{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Info: Nathan Shammah, RIKEN, nathan.shammah@gmail.com\n", "\n", "# Open Quantum Dynamics with QuTiP\n", " \n", " \n", " We use QuTiP's solvers to study the open dynamics of a quantum system evolving in time. \n", " \n", " \n", " - #### Lindblad Master Equation\n", " \n", " - #### Lindblad Master Equation: Time evolution\n", " \n", " - #### Lindblad Master Equation: steady-state solution\n", " \n", "- #### Stochastic Dynamics: Quantum Trajectories with Monte Carlo" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from qutip import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the operators and Hamiltonian\n", "\n", "We consider the spin-boson system, which is a prototypical model of light-matter interaction in cavity quantum electrodynamics (cQED): a single two-level system coupled to a single mode of the photonic field. Its Hamiltonian is described by\n", "\n", "\\begin{eqnarray}\n", "H &=& \\omega_c a^\\dagger a + \\frac{\\omega_0}{2}\\sigma_z\n", "+\\frac{g}{2}\\sigma_x\\left(a+a^\\dagger\\right)+\\frac{\\omega_x}{2}\\sigma_x,\n", "\\end{eqnarray}\n", "\n", "where we added also the possibility of the system of a classical drive onto the system at a frequency $\\omega_x$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# spins\n", "sx_reduced = sigmax()\n", "sy_reduced = sigmay()\n", "sz_reduced = sigmaz()\n", "sp_reduced = sigmap()\n", "sm_reduced = sigmam()\n", "\n", "# photons\n", "nph = 4\n", "a_reduced = destroy(nph)\n", "\n", "# tensor space\n", "sz = tensor(sz_reduced,qeye(nph))\n", "sx = tensor(sx_reduced,qeye(nph))\n", "sm = tensor(sm_reduced,qeye(nph))\n", "sp = sm.dag()\n", "a = tensor(qeye(2), a_reduced)\n", "\n", "# hamiltonians\n", "wc = 1\n", "w0 = 0.5*wc\n", "g = 0.1*w0\n", "wx = 0.2*w0\n", "Hcav = wc*a.dag()*a\n", "Hspin = w0*sz #+ wx*sx\n", "Hint = g*sx*(a+a.dag())\n", "HintCheck = g*tensor(sx_reduced,a_reduced+a_reduced.dag())\n", "H = Hcav + Hspin + Hint\n", "np.testing.assert_(Hint == HintCheck)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the initial state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The initial state of the system is given by \n", "\\begin{eqnarray}\n", "\\rho&=&\\rho_\\text{spin}\\otimes\\rho_\\text{phot}\n", "\\end{eqnarray}\n", "and in the case of a initially pure state, \n", "\\begin{eqnarray}\n", "\\rho&=&|\\psi\\rangle_\\text{spin}\\otimes|\\psi\\rangle_\\text{phot}\n", "\\end{eqnarray}\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# initial state\n", "psi0_spin = basis(2,0)\n", "psi0_phot = basis(nph,nph-int(nph/2))\n", "psi0 = tensor(psi0_spin,psi0_phot)\n", "rho0 = ket2dm(psi0)\n", "\n", "# times at which to calculate the variables\n", "tlist = np.linspace(0,50,2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lindblad master equation: $\\texttt{mesolve}$\n", "\n", "We now consider the time evolution of the open quantum system, in which $\\rho$ is dissipatively coupled to a spin and photonic bath,\n", "\n", "\\begin{eqnarray}\n", "\\frac{d}{dt}\\rho =-i\\lbrack H,\\rho\\rbrack+\\gamma\\mathcal{D}_{[\\sigma_-]}\\rho+\\kappa\\mathcal{D}_{[a]}\\rho.\n", "\\end{eqnarray}" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.0%. Run time: 0.02s. Est. time left: 00:00:00:00\n", "20.0%. Run time: 0.04s. Est. time left: 00:00:00:00\n", "30.0%. Run time: 0.06s. Est. time left: 00:00:00:00\n", "40.0%. Run time: 0.08s. Est. time left: 00:00:00:00\n", "50.0%. Run time: 0.10s. Est. time left: 00:00:00:00\n", "60.0%. Run time: 0.12s. Est. time left: 00:00:00:00\n", "70.0%. Run time: 0.14s. Est. time left: 00:00:00:00\n", "80.0%. Run time: 0.16s. Est. time left: 00:00:00:00\n", "90.0%. Run time: 0.18s. Est. time left: 00:00:00:00\n", "Total run time: 0.20s\n" ] } ], "source": [ "kappa = 0.3\n", "gamma = 0.3\n", "\n", "my_options = Options(average_states = True, store_states = True)\n", "results = mesolve(H, psi0, tlist, \n", " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", " e_ops=[a.dag()*a,sz], \n", " options=my_options, progress_bar=True)\n", "\n", "# store time evoluted variables\n", "nph_t = results.expect[0]\n", "sz_t = results.expect[1]\n", "rho_t = results.states" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fs=20\n", "plt.figure(figsize=(14,4))\n", "plt.subplot(121)\n", "plt.plot(tlist, sz_t)\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", "plt.subplot(122)\n", "plt.plot(tlist, nph_t/nph/0.5)\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", "plt.suptitle(\"Time evolution for spin and photonic excitations of a driven cavity with single two level system, with dissipation\")\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Steady state solver: $\\texttt{steadystate}$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "rhoss = steadystate(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", "nph_ss= expect(a.dag()*a,rhoss)\n", "sz_ss= expect(sz,rhoss)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.imshow(abs(rhoss.full()))\n", "plt.show()\n", "plt.close()\n", "plt.figure()\n", "plt.subplot(121)\n", "plt.imshow(abs(ptrace(rhoss,0).full()))\n", "plt.xlabel(\"atom\",fontsize=fs)\n", "plt.subplot(122)\n", "plt.imshow(abs(ptrace(rhoss,1).full()))\n", "plt.xlabel(\"photon\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Liouvillian structure\n", "\n", "We can derive thermodynamical properties of the out-of-equilibrium system by studying the spectrum of the Liouvillian." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", "\n", "# represent the Liouvillian\n", "plt.figure(figsize=(14,6))\n", "plt.subplot(121)\n", "plt.imshow(np.real(L.full()))\n", "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", "plt.subplot(122)\n", "plt.imshow(np.imag(L.full()))\n", "plt.title(\"Imaginary values of the Liouvillian\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Liouvillian Spectrum, $\\texttt{eigenstates}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "L = liouvillian(H,[np.sqrt(kappa)*a,np.sqrt(gamma)*sz])\n", "\n", "# Plot the Liouvillian spectrum in the complex plane\n", "eigenvalues_L, eigenvectors_L = L.eigenstates()\n", "\n", "\n", "real_eigenvalues = np.real(eigenvalues_L)\n", "imag_eigenvalues = np.imag(eigenvalues_L)\n", "\n", "plt.figure(figsize=(10,10))\n", "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", "plt.title(\"Real values of the Liouvillian\",fontsize=fs)\n", "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us decipher the spectrum of the Liouvillian:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "plt.plot(real_eigenvalues, imag_eigenvalues,\"o\")\n", "plt.title(\"Real values of the Liouvillian\")\n", "plt.axvline(x=0,color=\"red\")\n", "plt.axhline(y=0,color=\"black\",linestyle=\"dashed\")\n", "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We find symmetries in the Liouvillian spectrum with respect to the real and imaginary axis." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "plt.plot(real_eigenvalues[-1],imag_eigenvalues[-1],\"o\",markersize=20,label=\"$\\lambda_0$\")\n", "plt.plot(real_eigenvalues[-2],imag_eigenvalues[-2],\"*\",markersize=20,label=\"$\\lambda_1$\")\n", "plt.plot(real_eigenvalues[-3],imag_eigenvalues[-3],\"s\",markersize=20,label=\"$\\lambda_2$\")\n", "plt.xlim([-2,2])\n", "plt.ylim([-2,2])\n", "plt.legend(fontsize=20)\n", "plt.ylabel(\"Im($\\lambda_i$)\",fontsize=fs)\n", "plt.xlabel(\"Re($\\lambda_i$)\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Photon counting statistics: $\\texttt{mcsolve}$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.0%. Run time: 4.65s. Est. time left: 00:00:00:41\n", "20.0%. Run time: 9.36s. Est. time left: 00:00:00:37\n", "30.0%. Run time: 14.29s. Est. time left: 00:00:00:33\n", "40.0%. Run time: 19.73s. Est. time left: 00:00:00:29\n", "50.0%. Run time: 27.13s. Est. time left: 00:00:00:27\n", "60.0%. Run time: 32.55s. Est. time left: 00:00:00:21\n", "70.0%. Run time: 37.79s. Est. time left: 00:00:00:16\n", "80.0%. Run time: 42.91s. Est. time left: 00:00:00:10\n", "90.0%. Run time: 48.88s. Est. time left: 00:00:00:05\n", "100.0%. Run time: 54.61s. Est. time left: 00:00:00:00\n", "Total run time: 54.67s\n" ] } ], "source": [ "# set dynamics options\n", "my_options = Options(average_states = False, store_states = True)\n", "# solve dynamics\n", "results_mc = mcsolve(H, psi0, tlist, \n", " c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", " e_ops=[a.dag()*a,sz], \n", " options=my_options, progress_bar=True)\n", "\n", "# store time evoluted variables\n", "nph_mc_t = results_mc.expect[0]\n", "sz_mc_t = results_mc.expect[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The default options for $\\texttt{mcsolve}$ imply solving the dynamics for 500 trajectories. \n", "\n", "This option can be controlled by setting a different number in $\\texttt{Options(ntraj=500})$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "500" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rho_mc_t = results_mc.states\n", "len(rho_mc_t)\n", "#help(expect)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "sz_stoch_t = []\n", "nph_stoch_t = []\n", "for i in range(len(rho_mc_t)):\n", " sz_stoch_t.append(expect(sz,rho_mc_t[i]))\n", " nph_stoch_t.append(expect(a.dag()*a,rho_mc_t[i]))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14,4))\n", "plt.subplot(121)\n", "plt.plot(tlist, sz_t, label=\"me solve\")\n", "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", "plt.legend(fontsize=15)\n", "plt.subplot(122)\n", "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", "plt.legend(fontsize=15)\n", "plt.show()\n", "plt.close()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lindblad master equation as the limit of the stochastic evolution: $\\texttt{mesolve}$ and $\\texttt{mcsolve}$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.0%. Run time: 0.36s. Est. time left: 00:00:00:03\n", "20.0%. Run time: 0.53s. Est. time left: 00:00:00:02\n", "30.0%. Run time: 0.74s. Est. time left: 00:00:00:01\n", "40.0%. Run time: 0.90s. Est. time left: 00:00:00:01\n", "50.0%. Run time: 1.09s. Est. time left: 00:00:00:01\n", "60.0%. Run time: 1.26s. Est. time left: 00:00:00:00\n", "70.0%. Run time: 1.45s. Est. time left: 00:00:00:00\n", "80.0%. Run time: 1.63s. Est. time left: 00:00:00:00\n", "90.0%. Run time: 1.82s. Est. time left: 00:00:00:00\n", "100.0%. Run time: 2.00s. Est. time left: 00:00:00:00\n", "Total run time: 2.12s\n", "10.0%. Run time: 0.40s. Est. time left: 00:00:00:03\n", "20.0%. Run time: 0.76s. Est. time left: 00:00:00:03\n", "30.0%. Run time: 1.14s. Est. time left: 00:00:00:02\n", "40.0%. Run time: 1.52s. Est. time left: 00:00:00:02\n", "50.0%. Run time: 1.96s. Est. time left: 00:00:00:01\n", "60.0%. Run time: 2.33s. Est. time left: 00:00:00:01\n", "70.0%. Run time: 2.72s. Est. time left: 00:00:00:01\n", "80.0%. Run time: 3.11s. Est. time left: 00:00:00:00\n", "90.0%. Run time: 3.49s. Est. time left: 00:00:00:00\n", "100.0%. Run time: 3.99s. Est. time left: 00:00:00:00\n", "Total run time: 4.05s\n", "10.0%. Run time: 1.32s. Est. time left: 00:00:00:11\n", "20.0%. Run time: 2.80s. Est. time left: 00:00:00:11\n", "30.0%. Run time: 3.91s. Est. time left: 00:00:00:09\n", "40.0%. Run time: 4.96s. Est. time left: 00:00:00:07\n", "50.0%. Run time: 5.83s. Est. time left: 00:00:00:05\n", "60.0%. Run time: 6.61s. Est. time left: 00:00:00:04\n", "70.0%. Run time: 7.64s. Est. time left: 00:00:00:03\n", "80.0%. Run time: 8.43s. Est. time left: 00:00:00:02\n", "90.0%. Run time: 9.18s. Est. time left: 00:00:00:01\n", "100.0%. Run time: 9.92s. Est. time left: 00:00:00:00\n", "Total run time: 10.04s\n" ] } ], "source": [ "# 50 trajectories\n", "my_options50 = Options(ntraj=50)\n", "results_mc50 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", " e_ops=[a.dag()*a,sz], options=my_options50, progress_bar=True)\n", "nph_mc_t50 = results_mc50.expect[0]\n", "sz_mc_t50 = results_mc50.expect[1]\n", "# 100 trajectories\n", "my_options100 = Options(ntraj=100)\n", "results_mc100 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", " e_ops=[a.dag()*a,sz], options=my_options100, progress_bar=True)\n", "nph_mc_t100 = results_mc100.expect[0]\n", "sz_mc_t100 = results_mc100.expect[1]\n", "# 200 trajectories\n", "my_options200 = Options(ntraj=200)\n", "results_mc200 = mcsolve(H, psi0, tlist, c_ops=[np.sqrt(kappa)*a,np.sqrt(gamma)*sz], \n", " e_ops=[a.dag()*a,sz], options=my_options200, progress_bar=True)\n", "nph_mc_t200 = results_mc200.expect[0]\n", "sz_mc_t200 = results_mc200.expect[1]" ] }, { "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": [ "plt.figure(figsize=(16,6))\n", "# spin excitation\n", "plt.subplot(121)\n", "plt.plot(tlist, sz_mc_t50, label=\"mc solve (50 trajectories)\")\n", "plt.plot(tlist, sz_mc_t100, label=\"mc solve (100 trajectories)\")\n", "plt.plot(tlist, sz_mc_t200, label=\"mc solve (200 trajectories)\")\n", "plt.plot(tlist, sz_mc_t, label=\"mc solve (500 trajectories)\")\n", "plt.plot(tlist, sz_t, label=\"me solve\")\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle \\sigma_z \\rangle$\",fontsize=fs)\n", "plt.legend(fontsize=15)\n", "# photonic excitation\n", "plt.subplot(122)\n", "plt.plot(tlist, nph_mc_t50/nph/0.5, label=\"mc solve (50 trajectories)\")\n", "plt.plot(tlist, nph_mc_t100/nph/0.5, label=\"mc solve (100 trajectories)\")\n", "plt.plot(tlist, nph_mc_t200/nph/0.5, label=\"mc solve (200 trajectories)\")\n", "plt.plot(tlist, nph_mc_t/nph/0.5, label=\"mc solve (500 trajectories)\")\n", "plt.plot(tlist, nph_t/nph/0.5, label=\"me solve\")\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle a^\\dagger a \\rangle$\",fontsize=fs)\n", "plt.legend(fontsize=15)\n", "plt.show()\n", "plt.close()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe that progressively, as the number of trajectories is increased, the value given by the average over the trajectories gets closer to the master equation value." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,4))\n", "plt.subplot(121)\n", "plt.plot(tlist, sz_t)\n", "plt.plot(tlist, sz_mc_t)\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle s_z \\rangle$\",fontsize=fs)\n", "plt.subplot(122)\n", "plt.plot(tlist, nph_t/nph/0.5)\n", "plt.plot(tlist, nph_mc_t/nph/0.5)\n", "\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle n_{ph} \\rangle$\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting single quantum trajectories\n", "\n", "By setting:\n", "my_options = Options(average_states = False, store_states = True)\n", "\n", "we can inspect single quantum trajectories and their behaviour." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14,5))\n", "plt.subplot(121)\n", "for i in range(len(sz_stoch_t)):\n", " plt.plot(tlist, sz_stoch_t[i],alpha=0.1)\n", "\n", "plt.plot(tlist, sz_t,\"b\",linewidth=3)\n", "plt.plot(tlist, sz_mc_t,\"y\",linewidth=2)\n", "plt.plot(tlist, sz_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", "plt.plot(tlist, sz_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", "plt.subplot(122)\n", "for i in range(len(sz_stoch_t)):\n", " plt.plot(tlist, nph_stoch_t[i]/nph/0.5,alpha=0.1)\n", "plt.plot(tlist, nph_t/nph/0.5,\"b\",linewidth=3)\n", "plt.plot(tlist, nph_mc_t/nph/0.5,\"y\",linewidth=2)\n", "plt.plot(tlist, nph_stoch_t[4]/nph/0.5,\"g\",linewidth=5)\n", "plt.plot(tlist, nph_stoch_t[6]/nph/0.5,\"r\",linewidth=5)\n", "plt.xlabel(r\"$t$\",fontsize=fs)\n", "plt.ylabel(r\"$\\langle X \\rangle$\",fontsize=fs)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We obseverve that the single trajectories can provide information about the phase of the system. In presence of a phase transition the quantum trajectory jumps between possible choices of the degenerate steady state. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "QuTiP: Quantum Toolbox in Python\n", "Copyright (c) 2011 and later.\n", "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n", "\n", "QuTiP Version: 4.3.1\n", "Numpy Version: 1.15.4\n", "Scipy Version: 1.2.1\n", "Cython Version: 0.29.8\n", "Matplotlib Version: 3.0.3\n", "Python Version: 3.7.3\n", "Number of CPUs: 2\n", "BLAS Info: OPENBLAS\n", "OPENMP Installed: False\n", "INTEL MKL Ext: False\n", "Platform Info: Darwin (x86_64)\n", "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", "==============================================================================\n", "Please cite QuTiP in your publication.\n", "==============================================================================\n", "For your convenience a bibtex file can be easily generated using `qutip.cite()`\n" ] } ], "source": [ "qutip.about()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }