{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Two implementations of heterodyne detection: direct heterodyne and as two homodyne measurements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Copyright (C) 2011 and later, Paul D. Nation & Robert J. Johansson" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [], "source": [ "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Homodyne and hetrodyne detection are techniques for measuring the quadratures of a field using photocounters. Homodyne detection (on-resonant) measures one quadrature and with heterodyne detection (off-resonant) both quadratures can be detected simulateously.\n", "\n", "The evolution of a quantum system that is coupled to a field that is monitored with homodyne and heterodyne detector can be described with stochastic master equations. This notebook compares two different ways to implement the heterodyne detection stochastic master equation in QuTiP." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deterministic reference" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": true }, "outputs": [], "source": [ "N = 15\n", "w0 = 1.0 * 2 * np.pi\n", "A = 0.1 * 2 * np.pi\n", "times = np.linspace(0, 15, 301)\n", "gamma = 0.25\n", "\n", "ntraj = 150\n", "nsubsteps = 50\n", "\n", "a = destroy(N)\n", "x = a + a.dag()\n", "y = -1.0j*(a - a.dag())\n", "\n", "H = w0 * a.dag() * a + A * (a + a.dag())\n", "\n", "rho0 = coherent(N, np.sqrt(5.0), method='analytic')\n", "c_ops = [np.sqrt(gamma) * a]\n", "e_ops = [a.dag() * a, x, y]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [], "source": [ "result_ref = mesolve(H, rho0, times, c_ops, e_ops)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { 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\n", 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