Crosstalk-constrained multimode capacity of spectro-temporally multiplexed quantum memories

The time-bandwidth product (TBP) commonly characterizes the multimode capability of optical quantum memories. However, overlap between neighboring spectral and temporal modes causes crosstalk, reducing fidelity and the number of usable modes. Here, we develop a Gaussian crosstalk model for spectro-temporally multiplexed quantum memories and derive the maximum usable multimode capacity under a given fidelity requirement. For Fourier-transform-limited Gaussian photons, the multimode capacity can be expressed analytically in terms of the TBP, the required fidelity, and the timing jitter. For unit intrinsic fidelity and zero jitter, the multimode capacity is approximately 0.827, 0.628, and 0.399 times the TBP for fidelities of 0.90, 0.95, and 0.99, respectively. Timing jitter further reduces the achievable multimode capacity. These results provide a simple framework for estimating the usable multimode capacity of multiplexed quantum memories.