{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 4: Dynamical decoupling of a non-Markovian environment" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introduction\n", "\n", "Followings https://journals.aps.org/pra/pdf/10.1103/PhysRevA.58.2733 we consider an example of dynamical decoupling.\n", "We choose a drive which performs pi rotations, interspersed with short periods where the bath causes dephasing.\n", "\n", "We first show the standard example of equally spaced pulses, and then consider the 'optimal' Uhrig spacing (Götz S. Uhrig\n", "Phys. Rev. Lett. 98, 100504 (2007))." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "from qutip import *" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from qutip.nonmarkov.bofin_solvers import HEOMSolver\n", "from qutip.nonmarkov.bofin_baths import DrudeLorentzPadeBath, DrudeLorentzBath" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def coth(x):\n", " \"\"\"\n", " coth function\n", " \"\"\"\n", " return 1./np.tanh(x)\n", "\n", "def cot(x):\n", " return 1./np.tan(x)\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'J')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "pref = 1.\n", "Nk = 3\n", "\n", "Q = sigmaz()\n", "T = .05\n", "beta = 1./T\n", "\n", "lam = 0.0005\n", "gamma = 0.005\n", "\n", "bath = DrudeLorentzBath(Q, lam=lam, gamma=gamma, T=T, Nk=Nk, tag=\"bath1\")\n", "\n", "wlist = np.linspace(0, 0.5, 1000)\n", "pref = 1.\n", "\n", "J = [w * 2 * lam * gamma / ((gamma**2 + w**2)) for w in wlist]\n", "\n", "\n", "fig, axes = plt.subplots(1, 1, sharex=True, figsize=(8,8))\n", "axes.plot(wlist, J, 'r', linewidth=2)\n", "axes.set_xlabel(r'$\\omega$', fontsize=28)\n", "axes.set_ylabel(r'J', fontsize=28)\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "wq = 1.\n", "Hsys = 0.0 * sigmaz()\n", "\n", "\n", "optionsODE = Options(nsteps=1500, store_states=True,rtol=1e-12,atol=1e-12,max_step = 1/(20))\n", "\n", "ttotal=400.\n", "tlist2 = np.linspace(0, ttotal, 50000)\n", "\n", "NC = 10\n", "\n", "def drive(t):\n", " V = .5\n", " tp = pi/(2.*V) \n", "\n", " delt = 20.\n", " N = int(ttotal/(tp + delt))\n", " RF = 0.\n", " for n in arange(1,N+1):\n", " if t >= n*delt+(n-1)*tp:\n", " if t<=n*delt + n*tp:\n", " \n", "\n", " RF += V\n", " return RF\n", "\n", "\n", "# start with a superposition so there is something to dephase!\n", "\n", "sup = (basis(2,1)+basis(2,0))/sqrt(2.)\n", "initial_state2 = sup * sup.dag()\n", "\n", "#With pulses\n", "H_d = [Hsys,[sigmax(), drive]]\n", "resultHEOM = HEOMSolver(H_d, bath, NC, options=optionsODE)\n", "outputDD = resultHEOM.run(initial_state2,tlist2)\n", "\n", "\n", "\n", "#Without pulses\n", "H_d = [Hsys,[0.*sigmax(), drive]]\n", "resultHEOM = HEOMSolver(H_d, bath, NC, options=optionsODE)\n", "outputnoDD = resultHEOM.run(initial_state2,tlist2)\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "\n", "\n", "def driveslow(t):\n", " V = .01\n", " tp = pi/(2.*V) #here i need factor of 1/2 for RWA\n", "\n", " delt = 20.