Two Projects on the Exact Rotating Wave Approximation

Introduction

The projects in this repository are based on the "exact rotating wave approximation", see https://arxiv.org/abs/1807.02858

Physical background: The exact rotating wave approximation (exact RWA) can be viewed as a generalization of the regular rotating wave approximation (RWA), which is used to simplify the theoretical description of a linearly driven quantum system --- usually a two-level system, or qubit. The theory of the exact RWA features effective Hamiltonians that generate effective time evolutions, which agree with the exact driven-qubit trajectory at stroboscopic points in time.

1. Plotting program for a driven qubit

• Requires Mathematica 11 or higher

• Description: Convenient Mathematica notebook used for plotting various Bloch-sphere (a Bloch sphere is a three-dimensional representation of a quantum two-level system, or qubit) trajectories of a linearly driven qubit. Three different trajectories can be plotted: (i) the actual, or exact trajectory, (ii) the RWA trajectory, and (iii) effective trajectories corresponding to the exact RWA in second order.

• Launch: run videos/plotting.nb and run entire notebook.

2. Computation of two-dimensional integrals for testing an axiomatic definition of the exact RWA

• Best used with Python 3

Python program for the minimization of a variational integral (as of August 2020, this is work in progress).