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An experimentally feasible magnetometer based on a dual-coupling optomechanical system is proposed, where the radiation-pressure coupling transduces the magnetic signal to the optical phase, and the quadratic optomechanical interaction…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
The resonance characteristics of a driven damped harmonic oscillator are well known. Unlike harmonic oscillators which are guided by parabolic potentials, a simple pendulum oscillates under sinusoidal potentials. The problem of an undamped…
Though algorithms for quantum simulation of Quantum Harmonic Oscillator (QHO) have been proposed, still they have not yet been experimentally verified. Here, for the first time, we demonstrate a quantum simulation of QHO in the presence of…
Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined…
A detailed study of the relativistic classical and quantum mechanics of the massless harmonic oscillator is presented.
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
We propose a quantum harmonic oscillator measurement engine fueled by simultaneous quantum measurements of the non-commuting position and momentum quadratures of the quantum oscillator. The engine extracts work by moving the harmonic trap…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
We establish the principles for a new generation of simplified and accurate watt balances in which an oscillating magnet generates Faraday's voltage in a stationary coil. A force measuring system and a mechanism providing vertical movements…
A magnetic-mechanical oscillating system consists of two identical leaf springs, a non-magnetic base, and some magnets. The leaf springs are fixed at the bottom to the non-magnetic base, while the magnet is attached to the top of the leaf…
Long-lived mechanical oscillators are actively pursued as critical resources for quantum storage, sensing, and transduction. However, achieving deterministic quantum control while limiting mechanical dissipation remains a persistent…
We discuss theoretically the properties of an electromechanical oscillator whose operation is based upon the cyclic, quasi-conservative conversion between gravitational potential, kinetic, and magnetic energies. The system consists of a…
A quantum emitter coupled to a nano-mechanical oscillator is a hybrid system where a macroscopic degree of freedom is coupled to a purely quantum system. Recent progress in nanotechnology has led to the realization of such devices by…
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate…
Nanomechanical oscillators have been employed as transducers to measure force, mass and charge with high sensitivity. They are also used in opto- or electromechanical experiments with the goal of quantum control and phenomena of mechanical…
The longitudinal oscillations of air columns composed of contractions and rarefaction make up sound. Sound amplification is widely used in medical, electronic and communication fields. A simplistic technique for producing and amplifying can…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
This article presents the calculation of gravitational and electromagnetic radiation emitted from a classical simple harmonic oscillator (SHO). Here we show only the selected formulae and apply them to a toy problem without rigorous…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…