{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from scipy.constants import *\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import *\n", "import numpy as np\n", "import sympy as sp\n", "import qucat as qc\n", "phi_0 = h/(2*e) #the flux quantum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulating the SNAIL non-linearity\n", "\n", "The goal of this tutorial is to simulate a SNAIL embedded in a superconducting circuit, and eliminate fourth order non-linearities in favor of third-order non-linearities.\n", "The SNAIL is a dipole containing three small Josephson juntions on one side, and a large one on the other side :\n", "\n", "\n", "\n", "SNAIL scheme taken from *N. E. Frattini, V. V. Sivak, A. Lingenfelter, S. Shankar et M. H. Devoret : Optimizing the Nonlinearity and Dissipation of a SNAIL Parametric Amplifier for Dynamic Range. Physical Review Applied, 10(5):1–17, 2018.*\n", "\n", "Its inductive energy writes :\n", "\n", "$$U_{SNAIL}(\\phi) = -E_J\\left(\\alpha \\cos\\phi + 3 \\cos \\frac{\\phi_\\text{ext}-\\phi}{3}\\right)$$\n", "\n", "It depends on :\n", "- the flux bias in its loop $\\phi_\\text{ext}$\n", "- a characteristic Josphson energy $E_J$\n", "- a characteristic coeeficient $\\alpha$\n", "\n", "For a given $\\phi_\\text{ext}$, $E_J$ and $\\alpha$, one can find the minimum of this inductive energy $\\phi_{min}$ and develop it around it:\n", "\n", "$$U_{SNAIL}|_{\\alpha, E, phi_{ext}}(\\phi) = \\frac{E2}{2}(\\phi-\\phi_{min})^2 + \\frac{E3}{6}(\\phi-\\phi_{min})^3 + \\frac{E4}{24}(\\phi-\\phi_{min})^4$$\n", "\n", "one can then make use of the `NonLinearInductor` component to define this energy term in a QuCAT circuit as follows" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "circuit = qc.GUI(\"circuits/snail.txt\", edit=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where the text file `circuits/snail.txt` contains the following:\n", "\n", "```\n", "C;-2,-2;-1,-2;1.0e-13;\n", "W;-2,-3;-2,-2;;\n", "W;-1,-3;-1,-2;;\n", "L;-2,-3;-1,-3;1.0e-08;\n", "C;0,-2;1,-2;1.5e-13;\n", "W;0,-3;0,-2;;\n", "W;1,-3;1,-2;;\n", "L;0,-3;1,-3;1.0e-08;\n", "C;2,-2;3,-2;2.0e-13;\n", "W;2,-3;2,-2;;\n", "W;3,-3;3,-2;;\n", "L;2,-3;3,-3;1.0e-08;\n", "G;4,-2;3,-2;;\n", "W;1,-2;2,-2;;\n", "G;-3,-2;-2,-2;;\n", "NonLinearInductor;-1,-2;0,-2;,,;E2,E3,E4\n", "```\n", "\n", "The `NonLinearInductor` differs from other components in that it is characterized by multiple parameters (in units of Hertz), such that in this case, its contribution to the Hamiltonian will be\n", "\n", "$$U/h = \\frac{E2}{2!}\\phi^2 + \\frac{E3}{3!}\\phi^3 + \\frac{E4}{4!}\\phi^4$$\n", "\n", "These parameters are seperated by commas in the graphical user interface, or entered as a list when creating the circuit programmatically.\n", "\n", "The following code generates the correct parameters for a given $E_J$ and $\\alpha$, and allow for sweeping of $\\phi_\\text{ext}$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "## Parameters for the circuit\n", "\n", "order = 4 #order at which the SNAIL will be expanded\n", "alpha = 0.12\n", "L_J = 1e-8\n", "E_J = 1/h*phi_0**2/(4*pi)**2/L_J #the Josephson energy of the small junctions, in Hz\n", "\n", "# We use sympy to create the derivatives of the energy \n", "phi = sp.Symbol(\"phi\")\n", "a = sp.Symbol(\"a\")\n", "E = sp.Symbol(\"E\")\n", "phi_ext = sp.Symbol(\"phi_ext\")\n", "\n", "U_sym = -E*(a*sp.cos(phi) + 3*sp.cos((phi_ext-phi)/3))\n", "dnU_sym =[sp.diff(U_sym, phi, i) for i in range(order+1)] # Symbolic