Large-scale cluster quantum microcombs

Abstract

An optical frequency comb comprises a cluster of equally spaced, phase-locked spectral lines. Replacing these classical components with correlated quantum light gives rise to cluster quantum frequency combs, providing abundant quantum resources for measurement-based quantum computation, and multi-user quantum networks. We propose and generate cluster quantum microcombs within an on-chip optical microresonator driven by multi-frequency lasers. Through resonantly enhanced four-wave mixing processes, continuous-variable cluster states with 60 qumodes are deterministically created. The graph structures can be programmed into one- and two-dimensional lattices by adjusting the configurations of the pump lines, which are confirmed inseparable based on the measured covariance matrices. Our work demonstrates the largest-scale cluster states with unprecedented raw squeezing levels from a photonic chip, offering a compact and scalable platform for computational and communicational tasks with quantum advantages.

Fig. 1. Schematic illustration of cluster quantum microcombs.

The microresonator hosts many spectral qumodes and several qumodes are simultaneously pumped by equally spaced continuous-wave lasers. Quantum microcombs with different entanglement structures are generated by two-mode squeezing (TMS), induced by either degenerate or non-degenerate four-wave mixing (FWM) processes

Fig. 2. Experimental setup and performance benchmark.

a Experimental setup. CW laser continuous-wave laser, EO comb electro-optic comb, EDFA erbium-doped fiber amplifier, PM phase modulator, IM intensity modulator, BPD balanced photodetector, ESA electrical spectrum analyzer, FPGA field-programmable gate array. b Photo (left) and scanning-electron-microscopy (right) images of the microresonators. c Transmission spectrum of the micro-resonator. Inset: Cross-sectional profiles of the microresonator and the optical mode, with the tapered fiber coupler indicated. d Upper panel: Pumping scheme and FWM processes. Lower panel: Electrical spectra showing quadrature noise variance relative to shot noise (gray) for the qumode pair (−16, 16)

Fig. 3. 1D cluster quantum microcombs.

a Experimentally measured 60-mode covariance matrix. Measurements in the gray shades are not taken. Quantum correlations induced by the major TMSs are indicated between the dashed lines in the zoom-in views. b PPT inseparability criteria for 2047 bipartitions for 6 sets of 12 qumodes. All bipartitions with PPT values below 1 indicate complete inseparability of the state. c Graph structures (left panel) and the measured squeezing of nullifiers ${\hat{N}}_k={\hat{p}}_k+0.65\left({\hat{x}}_{-k}+{\hat{x}}_{-k-1}\right)$ (right panel). The colors of the edges indicate different sets of major TMSs, and the purple shading indicates the nullifier. Quadrature noise variances for ${\hat{p}}_k+{\hat{x}}_{-k}$ and ${\hat{p}}_k+{\hat{x}}_{-k-1}$ are also plotted for comparison

Fig. 4. 2D cluster quantum microcombs.

a Experimentally measured 56-mode covariance matrix. Measurements in the gray shades are not taken. Quantum correlations induced by the major TMSs are indicated between the dashed lines in the zoom-in views. b PPT inseparability criteria for 2047 bipartitions for 6 sets of 12 qumodes. All bipartitions with PPT values below 1 indicate complete inseparability of the state. c Graph structures (left panel) and the measured squeezing of nullifiers ${\hat{N}}_k={\hat{p}}_k+0.5\left({\hat{x}}_{-k}+{\hat{x}}_{-k-1}+{\hat{x}}_{-k-2}\right)$ (right panel). The colors of the edges indicate different sets of major TMSs, and the purple shading indicates the nullifier. Quadrature noise variances for ${\hat{p}}_k+{\hat{x}}_{-k}$, ${\hat{p}}_k+{\hat{x}}_{-k-1}$ and ${\hat{p}}_k+{\hat{x}}_{-k-2}$ are also plotted for comparison

Fig. 5. A comparison of the raw squeezing and the size of cluster state in CV quantum states generated on photonic chips.

The dashed line indicates 3 dB value of raw squeezing. Results obtained in Si₃N₄ microresonators^,, and silica microresonators^, are plotted for comparison