\n", " N = int(ttotal/(tp + delt))\n", " RF = 0.\n", " for n in arange(1,N+1):\n", " if t >= n*delt+(n-1)*tp:\n", " if t<=n*delt + n*tp:\n", " \n", "\n", " RF += V\n", " return RF\n", "\n", "\n", "#With pulses\n", "H_d = [Hsys,[sigmax(), driveslow]]\n", "resultHEOM = HEOMSolver(H_d, bath, NC, options=optionsODE)\n", "outputDDslow = resultHEOM.run(initial_state2,tlist2)\n", "\n", "\n", "\n", "#Without pulses\n", "H_d = [Hsys,[0.*sigmax(), driveslow]]\n", "resultHEOM = HEOMSolver(H_d, bath, NC, options=optionsODE)\n", "outputnoDDslow = resultHEOM.run(initial_state2,tlist2)\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "matplotlib.rcParams['figure.figsize'] = (7, 5)\n", "matplotlib.rcParams['axes.titlesize'] = 25\n", "matplotlib.rcParams['axes.labelsize'] = 30\n", "matplotlib.rcParams['xtick.labelsize'] = 28\n", "matplotlib.rcParams['ytick.labelsize'] = 28\n", "matplotlib.rcParams['legend.fontsize'] = 28\n", "matplotlib.rcParams['axes.grid'] = False\n", "matplotlib.rcParams['savefig.bbox'] = 'tight'\n", "matplotlib.rcParams['lines.markersize'] = 5\n", "matplotlib.rcParams['font.family'] = 'STIXgeneral' \n", "matplotlib.rcParams['mathtext.fontset'] = 'stix'\n", "matplotlib.rcParams[\"font.serif\"] = \"STIX\"\n", "matplotlib.rcParams['text.usetex'] = False" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, 1, sharex=False, figsize=(12,10))\n", "\n", "\n", "\n", "P12DD=expect(outputDD.states,basis(2,1)*basis(2,0).dag())\n", "P12noDD=expect(outputnoDD.states,basis(2,1)*basis(2,0).dag())\n", "\n", "P12DDslow=expect(outputDDslow.states,basis(2,1)*basis(2,0).dag())\n", "P12noDDslow=expect(outputnoDDslow.states,basis(2,1)*basis(2,0).dag())\n", "\n", "plt.sca(axes[0])\n", "plt.yticks([0.,0.4],[0,0.4])\n", "axes[0].plot(tlist2*0.5, real(P12DD), 'green', linestyle='-', linewidth=2, label=\"HEOM with fast DD\")\n", "axes[0].plot(tlist2*0.5, real(P12DDslow), 'blue', linestyle='-', linewidth=2, label=\"HEOM with slow DD\")\n", "axes[0].plot(tlist2*0.5, real(P12noDD), 'orange', linestyle='--', linewidth=2, label=\"HEOM no DD\")\n", "\n", "\n", "axes[0].locator_params(axis='y', nbins=3)\n", "axes[0].locator_params(axis='x', nbins=3)\n", "\n", "\n", "axes[0].set_ylabel(r\"$\\rho_{01}$\", fontsize=30)\n", "\n", "axes[0].legend()\n", "axes[0].text(0,0.3,\"(a)\",fontsize=28)\n", "\n", "pulse = [drive(t) for t in tlist2]\n", "pulseslow = [driveslow(t) for t in tlist2]\n", "\n", "plt.sca(axes[1])\n", "plt.yticks([0.,0.5,1],[0,0.5,1])\n", "\n", "axes[1].plot(tlist2*0.5, 2*array(pulse), 'green', linestyle='-', linewidth=2, label=\"Drive fast\")\n", "axes[1].plot(tlist2*0.5, 2*array(pulseslow), 'blue', linestyle='--', linewidth=2, label=\"Drive slow\")\n", "axes[1].legend()\n", "\n", "\n", "\n", "axes[1].locator_params(axis='y', nbins=3)\n", "axes[1].locator_params(axis='x', nbins=3)\n", "\n", "\n", "\n", "#axes[1].set_xlim(200,600)\n", "axes[1].set_xlabel(r'$t\\bar{V}_{\\mathrm{f}}$', fontsize=30)\n", "axes[1].set_ylabel(r'Drive