# Preparing quasienergy states on demand: A parametric oscillator

## TL;DR

This paper demonstrates a method to prepare specific quasienergy states in a nonlinear parametric oscillator using adiabatic techniques and Landau-Zener transitions, analyzing the resulting quantum states and emitted radiation.

## Contribution

It introduces a controlled protocol for on-demand quasienergy state preparation in a nonlinear oscillator, including state characterization and emission spectrum analysis.

## Key findings

- Successful preparation of even quasienergy states from the ground state.
- Ability to create superpositions via Landau-Zener transitions.
- Characterization of the emitted radiation spectrum.

## Abstract

We study a nonlinear oscillator, which is parametrically driven at a frequency close to twice its eigenfrequency. By judiciously choosing the frequency detuning and linearly increasing the driving amplitude, one can prepare any even quasienergy state starting from the oscillator ground state. Such state preparation is effectively adiabatic. We find the Wigner distribution of the prepared states. For a different choice of the frequency detuning, the adiabaticity breaks down, which allows one to prepare on demand a superposition of quasienergy states using Landau-Zener-type transitions. We find the characteristic spectrum of the transient radiation emitted by the oscillator after it has been prepared in a given quasienergy state.