Enhancing quantum transduction via long-range waveguide-mediated interactions between quantum emitters

Efficient transduction of electromagnetic signals between different frequency scales is an essential ingredient for modern communication technologies as well as for the emergent field of quantum information processing. Recent advances in waveguide photonics have enabled a breakthrough in light-matter coupling, where individual two-level emitters are strongly coupled to individual photons. Here we propose a scheme that exploits this coupling to boost the performance of transducers between low-frequency signals and optical fields operating at the level of individual photons. Specifically, we demonstrate how to engineer the interaction between quantum dots in waveguides to enable efficient transduction of electric fields coupled to quantum dots. Owing to the scalability and integrability of the solid-state platform, our transducer can potentially become a key building block of a quantum internet node. To demonstrate this, we show how it can be used as a coherent quantum interface between optical photons and a two-level system like a superconducting qubit.

Figure 1

(a) A two-level system (TLS) represented by an oscillating electric dipole (1) is electrically coupled to a semiconductor QD (2) inside a waveguide (3). We consider several configurations with varying number and locations of the QDs. (b) Side view of the transducer. The TLS (orange) is a distance $d$ away from the photonic crystal of thickness $h=140\mathrm{nm}$, with a QD in the center (roughly corresponding to Ref. [26]). (c) Energy-level diagram of a single-QD transducer, with $|e\rangle \text{and}|g\rangle$ being the QD excited and ground state, respectively. The electrical coupling $g_s$ enables a Raman transfer between internal states $|0\rangle$ and $|1\rangle$ of the coherent TLS, separated by a frequency difference ${\omega }_q$, through the path indicated by arrows.

Figure 2

(a) Transducer based on two QDs in a waveguide. One of the QDs is electrically coupled to the TLS. (b) Energy-level diagram of the combined QD-TLS system. $\left\{\right|0\rangle ,|1\rangle \}$ represent the TLS internal states. $\left\{\right|A\rangle ,|S\rangle \}$ represent the (anti-)symmetric states of the two-QD coupled system. The incoming photon is tuned into resonance with $|A1\rangle$. (c) Four QDs in a waveguide are spaced equidistantly such that $k\mathrm{\Delta }z=\pi /2$. One of the central QDs is coupled to a coherent two-level system. (d) Energy-level diagram of the combined QD-TLS system for four QDs, with two sets of (anti-)symmetric eigenstates spaced by $\nu \approx 1.3{\mathrm{\Gamma }}_{\text{1D}}$, decaying at enhanced(reduced) decay rates.

Figure 3

(a) Raman transition probability as a function of coupling strength $g_s$. The exact forms (markers) include all scattering pathways, while approximate forms (lines) include only the most significant pathway, as given by Eqs. (2), (4), and (5). For the one-QD (red) and two-QD (blue) cases, we set ${\omega }_q=2\pi \times 5$ GHz, ${\mathrm{\Gamma }}_{\text{1D}}=1{\text{ns}}^{-1}$, $\beta =0.9$. In the four-QD case (green), we assume a Purcell enhanced emitter decay rate $1/{\mathrm{\Gamma }}_{\text{1D}}=1.27/{\omega }_q\approx 250$ ps and $\beta =0.9$. We optimize the detunings $\delta$ and $\mathrm{\Delta }$ in the full numerics and fix the inter-QD spacing $k\mathrm{\Delta }z=n\pi$ (with integer $n$) in the two-QD case and to $k\mathrm{\Delta }z=\pi /2$ in the four-QD case. (b) Infidelity ($1-F$, solid lines) and success probability $P_{\text{suc}}$ (dashed lines) of entanglement generation for a coherent pulse input, as a function of average photon number. Detection efficiency $\eta =0.7$, coupling $g_s=2\pi \times 1$ GHz, and the other parameters as in panel (a).

Figure 4

(a) The qubit (orange) is positioned at a distance $d$ away from the waveguide (blue) of thickness $h=140$ nm with a quantum dot in the middle. (b) Top view of the qubit, with numbers labeling the relative position of the QD underneath the qubit. Assumed dimension are short edge 200 nm, long edge 700 nm, and thickness 20 nm. (c) Coupling $g_s$ derived from an electrostatic simulation of the device. Different relative positions of the QD are labeled with indices defined in panel (b). Suffix (v) refers to the vertical geometry (e), whereas the remaining curves are for the horizontal geometry (d). (f) Simulation of optical absorption as a function of distance $d$, for the two different configurations in panels (d) and (e), assuming the short edge of the qubit to be aligned with the center of the waveguide.

Figure 5

Raman-scattering probability as a function of relative emitter decay rates. We assume the same $\beta$ factors for both emitters, but different decay rates per emitter. We fix the sum of the decay rates ${\mathrm{\Gamma }}_{1,\text{1D}}+{\mathrm{\Gamma }}_{2,\text{1D}}\equiv {\mathrm{\Gamma }}_{\text{1D}}$ and change the ratio ${\mathrm{\Gamma }}_{2,\text{1D}}/{\mathrm{\Gamma }}_{1,\text{1D}}$ on the $x$ axis. Both the reflected and the transmitted light are caught, are filtered for red, and then the amplitudes are added together (with a tunable phase between them) such that the magnitudes add up completely constructively. We set ${\omega }_q=5{\mathrm{\Gamma }}_{\text{1D}}$, $g_s=0.4{\mathrm{\Gamma }}_{\text{1D}}$ and optimize the detunings using Newton's method.