amplitude/$\\bar{V}_{\\mathrm{f}}$', fontsize=30)\n", "#axes[1].legend(loc=0)\n", "\n", "axes[1].text(-1,0.8,\"(b)\",fontsize=28)\n", "\n", "fig.tight_layout()\n", "#fig.savefig(\"ddfig.pdf\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we consider non-equally spaced pulses. Rather than plot as a function of time we just consider the final coherence after time $T$ and 100 pulses. We change the width of the environment to demonstate that the Uhrig sequence can be sub-optimal when the bath is very broad." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "7\n", "8\n", "9\n", "10\n", "11\n", "12\n", "13\n", "14\n", "15\n", "16\n", "17\n", "18\n", "19\n", "1016.8145733000129\n", "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "7\n", "8\n", "9\n", "10\n", "11\n", "12\n", "13\n", "14\n", "15\n", "16\n", "17\n", "18\n", "19\n", "924.9250295000384\n", "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "7\n", "8\n", "9\n", "10\n", "11\n", "12\n", "13\n", "14\n", "15\n", "16\n", "17\n", "18\n", "19\n", "794.3191641000449\n" ] } ], "source": [ "#change plotting style so we have set N_pulses and plot for gamma*Tmax\n", "import timeit\n", "\n", "pref = 1.\n", "Nk = 5\n", "Q = sigmaz()\n", "T = .5\n", "beta = 1./T\n", "\n", "\n", "sup = (basis(2,1)+basis(2,0))/sqrt(2.)\n", "initial_state2 = sup * sup.dag()\n", "\n", "V = 10. #in short, _s data\n", "tp = pi/(2.*V) #we need Vtp = pi/2\n", "Tmax = 100\n", "gamma_list = np.linspace(0.005,0.05, 20)\n", "\n", "\n", "\n", "DD_eq_gamma_plot = []\n", "DD_opt_gamma_plot = []\n", "\n", "\n", "N_pulse = 100\n", "\n", "\n", "def gather_data(lam2, NC2):\n", " start = timeit.default_timer()\n", " DD_eq_t = []\n", " DD_opt_t = []\n", " for gamkk,gamma in enumerate(gamma_list):\n", " print(gamkk)\n", "\n", "\n", "\n", " \n", " bath = DrudeLorentzBath(Q, lam=lam2, gamma=gamma, T=T, Nk=Nk, tag=\"bath1\")\n", " tlist2 = np.linspace(0, Tmax, 10000)\n", "\n", " Hsys = 0.0 * sigmaz()\n", " # we need to set max integration step so pulses are not skipped.\n", " # shortest time scale are the pulses themselves, with width pi/2*V\n", " # other time scales for pulses are Tmax/Npulses\n", " max_step = 1/(20.) #\n", " optionsODE = Options(nsteps=1500, store_states=True,rtol=1e-12,atol=1e-12,max_step = max_step)\n", " \n", "\n", "\n", " def drive(t): # equidistant pulses\n", "\n", " N = N_pulse+1#int(ttotal/(tp + delt))\n", " delt = (Tmax-(N-1)*tp)/N\n", "\n", " RF = 0.\n", " for n in arange(1,N):\n", " #between n and n+1 apply pulse:\n", " if t >= n*delt+(n-1)*tp: \n", " if t<=n*delt + n*tp:\n", " RF += V\n", " return RF\n", "\n", "\n", "\n", "\n", " H_d = [liouvillian(Hsys,[]),[liouvillian(sigmax(),[]), drive]]\n", " resultHEOM = HEOMSolver(H_d, bath, NC2, options=optionsODE)\n", " outputDD = resultHEOM.run(initial_state2,tlist2)\n", "\n", " DD_eq_t.append(outputDD.states)\n", "\n", "\n", "\n", " #optimized\n", "\n", "\n", "\n", " def