Related papers: Quantum Synchronization in quadratically coupled q…
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior.…
This paper investigates the synchronization of three identical oscillators, or clocks, suspended from a common rigid support. We consider scenarios where each clock interacts with the other two, achieving synchronization through small…
The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential is studied. The (non-exponential) decoherence induced on the oscillator by the…
We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the…
Quantum optomechanical system serves as an interface for coupling between photons and phonons due to mechanical oscillations. We used the Heisenberg-Langevin approach under Markovian white noise approximation to study a quadratically…
Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been…
We theoretically analyze antibunching of the phonon field in an optomechanical oscillator employ- ing the membrane-in-the-middle geometry. More specifically, a single-mode mechanical oscillator is quadratically coupled to a single-mode…
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…
Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic…
Synchronization of self-sustained oscillators under fixed-frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow, deterministic…
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On…
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global…
The dissipative quantum dynamics of an anharmonic oscillator is investigated theoretically in the context of carbon-based nano-mechanical systems. In the short-time limit, it is known that macroscopic superposition states appear for such…
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
We study synchronization in a two-node network built out of the smallest possible self-sustained oscillator: a spin 1. We first demonstrate that phase locking between the quantum oscillators can be achieved, even for limit cycles that…
Experiments and supporting theoretical analysis is presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation,…
Quantum harmonic oscillators model a wide variety of phenomena ranging from electromagnetic fields to vibrations of atoms in molecules. Their excitations can be represented by bosons such as photons, single particles of light, or phonons,…
Two non-harmonic canonical-dissipative limit cycle oscillators are considered that oscillate in one-dimensional Smorodinsky-Winternitz potentials. It is shown that the standard approach of the canonical-dissipative framework to introduce…
We begin with the simple model of phase sychronization in open classical nonlinear system which is represented in the language of angular momentum variables. After that we propose the relevant quantum counterpart of this system. Using the…