Numerical Simulation of Quantum Random Number Generation in Silicon Nitride Microresonators

Introduction

Random number generators (RNGs) are crucial components in many fields, such as scientific simulations (e.g., Monte Carlo simulations), cryptography (e.g., quantum key distribution), and fundamental physics tests (e.g., Bell's inequality). Traditional pseudorandom number generators based on classical processors have limitations, leading to the exploration of quantum mechanics as a source of true randomness. Quantum RNGs can be implemented using intrinsic sources like radioactive decay, photon emission, and vacuum fluctuations.

All-optical quantum RNGs without post-processing can be realized through degenerate optical parametric oscillators (OPOs) utilizing second-order (χ^(2)) or third-order (χ^(3)) nonlinearity. Recently, there has been growing interest in exploiting microresonator-based OPOs on the silicon photonics platform due to their CMOS process compatibility. This article theoretically and numerically investigates a dual-pumped silicon nitride-based quantum RNG using the non-equilibrium phase transitions of an unbiased OPO initiated by quantum noises.

System Design

The proposed system, as illustrated in Fig. 1, consists of a silicon nitride microresonator-based RNG utilizing two pumps modulated by electro-optic modulators (EOMs). The microresonator has a 100 μm radius, an intrinsic loss down to 0.1 dB/cm, and a coupling coefficient of 0.001 (critical coupling).

Fig. 1: Diagram showing the components of the microresonator-based quantum RNG system. It includes dual 10 mW pumps modulated by electro-optic modulators (EOM) with feedback control for thermal drift compensation. The signal generated by four-wave mixing (FWM) is analyzed using an asymmetric Mach-Zehnder interferometer. Additional components include an erbium-doped fiber amplifier (EDFA), bandpass filter (BPF), beam splitter (BS), and photodiode (PD).

Quantum noise due to vacuum fluctuation is amplified by the pumps via stimulated four-wave-mixing (FWM). The generated bi-phase bits are detected by a Mach–Zehnder interferometer (MZI) with a delay line.

To optimize the system, the intracavity power of the dual pumps on resonance near critical coupling is tuned to exceed the power threshold required for optical parametric oscillation, determined by the quality factor of the cavities. The Kerr-based OPOs should operate at the degenerate point with normal group velocity dispersion (GVD), where the generated signal frequencies overlap.

Additionally, the parametric gain of the phase-sensitive amplification (PSA) is tuned to obtain the maximum on-off extinction ratio in the parameter space of pump detuning and initial signal phase. The control of spectral phase transition has been studied in previous work.

Numerical Simulation

Figure 2 presents the numerical simulation results of the phase-sensitive amplification and the temporal response of the quantum RNG by exploring the parameter space of pump power, detuning, modulation frequency, and intrinsic loss.

Fig. 2: Displays the phase-sensitive amplification and temporal response of a degenerate OPO-based RNG. (a) Round-trip parametric gain depicted against pump power and signal phase, with nominal power marked at 10 mW. (b) Total parametric gain related to pump detuning and signal phase. (c) Temporal response of phase-sensitive gain for varying signal phases. (d) Temporal evolution of intracavity power for dual pumps, signal, and signal phase. (e) Intracavity signal power across different modulation frequencies. (f) Intracavity signal power varied by intrinsic waveguide loss.

Figure 2a and 2b depict the conditions for phase-sensitive amplification. First, the pump power should exceed the necessary threshold (sub-milliwatt) for parametric oscillations and remain under 46 mW. By setting the pump detuning to 1.9 GHz, a PSA gain with an extinction ratio of 20 dB is enabled, which is crucial for the optimum bi-phase state transition.

Figure 2c illustrates the temporal response of the PSA of the signal. Figures 2d, 2e, and 2f show the temporal responses of the degenerate OPO-based RNG. The temporal evolutions of the intracavity power of the pumps, signal, and signal phase are visualized with a pump power of 10 mW and a detuning of 1.9 GHz. As a result, random bits encoded in the signal phase in the cavity are generated with a repetition rate of 10 MHz.

The impacts of the pump modulation frequency and the intrinsic loss of the waveguide are also investigated. Figure 2e demonstrates that as the modulation frequency increases, the generated signal via FWM exhibits a larger overshoot. Figure 2f shows that the OPO-based RNG operates only in a cavity with a propagation loss of less than 1 dB/cm. However, a lower intrinsic loss resulting in a larger quality factor can limit the generation rate of the RNG.

Conclusion

This article numerically investigated and optimized the phase-sensitive amplification and quantum random number generation in a silicon nitride microresonator-based system. A pump power of 10 mW and a pump detuning of 1.9 GHz were selected to obtain an optimized PSA gain with an extinction ratio of 20 dB. The temporal response of the quantum RNG was simulated with different modulation frequencies (5 MHz, 10 MHz, and 20 MHz) in the silicon nitride microresonator.

The proposed system demonstrates the potential of silicon nitride microresonators for quantum random number generation, paving the way for integrated, CMOS-compatible quantum RNGs with applications in various fields, such as secure communications and scientific simulations.

Reference

[1] M. He, M.-T. Catuneanu, and K. Jamshidi, "Numerical Simulation of Quantum Random Number Generation in Silicon Nitride Microresonators," Integrated Photonic Devices Laboratory, Technische Universität Dresden, Helmholtzstrasse 16, Dresden 01069, Germany, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.