Phase Tetrastability in Parametric Oscillation

TL;DR

This paper introduces a universal method to induce tetrastability in parametric oscillators by periodically modulating the drive amplitude, expanding the potential for applications in various scientific fields.

Contribution

The paper presents a novel approach to achieve tetrastability in parametric oscillators through amplitude modulation, supported by theoretical analysis and experimental validation.

Findings

Theoretically and numerically validated the method for tetrastability.

Experimentally demonstrated tetrastability in an optical oscillator.

Potential applications in pattern formation, quantum information, and sensing.

Abstract

The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at the root of the extraordinary importance of parametric oscillation (and amplification) both in fundamental and applied scenarios. Here we put forward a universal method for exciting tetrastability in parametrically-driven systems, which consists in modulating the amplitude of the parametric drive in such a way that its sign alternates periodically in time. This way, multistability can emerge between four states whose phases differ by a multiple of \pi/2. We prove theoretically the validity of the method, both analytically and numerically, and demonstrate it experimentally in an optical oscillator. The method could be relevant to the fields of pattern formation, (quantum) information processing and simulation, metrology and sensing.