A Gaussian Oscillator

Preparing a mechanical oscillator in non-gaussian quantum states.

We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant ...

One-Parameter Squeezed Gaussian States of Time-Dependent Harmonic Oscillator

We show that the nonlinear auxiliary equation for the invariant introduced by Lewis and Riesenfeld for a time-dependent harmonic oscillator is satisfied by the amplitude of a complex soltuion to the classical equation of motion. One-parameter squeezed Gaussian states are found whose parameter denotes the mixing of positive and negative frequency solutions. The minimization of the energy expecta...

Dynamics of the Stochastic Duung Oscillator in Gaussian Approximation

The previously developed general concept of the Gaussian approximation allows the description of the driven stochastic Duung oscillator by ordinary diierential equations. These equations are analysed analytically as well as numerically to investigate the modiication of simple bifurcations and of the Feigenbaum cascade by stochastic forces. Furthermore the method allows a qualitative discussion ...

Post-Gaussian variational method for quantum anharmonic oscillator

Using the post-Gaussian trial functions, we calculate the variational solutions to the quantum-mechanical anharmonic oscillator. We evaluate not only the ground state but also some excited energies, and compare them with numerical results.

Gaussian Basis Sets for Model Anharmonic Oscillator Systems