From 328b51e3427a6921ec8c28bb215b3058ffebdee9 Mon Sep 17 00:00:00 2001 From: Mariana Bagulho Date: Mon, 10 Aug 2026 09:29:23 +0200 Subject: [PATCH] cv_1st --- .../cv_submissions/cv_tutorial_mariana.ipynb | 213 ++++++++++++++++++ 1 file changed, 213 insertions(+) create mode 100644 exercises/cv_submissions/cv_tutorial_mariana.ipynb diff --git a/exercises/cv_submissions/cv_tutorial_mariana.ipynb b/exercises/cv_submissions/cv_tutorial_mariana.ipynb new file mode 100644 index 0000000..681552c --- /dev/null +++ b/exercises/cv_submissions/cv_tutorial_mariana.ipynb @@ -0,0 +1,213 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "42232883-bfb8-4d5a-abb3-b93ba32caf80", + "metadata": {}, + "source": [ + "### Continuous Variables\n" + ] + }, + { + "cell_type": "markdown", + "id": "bc1c9d55-bb72-4383-9df6-9927332b1047", + "metadata": {}, + "source": [ + "When we refer discrete variables we usually divide into continuous ones and discrete ones. For a discrete variable we consider a finite number of possible states, while in continuous variables we use coherent states and infinite states inside a continuous possibility of states.\n", + "In previous courses of Quantum Mechanics we talked about the Fock states ( $|n\\rangle$ ) and how these describe the states on a specific energy level. This energy levels come from the hamiltonian:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "ca5d16c8-d5ae-4e6e-8a6d-bc6a1b236e2a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "x = np.linspace(-4, 4, 400) # Just defining an x-axis\n", + "V = 0.5 * x**2 # Harmonic Oscilattor potential V(x) = 1/2 x^2\n", + "\n", + "plt.figure(figsize=(7, 5)) \n", + "plt.plot(x, V, '--', label=r'Potencial $V(x) = \\frac{1}{2}x^2$') #Adding the potential to the X values defined before\n", + "\n", + "for n in range(4): #just looking at 4 levels\n", + " E_n = n + 0.5 # in h-bar omega units,to simplify\n", + " plt.axhline(y=E_n, color=colors[n], linestyle='-', alpha=0.6)\n", + " plt.text(2.2, E_n + 0.1, f\"$E_{n} = {n} + 1/2$\", color=colors[n], fontsize=11, fontweight='bold')\n", + "\n", + "plt.ylim(0, 4.5)\n", + "plt.xlim(-3.5, 3.5)\n", + "plt.xlabel(\"Position $x$\")\n", + "plt.ylabel(\"Energy $E$ (in h_bar*omega units)\")\n", + "plt.title(r\"QHO hamiltonian: $\\hat{H} = \\hbar\\omega \\left(\\hat{a}^\\dagger\\hat{a} + \\frac{1}{2}\\right)$\")\n", + "plt.legend(loc='upper right')\n", + "plt.grid(True, alpha=0.3)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "67c35989-34db-4491-92f7-a8822a882060", + "metadata": {}, + "source": [ + "**Quantum Harmonic Oscillator** " + ] + }, + { + "cell_type": "markdown", + "id": "6ef75ed6-a469-4fda-be9d-1b23cf75ead9", + "metadata": {}, + "source": [ + "The QHO is a system of continuous variables and is described by the creation ($\\hat{a}$) and aniquilation ($\\hat{a}^\\dagger$) operators, where $$ [\\hat{a}, \\hat{a}^\\dagger] = 1 $$" + ] + }, + { + "cell_type": "markdown", + "id": "bb3c28ee-b277-4ee3-b031-f4191136a43d", + "metadata": {}, + "source": [ + "For the quantum, instead of using energy levels we describe the system with quadratures acting like position ($\\hat{X}$) and momentum ($\\hat{P}$) in the phase space." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c29639af-30ec-4852-803e-92e0b87ed321", + "metadata": {}, + "source": [ + "**Photon Number Distribution $p(n)$**\n", + "\n", + "The photon number distribution gives the probability $p(n)$ of detecting exactly $n$ photons in a given quantum state.\n", + "We can consider pure states and mixed states:\n", + "- Pure states: $p(n) = |\\langle n | \\psi \\rangle|^2$, \n", + "- General / Mixed states: $p(n) = \\rho_{mn} = 2\\pi \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} W(x,p) W_{mn}(x,p) \\, dx \\, dp$ (found in equation 2.12 on the thesis provided).\n" + ] + }, + { + "cell_type": "markdown", + "id": "53143598", + "metadata": {}, + "source": [ + "We also have 3 ways to exibit the distinct photon numbers. One can use the Fock states as I refered before; or the coeherent states (statistic) and usually used for an ideal laser considering low losses as we discussed in class; and lastlly the squeezed state.\n", + "\n", + "For the squeezes state we consider the points where we have low losses on x and also obeying Heisenberg principle." + ] + }, + { + "cell_type": "markdown", + "id": "cc1546c7", + "metadata": {}, + "source": [ + "**Trying to Plott the Wigner function for different states**\n" + ] + }, + { + "cell_type": "markdown", + "id": "17309a2f", + "metadata": {}, + "source": [ + "The Wigner function works like a almost probability function, letting us analyse" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "07243570", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import qutip as qt\n", + "\n", + "xvec = np.linspace(-4, 4, 200) # just creating the axis for the phase space\n", + "pvec = np.linspace(-4, 4, 200)\n", + "X, P = np.meshgrid(xvec, pvec)\n", + "\n", + "N = 20 # Hilbert space number\n", + "\n", + "# Now, for the vaccum state we define it n=0\n", + "psi_vacuum = qt.basis(N, 0)\n", + "W_vacuum = qt.wigner(psi_vacuum, xvec, pvec)\n", + "\n", + "# Now we just do it for different states as requested\n", + "psi_fock1 = qt.basis(N, 1)\n", + "W_fock1 = qt.wigner(psi_fock1, xvec, pvec)\n", + "\n", + "# And now we try the coeherent state\n", + "psi_coherent = qt.coherent(N, 2.0)\n", + "W_coherent = qt.wigner(psi_coherent, xvec, pvec)\n", + "\n", + "# Plotiings\n", + "fig, axes = plt.subplots(1, 3, figsize=(15, 4.5))\n", + "\n", + "plots = [(\"Vacuum State n=0\", W_vacuum),(\"Fock State n=1\", W_fock1),(r\"Coherent State $|\\alpha = 2\\rangle$\", W_coherent),]\n", + "\n", + "for ax, (title, W) in zip(axes, plots):\n", + " c = ax.contourf( X, P, W, 100, cmap=\"bwr\", vmin=-1 / np.pi, vmax=1 / np.pi)\n", + " ax.set_title(title, fontsize=12)\n", + " ax.set_xlabel(\"Position $x$\")\n", + " ax.set_ylabel(\"Momentum $p$\")\n", + " fig.colorbar(c, ax=ax, fraction=0.046, pad=0.04)\n", + "\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "58c0559e", + "metadata": {}, + "source": [ + "We see that as the Fock state increases \"(bigger n)\" we have a bigger uncertainty and therefore we see a spreading of the state across the phase space." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "sciqis (3.14.7.final.0)", + "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": "3.14.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}