Mode Selection in Quantum Nonlinear Optics Using Optical Resonators

Abstract

Nonlinear optics underpins quantum photonics by enabling the generation and control of quantum states of light. We present new applications of optical resonators as mode selectors in nonlinear processes. First, we show that cavity-enhanced spontaneous parametric down-conversion can generate spectrally uncorrelated photon pairs with improved decorrelation and wavelength flexibility. Second, we demonstrate that a cavity-assisted sum-frequency generation process realizes a quantum pulse gate with high-resolution temporal-mode selectivity and precise spectral control. Our theoretical framework provides a general methodology for analyzing cavity-enhanced nonlinear processes and highlights the versatility of optical resonators as powerful tools for engineering quantum light.

Figures (4)

• Figure 1: Schematic illustration of the CSPDC. 'BS': Beamsplitter.
• Figure 2: (a) Amplitude of the JSF for Type-II SPDC in BBO pumped by a broadband field centered at 263 nm, with both signal and idler resonant at 525 nm ($\gamma_j=0.1$ THz); idler mode purity $p=0.9996$. (b) Normalized linewidth, biphoton generation rate, and heralding rate versus internal loss $\iota/\gamma$ for equal losses in signal and idler modes; all quantities are normalized to their respective lossless values. (c) Amplitude of the JSF for the single-resonator configuration with pump in the second Hermite–Gaussian mode ($\gamma_s=0.004$ THz). Colormaps in (a) and (c) are scaled individually.
• Figure 3: Schematic illustration of the CSFG. 'BS': Beamsplitter.
• Figure 4: (a) Amplitude of the frequency-domain transfer function $G_s(\omega_{n_i},\omega_{n_s})$ for CSFG. Parameters: $\gamma/\Delta\omega=\eta^{2}/2\pi=10^{-2}$. For numerical tractability, 100 frequency modes are used, with the pump spectrum in the second Hermite–Gaussian mode. (b) Separability of the target TM and its fidelity relative to the pump field $\beta(t)$ as functions of $\gamma/\Delta\omega$, with all other parameters fixed as in (a) and $\gamma/\Delta\omega$ varied under the constraint $\eta =\sqrt{\gamma T}$. Also shown is the CE of the target TM, as a function of the internal loss $\iota/\gamma$ in the limit $\eta=\sqrt{(\gamma+\iota)T}\to0$. (c) Amplitude of the three-output transfer function of a three-peak MQPG, with pump peaks shaped as the first three Hermite–Gaussian modes.