DickeModel.jl

A toolkit for the quantum and classical Dicke model in Julia.

This package contains numerical methods that allow to efficiently compute properties of the quantum and classical Dicke model, a fundamental model in quantum optics describing atoms interacting with light.

Installation

To install the package, use the following command inside the Julia REPL:

using Pkg
Pkg.add("DickeModel")

To load the package, run

using DickeModel

Getting started

There are many things you can do using the different submodules:

• ClassicalDicke allows to compute classical dynamics of the Dicke model, including a wide range of properites of its phase space (used in [12], [13], [14], [15], [19], [20]).
  See Examples for ClassicalDicke.
• DickeBCE provides multiple functions for analyzing the quantum Dicke model. It uses an efficient basis known as the Efficient Coherent Basis (BCE) [4], [5] for exact computations, and it also contains several semilcassical methods (used in [12], [13], [14], [15], [19], [20]).
  See Examples for DickeBCE.
• UPOs contains a set of functions to find unstable periodic orbits (UPOs) in the classical Dicke model and to study quantum scars (used in [13], [14], [15]).
  See Examples for UPOs.
• TWA allows to perform semiclassical calculations using the truncated Wigner approximation (TWA) (used in [12], [19]).
  See Examples for TWA.
• EnergyShellProjections contains a set of functions to integrate functions over the classical energy shells of the Dicke Model. It also contains specialized functions to compute these integrals for the Husimi functions of quantum states, which define phase-space localization measures known as Rényi occupations [20] (used in [14], [15], [20]).
  See Examples for EnergyShellProjections.
• ClassicalLMG provides very basic functions for the classical Lipkin-Meshkov-Glick model.
  See Examples for ClassicalLMG.

The following modules provide basic functionallity for the rest of the modules:

• ClassicalSystems provides a general framework for computing classical Hamiltonian dynamics, inlcuding Lyapunov exponents. It is mostly used for the Dicke model, but in principle it can be expanded to other Hamiltonians.
• PhaseSpaces provides some canonical transformations of the Bloch-Sphere.