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arXiv:2412.02887 · Physical Review Research

Quantum sensitivity of parametric oscillators

Alex Gu, Jamison Sloan, Charles Roques‐Carmes, Seou Choi, Eric I. Rosenthal, Michael Horodynski, Yannick Salamin, Jelena Vuckovic A, Marin Soljacic A

Published Jun 6, 2025• 3 citations
arXivHTMLPDF

Abstract

Many quantum systems exhibit high sensitivity to their initial conditions, where microscopic quantum fluctuations can significantly influence macroscopic observables. Understanding how quantum states may influence the behavior of nonlinear dynamic systems may open new avenues in controlling light-matter interactions. To explore this issue, we analyze the sensitivity of a fundamental quantum optical process – parametric oscillation – to quantum initializations. Focusing on optical parametric oscillators (OPOs), we demonstrate that the quantum statistics of arbitrary initial states are imprinted in the early-stage dynamics and can persist in the steady-state probabilities. We derive the “quantum sensitivity” of parametric oscillators, linking the initial quantum state to the system's steady-state outcomes, highlighting how losses and parametric gain govern the system's quantum sensitivity. Moreover, we show that these findings extend beyond OPOs to a broader class of nonlinear systems, including Josephson junction based superconducting circuits. Our work opens the way to a new class of experiments that can test the sensitivity of macroscopic systems to quantum initial conditions and offers a pathway for controlling systems with quantum degrees of freedom.

DOI
10.1103/physrevresearch.7.l022056

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Many quantum systems exhibit high sensitivity to their initial conditions, where microscopic quantum fluctuations can significantly influence macroscopic observables. Understanding how quantum states may influence the behavior of nonlinear dynamic systems may open new avenues in controlling light-matter interactions. To explore this issue, we analyze the sensitivity of a fundamental quantum optical process – parametric oscillation – to quantum initializations. Focusing on optical parametric oscillators (OPOs), we demonstrate that the quantum statistics of arbitrary initial states are imprinted in the early-stage dynamics and can persist in the steady-state probabilities. We derive the “quantum sensitivity” of parametric oscillators, linking the initial quantum state to the system's steady-state outcomes, highlighting how losses and parametric gain govern the system's quantum sensitivity. Moreover, we show that these findings extend beyond OPOs to a broader class of nonlinear systems, including Josephson junction based superconducting circuits. Our work opens the way to a new class of experiments that can test the sensitivity of macroscopic systems to quantum initial conditions and offers a pathway for controlling systems with quantum degrees of freedom.
Most treatments of noise characteristics of optical parametric oscillators (OPOs) have been based on linearization of the equations of motion. This approach, valid far below and far above threshold, breaks down in the threshold region as it ignores the nonlinearity of interaction. We present a treatment that takes into account both the nonlinearity and the quantum mechanical nature of noise in these oscillators. Analytical expressions for the steady-state amplitude distribution functions are derived. Both the degenerate and the nondegenerate OPOs are considered. These steady-state distributions are used to study the coherence properties of the OPOs in the threshold region. These studies bridge the noise characteristics of the OPOs below and above threshold. Results are compared with classical oscillators and differences and similarities are discussed. Special attention is given to quantum mechanical features that survive even as the oscillator amplitude grows and reaches macroscopic proportions.
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We have carried out a linearized quantum analysis of the steady-state operation of an optical parametric oscillator (OPO) without cavity detunings; our analysis emphasizes the effects of pump quantum noise and pump excess noise. We show that pump excess noise reduces the observable signal/idler intensity correlation at low frequencies only in the presence of a cavity-loss mismatch between these subharmonic waves. This effect is so strong that the combination of pump excess noise and cavity-loss mismatch explains the rapid low-frequency noise increase well above the shot-noise level that has been seen in recent signal/idler correlation measurements. Moreover, the critical dependence of intensity correlation on cavity-loss mismatch opens a new possibility for ultrasensitive intracavity absorption spectroscopy. Specifically, sinusoidal amplitude modulation of the OPO pump beam with lock-in amplification of the signal/idler photocurrent affords a sensitive probe of subharmonic cavity-loss mismatch. Although this robust measurement capability exploits the strong intracavity correlation between the signal and idler waves, it does not require that nonclassical correlation be externally observable, nor is it limited to near-threshold OPO operation.
Bistable driven-dissipative systems near bifurcations can exhibit noise-activated switching between steady states. Here, we investigate how quantum vacuum fluctuations induce such switching in a biased optical parametric oscillator (OPO), a nonlinear system with intrinsic bistability. We show how microscopic quantum fluctuations driving macroscopic transitions can be controlled with an external bias field that reshapes the OPO steady-state metapotential. We derive analytical expressions for the average switching time and validate them through simulations of the OPO field distribution and inter-state probability flow under bias injection. We further examine how switching depends on bias strength, pump gain, and optical nonlinearity. Our findings clarify how quantum noise can shape macroscopic dynamics and provide a foundation for noise-assisted photonic machine learning and probabilistic quantum gates.