{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-08-27T13:52:43.103000Z", "start_time": "2019-08-27T13:52:43.079000Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from qucat import GUI\n", "from scipy.constants import epsilon_0, pi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Computing an optomechanical coupling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this application, we show how QuCAT can be used for analyzing microwave optomechanics.\n", "\n", "One common implementation of microwave optomechanics involves a mechanically compliant capacitor, or drum, embedded in one or many microwave resonators.\n", "\n", "The quantity of interest is the single-photon optomechanical coupling.\n", "This quantity is the change in mode frequency $\\omega_m$ that occurs for a displacement $x_\\text{zpf}$ of the drum (the zero-point fluctuations in displacement)\n", "\n", "$g_0 = x_\\text{zpf}\\frac{\\partial \\omega_m}{\\partial x}$\n", "\n", "The change in mode frequency as the drum head moves $\\partial \\omega_m/\\partial x$ is not straightforward to compute for complicated circuits. One such example is that of https://arxiv.org/abs/1602.05779, where two microwave resonators are coupled to a drum via a network of capacitances as shown below\n", "\n", "![alt text](graphics/OM_circuit.png \"\")\n", "\n", "*illustration from https://arxiv.org/abs/1602.05779*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we will use QuCAT to calculate the optomechanical coupling of the drums to both resonator modes of this circuit.\n", "\n", "We start by reproducing the circuit with the GUI" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-08-27T13:53:24.717000Z", "start_time": "2019-08-27T13:52:45.219000Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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