Quantum sensitivity of parametric oscillators

TL;DR

This paper investigates how quantum initial states influence the dynamics and steady-state behavior of parametric oscillators, revealing persistent quantum sensitivity and potential for controlling nonlinear quantum systems.

Contribution

It introduces the concept of quantum sensitivity in parametric oscillators, linking initial quantum states to steady-state outcomes and extending the analysis to broader nonlinear systems.

Findings

Quantum initial states affect early dynamics and steady-state probabilities.

Losses and gain parameters govern quantum sensitivity.

Findings extend to superconducting circuits.

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.