Time-resolved characterization of pulsed squeezed light from a strongly driven silicon nitride microresonator

TL;DR

This work analyzes pulsed squeezed light generation in a silicon nitride microresonator across low-to-high parametric gain, highlighting how self- and cross-phase modulation and time-ordering affect spectral-temporal mode structure. A time-domain master-equation framework is developed and validated against experiments, revealing that an optimal pump detuning $\Delta_{opt}$ maximizes both photon flux and spectral purity, and that longer pulses can boost emission at fixed energy when detuned. The study also introduces a four-photon correction to time-resolved coincidences to mitigate multi-pair contamination in estimating the joint temporal intensity, enabling a more faithful reconstruction of time correlations. These findings provide practical guidelines for optimizing microresonator-based squeezed-light sources for scalable continuous-variable quantum computing and sensing applications.

Abstract

Silicon nitride microresonators driven by strong pump pulses can generate squeezed light in a dominant spectral-temporal mode, a central resource for continuous-variable quantum computation. In the high parametric gain regime, several effects, including self- and cross-phase modulation as well as time-ordering corrections, become significant and can degrade source performance. In this work, we comprehensively investigate the generation of squeezed light from a silicon nitride resonator under pulsed pumping, spanning from low to high parametric gain up to 16 photons/pulse. We experimentally study how the average photon number and the first- and second- order correlations of the squeezed marginal modes evolve with increasing pulse energy, across various frequency detunings and pulse durations. Furthermore, we analyze the errors introduced by multi-pair emissions in estimating the joint temporal intensity via time-resolved coincidence measurements. We propose and demonstrate an error-correction strategy based on the marginal distributions of time-resolved multi-photon events. Our results provide a practical strategy for optimizing the gain and the temporal mode structure of pulsed squeezed light sources in microresonators, elucidating the physical mechanisms and limitations that govern source performance in the high gain regime.

Figures (10)

• Figure 1: (a) Equivalent circuit representation of the sequence of operations transforming the input operators $(\mathbf{a}^{in},\mathbf{f}^{in})$ to the output operators $(\mathbf{a}^{out},\mathbf{f}^{out})$. (b) Top panel: sketch of the device layout and of the experimental setup. DeMUX: demultiplexer, BS: beasmplitter, SNSPD: superconducting nanowire single photon detector. Bottom panel: sketch of the pump (green), signal (red) and idler(blue) nonlinear resonances shifts $\Delta_{SPM}(t)$ and $\Delta_{XPM}(t)$ induced by SPM and XPM. The cold resonance frequencies are $\omega_{p0}$, $\omega_{s0}$ and $\omega_{i0}$ respectively. The pump spectrum, shown in gray, has the maximum detuned by $\Delta_p$ with respect to the cold cavity resonance frequency $\omega_{p0}$.
• Figure 2: (a) Measured average number of photons $\langle n_s (t)\rangle$ in the marginal signal beam as a function of time for different pump energies (both quantities are estimated on-chip) and $\Delta_p=0$. (b) Calculated $\langle n_s (t)\rangle$ at the same pulse energies indicated in panel (a) and with $\Delta_p=0$. (c) Measured and calculated (panel (d)) value of $\langle n_s (t)\rangle$ as a function of time for different pump energies at $\Delta_p=\Delta_{opt}$. (e) Simulation showing the incident pump envelope $\beta (t)$, the number of pump photons in the cavity $|\langle c_p(t)\rangle|^2$, the average number of signal photons $\langle n_s(t)\rangle$ in the output waveguide and the the energy mismatch $\Delta\omega$ (referred to the right vertical axis) for $\epsilon_p=1000$ pJ and $\Delta_p=0$. The values of $\beta (t)$, $|\langle c_p(t)\rangle|^2$ and $\langle n_s(t)\rangle$ have been all normalized to their maximum value for improved visualization. The same quantities are shown in panel (f) for $\epsilon_p=1500$ pJ and $\Delta_p=\Delta_{opt}.$
• Figure 3: (a) Measured average number of signal photons per pulse in the output waveguide as a function of the input pulse energy for different pulse durations. The dashed lines indicate the measurement performed at $\Delta_p=\Delta_{opt}$, while the continuous line is the measurement at $\Delta_p=0$. Error bars are smaller than the size of the data symbols. (b) Simulations of the average number of photons per pulse as a function of the input pulse energy for different pulse durations. Colors and line-style have the same meaning as in panel (a).
• Figure 4: (a) Measured average number of signal photons in the output waveguide as a function of the pump detuning $\Delta_p$ for different input powers. Error bars are smaller than the size of the data symbols. (b) Simulated average number of signal photons in the output waveguide as a function of the pump detuning $\Delta_p$.
• Figure 5: (a) Measured unheralded second-order correlation $g_{ss}^{(2)}$ of the signal mode as a function of the detuning between the pump and the cold resonance frequency for different pump pulse energies. (b) Numerical simulations of $g_{ss}^{(2)}$ for the same pump pulse energies shown in panel (a). (c) Measured unheralded second-order correlation of the $g_{ss}^{(2)}$ signal mode for different pulse durations as a function of the input pulse energy. The dashed lines report the measurements for $\Delta_p=\Delta_{opt}$, while the continuous lines for $\Delta_p=0$.