drive_opt(t): #optimized distance\n", "\n", "\n", " #N = int(ttotal/(tp + delt))\n", " N = N_pulse\n", " #lets imagine that tp-> 0\n", " #then lets arrange the pulses around this assumption\n", "\n", " #then the distribution is accross a range (ttotal - N*tp)\n", "\n", " #lets optimize this in the following way... no longer equidistant pulses of delt=20\n", "\n", " delt_list = [sin(pi*j/(2*N+2))**2 * (Tmax - N*tp) for j in arange(1,N+1)] #if Npulses is odd, N+2?\n", " RF = 0.\n", " for n in arange(1,N+1):\n", " if t >= delt_list[n-1]+(n-1)*tp:\n", " if t<= delt_list[n-1] + n*tp:\n", " RF += V\n", " return RF\n", "\n", "\n", "\n", "\n", " H_d = [Hsys,[sigmax(), drive_opt]]\n", " resultHEOM = HEOMSolver(H_d, bath, NC2, options=optionsODE)\n", " outputDD_opt = resultHEOM.run(initial_state2,tlist2)\n", "\n", "\n", "\n", " DD_opt_t.append(outputDD_opt.states)\n", " \n", " end = timeit.default_timer()\n", " print(end-start)\n", " P12_opt_gamma_plot=[]\n", " for DD in DD_opt_t:\n", " \n", " P12_opt_gamma_plot.append(expect(DD[-1],basis(2,1)*basis(2,0).dag()))\n", " \n", " \n", "\n", " P12_eq_gamma_plot=[]\n", " for DD in DD_eq_t:\n", " \n", "\n", " P12_eq_gamma_plot.append(expect(DD[-1],basis(2,1)*basis(2,0).dag()))\n", " \n", " \n", "\n", " return P12_opt_gamma_plot, P12_eq_gamma_plot\n", "\n", "P12_opt_gamma_plot_001, P12_eq_gamma_plot_001 = gather_data(0.01,4)\n", "P12_opt_gamma_plot_0005, P12_eq_gamma_plot_0005 = gather_data(0.005,4)\n", "P12_opt_gamma_plot_00005, P12_eq_gamma_plot_00005 = gather_data(0.0005,4)\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Pade Nk5\n", "fig, axes = plt.subplots(1, 1, sharex=False, figsize=(10,7))\n", "\n", "\n", "axes.plot(array(gamma_list)/10 , real(P12_opt_gamma_plot_00005), 'green', linestyle='-', linewidth=2, label=r\"UDD $\\lambda=0.00005 \\bar{V}$\")\n", "axes.plot(array(gamma_list)/10, real(P12_eq_gamma_plot_00005), 'green', linestyle='-.', linewidth=2, label=r\"DD $\\lambda=0.00005\\bar{V}$\")\n", "\n", "axes.plot(array(gamma_list)/10 , real(P12_opt_gamma_plot_0005), 'red', linestyle='-', linewidth=2, label=r\"UDD $\\lambda=0.0005\\bar{V}$\")\n", "axes.plot(array(gamma_list)/10 , real(P12_eq_gamma_plot_0005), 'red', linestyle='-.', linewidth=2, label=r\"DD $\\lambda=0.0005\\bar{V}$\")\n", "\n", "axes.plot(array(gamma_list)/10 , real(P12_opt_gamma_plot_001), 'blue', linestyle='-', linewidth=2, label=r\"UDD $\\lambda=0.001 \\bar{V}$\")\n", "axes.plot(array(gamma_list)/10 , real(P12_eq_gamma_plot_001), 'blue', linestyle='-.', linewidth=2, label=r\"DD $\\lambda=0.001\\bar{V}$\")\n", "\n", "\n", "axes.set_ylabel(r\"$\\rho_{01}$\")\n", "\n", "\n", "\n", "axes.set_xlabel(r\"$\\gamma/\\bar{V}$\")\n", "\n", "axes.legend(fontsize=16)\n", "\n", "\n", "fig.tight_layout()\n", "#fig.savefig(\"ddoptcomparev6.pdf\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "jupytext": { "formats": "ipynb,md:myst" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 1 }