ mK, at unity cooperativity. The red dot marks the numerically simulated geometry for microwave-to-optical transduction.

Figure 2

(a) Two-step transduction using the kinetic inductance and electro-optic nonlinearities. (b) The intermediate frequency mode occupancy and (c) the external conversion efficiency as a function of $w$ and $L$ for ${\omega }_i=2\pi \times 600\mathrm{GHz}$, 1 − $R ={10}^{-3}$, and base temperatures $T_{\mathrm{KI}}=T_{\mathrm{EO}}=10$ mK at unity cooperativity. The red dot marks the numerically simulated geometry for two-step transduction via 600 GHz.

Figure 3

(a) Cross section and top view of simulated second-step transducer, consisting of a superconducting NbN resonator whose capacitor rings are placed around a LN ring resonator. The NbN resonator also contains a larger inductive ring whose radius is determined by the operating wavelength. Cross-sectional profiles for (b) $s_i$ and $p_o$ fields and (c) $\mathrm{\Delta }{T}_{\mathrm{EO}}$. Colors in (b) represent the electric field norm corresponding to an optical pump in linear scale, and the arrows represent intermediate-frequency electric field strength and direction. Colors in (c) represent the temperature distribution in logarithmic scale. Analytical and numerical calculations of (d)–(f) mode occupancy and (g)–(i) external conversion efficiency of the EO step at 10 mK, 1 K, and 4 K.

Figure 4

Analytical and numerical calculations of (a) mode occupancy and (b) external conversion efficiency of the EO step at 10 mK for lower $C_{\mathrm{EO}}$ values of ${10}^{-2}$, 0.1, 0.3, and 0.5.

Figure 5

(a) Real and imaginary parts of complex conductivity from 1 mK to 10 K for NbN [70, 71, 72, 73, 74, 75].

Figure 6

Extended single-step transduction calculations of mode occupancy and external conversion efficiency for 1 – R$={10}^{-2}$ (a,b) and 1 − $R ={10}^{-4}$ (c,d). The shaded regions in (a,b) are no longer strictly in the resolved-sideband regime.

Figure 7

Extended two-step transduction calculations of mode occupancy and external conversion efficiency for 1 − $R ={10}^{-2}$ (a), (b) and 1 − $R ={10}^{-4}$ (c), (d). The shaded regions in (a), (b) are no longer strictly in the resolved-sideband regime.

Figure 8

(a) $\mathrm{\Delta }{T}_{\mathrm{KI}}$ depending on $w\prime$ and $L$′. Inset is the kinetic inductor geometry with 20 nm thickness. The red dot marks a device design that is estimated to perform with $\eta \sim 0.99$ and $n_{\mu }\ll {10}^{-6}$. (b) $\mathrm{\Delta }{T}_{\mathrm{EO}}$ depending on $w$ and $L$.

Figure 9

(a) Transduction fidelity for a coherent state with ${\left|\alpha \right|}^2=1$. (b) Lower-bound and (c) upper-bound quantum channel capacity. The straight lines (markers) indicate values estimated based on analytically (numerically) calculated transduction parameters.