Electro-Optic Frequency Beam Splitters and Tritters for High-Fidelity Photonic Quantum Information Processing

We report the experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity ($0.99998\pm 0.00003$), requires only a single microwave drive tone for near-ideal performance, functions across the entire $C$ band (1530–1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits, we implement a $3\times 3$ extension of the Hadamard gate: the balanced tritter. This tritter—the first ever demonstrated for frequency modes—attains fidelity $0.9989\pm 0.0004$. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.

Figure 1

Experimental setup. See the text and Ref. [35] for details.

Figure 2

Experimentally measured beam splitter output spectra for specific coherent state inputs. (a) Pure mode 0, $|{\alpha }_{{\omega }_0}{0}_{{\omega }_1}⟩$. (b) Pure mode 1, $|0_{{\omega }_0}{\alpha }_{{\omega }_1}⟩$. (c) Mode 0 and mode 1 in phase, $|{\alpha }_{{\omega }_0}{\alpha }_{{\omega }_1}⟩$. (d) Mode 0 and mode 1 out of phase, $|{\alpha }_{{\omega }_0}(-\alpha {)}_{{\omega }_1}⟩$.

Figure 3

(a) Fidelity and success probability as a function of the center wavelength. (b) Parallel beam splitter performance against frequency separation.

Figure 4

Experimentally measured tritter output spectra for specific coherent-state inputs. (a) Pure mode 0, $|{\alpha }_{{\omega }_0}{0}_{{\omega }_1}{0}_{{\omega }_2}⟩$. (b) Pure mode 1, $|0_{{\omega }_0}{\alpha }_{{\omega }_1}{0}_{{\omega }_2}⟩$. (c) Pure mode 2, $|0_{{\omega }_0}{0}_{{\omega }_1}{\alpha }_{{\omega }_2}⟩$. (d) Outputs for the superposition state input $|{\alpha }_{{\omega }_0}(e^{-i\varphi }\alpha {)}_{{\omega }_1}(e^{-2i\varphi }\alpha {)}_{{\omega }_2}⟩$ for (I) $\varphi =0$, (II) $\varphi =2\pi /3$, and (III) $\varphi =4\pi /3$.

Figure 5

Spectral interference with weak coherent states. (a) Output count rates for the two frequency modes of the beam splitter, as the phase $\varphi$ of the single-photon-level state $|{\alpha }_{{\omega }_0}(e^{-i\varphi }\alpha {)}_{{\omega }_1}⟩$ is scanned. (b) Counts for the three output modes of the frequency tritter as the phase $\varphi$ of the three-mode state $|{\alpha }_{{\omega }_0}(e^{-i\varphi }\alpha {)}_{{\omega }_1}(e^{-2i\varphi }\alpha {)}_{{\omega }_2}⟩$ is scanned. The plotted best-fit curves are Fourier series of the form $\sum _n{A}_n\cos (n\varphi +B_n)$, summed from $n=0$ to 1 for (a) and $n=0$ to 2 for (b).