Ground States of the Jaynes Cummings Hamiltonian

The Jaynes-Cummings Hamiltonian models the dynamics of a qubit, or two-level system, with a harmonic oscillator. We can write it using three terms: one for the harmonic oscillator (resonator), of for the spin-1/2 (qubit) and an interaction term:

$$ H = \hbar \omega_r a^\dagger a - \frac{1}{2} \hbar \omega_q \sigma_z + \hbar g (a + a^\dagger)(\sigma_+ + \sigma_-) $$

Note that this equation is valid before the rotating wave approximation.

In this tutorial, we explore the ground states of the Hamiltonian above when varying the strenght of the coupling g. We start by loading the JaynesCummings package, and a plotting package.

In [1]:
using JaynesCummings, PlotlyJS