expression for the derivatives\n", "dnU = [sp.lambdify([phi, E, a, phi_ext], c) for c in dnU_sym] # creates the python functions for the derivatives\n", "\n", "def make_dict_vect(E, a, phi_ext): \n", " labels = {}\n", " for i, c in enumerate(dnU[2::]): #initialisation of the lists\n", " labels[\"E\"+str(i+2)] = []\n", "\n", " phi_min = [0]\n", "\n", " for c in phi_ext:\n", " phi_min.append((minimize(dnU[0], 11, \n", " method = 'L-BFGS-B' , \n", " bounds = [(-1, 7*np.pi)],args = (1, alpha, c)).x)[0]%(6*np.pi))\n", " phi_min.pop(0)\n", " \n", " for i,c in enumerate(phi_min):\n", " for j, d in enumerate(dnU[2::]):\n", " labels[\"E\"+str(j+2)] = labels[\"E\"+str(j+2)]+[d(c, E, a, phi_ext[i])]\n", " return labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check the evolution of the derivatives at the minimum as a function of $\\phi_{ext}$ :" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "phi_exts = np.linspace(0,6*np.pi, 1000)\n", "\n", "labels = make_dict_vect(E_J, alpha, phi_exts) #labels is a dictionnary where each key corresponds to a list of values\n", "\n", "plt.plot(phi_exts/np.pi, np.array(labels[\"E2\"])/1e9, label = \"E2\")\n", "plt.plot(phi_exts/np.pi, np.array(labels[\"E3\"])/1e9, label = \"E3\")\n", "plt.plot(phi_exts/np.pi, np.array(labels[\"E4\"])/1e9, label = \"E4\")\n", "plt.xlabel(r\"$\\phi/_{ext}/\\pi\\phi_0}$\")\n", "plt.ylabel(r\"Hamiltonian energy terms\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The unbiased SNAIL has no third order term since it's has a parity in the flux.\n", "Let's look at the frequencies, given by E2 :" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "freqs = circuit.eigenfrequencies(**labels)/1e9\n", "\n", "plt.xlabel(r\"$\\phi/_{ext}/\\pi\\phi_0}$\")\n", "plt.ylabel(\"Eigenfrequencies (GHz)\")\n", "plt.title(\"Eigenfrequencies as a function of $\\phi_{ext}$\")\n", "[plt.plot(phi_exts/np.pi, np.real(c)) for c in freqs]\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They follow the evolution of E2, which is expected.\n", "\n", "Let's look at the three waves mixing term :" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "three_waves = circuit.three_waves(0, 1, 2, **labels)/1e6 # In MHz\n", "plt.xlabel(r\"$\\phi/\\pi\\phi_0}$\")\n", "plt.ylabel(\"Three waves mixing term (MHz)\")\n", "plt.title(\"Three waves mixing term (MHz) as a function of the imposed phase\")\n", "plt.plot(phi_exts/np.pi, np.real(three_waves))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It has the same shape as the E3 term.\n", "\n", "And now, the self-Kerr terms : " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kerr_coeffs = circuit.kerr(**labels)/1e6 # in MHz\n", "for i in range(len(kerr_coeffs)):\n", " plt.plot(phi_exts/np.pi, np.real(kerr_coeffs[i, i]), label = \"Mode \"+ str(i))\n", "plt.legend()\n", "plt.xlabel(r\"$\\phi/\\pi}$\")\n", "plt.ylabel(\"Self Kerr coefficient (MHz)\")\n", "plt.title(\"Self Kerr coefficients as a function of the exterior phase\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clearly see the existence of the sweet spot, point where all the Kerr terms vanish, but the three waves mixing term still exists, allowing to make a parametric amplifier without beeing limited by the Kerr terms, see *N. E. Frattini, V. V. Sivak, A. Lingenfelter, S. Shankar et M. H. Devoret : Optimizing the Nonlinearity and Dissipation of a SNAIL Parametric Amplifier for Dynamic Range. Physical Review Applied, 10(5):1–17, 2018.*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }