{ "cells": [ { "cell_type": "markdown", "id": "6aed7889", "metadata": {}, "source": [ "# Lecture 4 - Correlation functions \n", "\n", "Author: J. R. Johansson (robert@riken.jp), https://jrjohansson.github.io/\n", "\n", "This lecture series was developed by J.R. Johannson. The original lecture notebooks are available [here](https://github.com/jrjohansson/qutip-lectures).\n", "\n", "This is a slightly modified version of the lectures, to work with the current release of QuTiP. You can find these lectures as a part of the [qutip-tutorials repository](https://github.com/qutip/qutip-tutorials). This lecture and other tutorial notebooks are indexed at the [QuTiP Tutorial webpage](https://qutip.org/tutorials.html)." ] }, { "cell_type": "code", "execution_count": 1, "id": "fd1290e4", "metadata": { "execution": { "iopub.execute_input": "2024-03-24T15:01:39.268354Z", "iopub.status.busy": "2024-03-24T15:01:39.268182Z", "iopub.status.idle": "2024-03-24T15:01:39.887537Z", "shell.execute_reply": "2024-03-24T15:01:39.886975Z" } }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from qutip import (about, coherent_dm, correlation, destroy, fock_dm, mesolve,\n", " qeye, steadystate, tensor)\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "2010a5ca", "metadata": {}, "source": [ "## First-order coherence function\n", "\n", "\n", "Consider an oscillator that is interacting with a thermal environment. If the oscillator initially is in a coherent state, it will gradually decay to a thermal (incoherent) state. The amount of coherence can be quantified using the first-order optical coherence function\n", "\n", "