{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Superradiance in the open Dicke model: $N$ qubits in a bosonic cavity \n", "\n", "Author: Nathan Shammah (nathan.shammah@gmail.com)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider a system of $N$ two-level systems (TLSs) coupled to a cavity mode. This is known as the Dicke model \n", "\n", "\\begin{eqnarray*}\n", "H &=&\\omega_{0}J_z + \\omega_{c}a^\\dagger a + g\\left(a^\\dagger + a\\right)\\left(J_{+} + J_{-}\\right)\n", "\\end{eqnarray*}\n", "\n", "where each TLS has identical frequency $\\omega_{0}$. The light matter coupling can be in the ultrastrong coupling (USC) regime, $g/\\omega_{0}>0.1$.\n", "\n", "If we study this model as an open quantum system, the cavity can leak photons and the TLSs are subject to local processes. For example the system can be incoherently pumped at a rate $\\gamma_\\text{P}$, the TLSs are subject to dephaisng at a rate $\\gamma_\\text{D}$, and local incoherent emission occurs at a rate $\\gamma_\\text{E}$. The dynamics of the coupled light-matter system is governed by\n", "\n", "\\begin{eqnarray}\n", "\\dot{\\rho} &=& \n", "-i\\lbrack \\omega_{0}J_z + \\omega_{a}a^\\dagger a + g\\left(a^\\dagger + a\\right)\\left(J_{+} + J_{-}\\right),\\rho \\rbrack\n", "+\\frac{\\kappa}{2}\\mathcal{L}_{a}[\\rho]\n", "+\\sum_{n=1}^{N}\\left(\\frac{\\gamma_\\text{P}}{2}\\mathcal{L}_{J_{+,n}}[\\rho] \n", "+\\frac{\\gamma_\\text{E}}{2}\\mathcal{L}_{J_{+,n}}[\\rho]\n", "+\\frac{\\gamma_\\text{D}}{2}\\mathcal{L}_{J_{+,n}}[\\rho]\\right)\n", "\\end{eqnarray}\n", "\n", "When only the dissipation of the cavity is present, beyond a critical value of the coupling $g$, the steady state of the system becomes superradiant. This is visible by looking at the Wigner function of the photonic part of the density matrix, which displays two displaced lobes in the $x$ and $p$ plane. \n", "\n", "As it has been shown in Ref. [1], the presence of dephasing suppresses the superradiant phase transition, while the presence of local emission restores it [2].\n", "\n", "In order to study this system using QuTiP and $PIQS$, we will first build the TLS Liouvillian, then we will build the photonic Liouvillian and finally we will build the light-matter interaction. The total dynamics of the system is thus defined in a Liouvillian space that has both TLS and photonic degrees of freedom. \n", "\n", "This is driven-dissipative system dysplaying out-of-equilibrium quantum phase transition." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib as mpl\n", "from matplotlib import cm\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from qutip import *\n", "from qutip.piqs import *" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "#TLS parameters\n", "N = 6\n", "ntls = N\n", "nds = num_dicke_states(ntls)\n", "[jx, jy, jz] = jspin(N)\n", "jp = jspin(N,\"+\")\n", "jm = jp.dag()\n", "w0 = 1\n", "gE = 0.1\n", "gD = 0.01\n", "h = w0 * jz\n", "#photonic parameters\n", "nphot = 20\n", "wc = 1\n", "kappa = 1\n", "ratio_g = 2\n", "g = ratio_g/np.sqrt(N)\n", "a = destroy(nphot)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [], "source": [ "#TLS liouvillian\n", "system = Dicke(N = N)\n", "system.hamiltonian = h \n", "system.emission = gE \n", "system.dephasing = gD\n", "liouv = system.liouvillian() \n", "\n", "#photonic liouvilian\n", "h_phot = wc * a.dag() * a\n", "c_ops_phot = [np.sqrt(kappa) * a]\n", "liouv_phot = liouvillian(h_phot, c_ops_phot)\n", "\n", "#identity operators\n", "id_tls = to_super(qeye(nds))\n", "id_phot = to_super(qeye(nphot))\n", "\n", "#light-matter superoperator and total liouvillian\n", "liouv_sum = super_tensor(liouv_phot, id_tls) + super_tensor(id_phot, liouv)\n", "h_int = g * tensor(a + a.dag(), jx)\n", "liouv_int = -1j* spre(h_int) + 1j* spost(h_int)\n", "liouv_tot = liouv_sum + liouv_int" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "#total operators\n", "jz_tot = tensor(qeye(nphot), jz)\n", "jpjm_tot = tensor(qeye(nphot), jp*jm)\n", "nphot_tot = tensor(a.dag()*a, qeye(nds))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "rho_ss = steadystate(liouv_tot, method=\"eigen\")\n", "jz_ss = expect(jz_tot, rho_ss)\n", "jpjm_ss = expect(jpjm_tot, rho_ss)\n", "nphot_ss = expect(nphot_tot, rho_ss)\n", "psi = rho_ss.ptrace(0)\n", "xvec = np.linspace(-6, 6, 100)\n", "W = wigner(psi, xvec, xvec)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wigner Function\n", "Below we calculate the Wigner function of the photonic part of the steady state. It shows two displaced squeezed states in the reciprocal photonic space. The result is in agreement with the findings of Ref [2]." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "jmax = (0.5 * N)\n", "j2max = (0.5 * N + 1) * (0.5 * N)\n", "\n", "plt.rc('text', usetex = True)\n", "label_size = 20\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "wmap = wigner_cmap(W) # Generate Wigner colormap\n", "nrm = mpl.colors.Normalize(0, W.max())\n", "max_cb =np.max(W)\n", "min_cb =np.min(W)\n", "\n", "fig2 = plt.figure(2)\n", "plotw = plt.contourf(xvec, xvec, W, 100, cmap=wmap, norm=nrm)\n", "plt.title(r\"Wigner Function\", fontsize=label_size);\n", "plt.xlabel(r'$x$', fontsize = label_size)\n", "plt.ylabel(r'$p$', fontsize = label_size)\n", "cb = plt.colorbar()\n", "cb.set_ticks( [min_cb, max_cb])\n", "cb.set_ticklabels([r'$0$',r'max']) \n", "\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time Evolution\n", "\n", "Here we calculate the time evolution of a state initialized in the most excited spin state with no photons in the cavity. We calculate the full density matrix evolution as well as spin and photon operator mean values. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "#set initial conditions for spins and cavity\n", "tmax = 40\n", "nt = 1000\n", "t = np.linspace(0, tmax, nt)\n", "rho0 = dicke(N, N/2, N/2)\n", "rho0_phot = ket2dm(basis(nphot,0))\n", "rho0_tot = tensor(rho0_phot, rho0)\n", "result = mesolve(liouv_tot, rho0_tot, t, [], e_ops = [jz_tot, jpjm_tot, nphot_tot])\n", "rhot_tot = result.states\n", "jzt_tot = result.expect[0]\n", "jpjmt_tot = result.expect[1]\n", "adagat_tot = result.expect[2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plots" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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tlkgkknEtl8ulXq835bhgMJgRk8fjUbfbnXg+NTWlADQUChXt/eUSv53lUwy5fr4BjGoO37GsudjknnvuQTwex/T0tNOhEBWF1+sFABw8eDCvjuloNJrozLaam0QE0Wh00Wt4PB4ASPxyt65h1Uws2WoiR48eRSwWS1zbqsX09PQU5f3lEv9SVlI+5WCN0wFUiuThyPfdd5/D0RDZz+VyYWRkBIFAINEc5fV6E809i7G+YCORSEYyaGpqSvw9PDyMwcFBxGKxjC9l67nb7V42zu7ubrhcLgwODsLj8WBwcBDd3d1Fe3+5xL+UXMun3LDmYhPrpmHj4+MOR0JUPF6vF5FIBFNTUwgGgwiHw+jr61vynOSE4Ha7Ux7Wl2lXVxcCgQC6urowMDCA559/Pus1Jicnc4rz0KFD6O/vRzweRzQazajx2Pn+col/KbmUTzlicrFJa2srACYXqg4ulwu9vb3weDw4duwYgMV/ZXs8HrhcrozOd8CY+xGLxRAOhxEMBtHT0wOPx5NRQ7GuYXWcW8bGxrK+ZiAQQDweR39/P1wuV6LJqxjvL5f4lzp/ufIpV2wWs0lLSwsA4OLFiw5HQlQc/f39CAaD8Pv9cLvdiX4Nq1Zg/cq2EkAoFEo0KQ0MDMDn88Hn8yWGEIdCIbjdboRCoZQvV5fLhWAwmPH6R48eRSAQgN/vh8/nQzQaXbRW4Xa74fF48Oyzz+LQoUNFfX9WDWO5+Aspn7KUS69/JT7sHi22sLCgdXV1GggEbL0ulY5qHy02NTWlvb296na7FYC63e6M0Uy9vb2L7otEIur1ehWAulwu7enpSYzMGhoaUpfLpQDU4/FoKBRSABoMBjOu73K5EtfPNlrMYl0jEokU/f3lE/9Kymc12D1aTIxjq09nZ6eOjo7aes22tjY88cQTeO6552y9LpWGN954Aw888IDTYVCO+vr6EnNKaHm5fr5FJKKqncsdxz4XG7W2trLPhahEhEKhnDvyyX7sc7FRS0sLTp065XQYRFXL6ic5duwYYrHYsnNbqHiYXGzU2tqKF1980ekwiKpWPB7HkSNHAABDQ0NlPZS33DG52Ki1tRWXL1/G3Nwc6urqnA6HqOp4PB5MTU05HQaBfS62soYjX7p0yeFIiIicxeRiI06kJCIyMLnYyKq5MLlUrmoduk+VrRifayYXG1k1F87Sr0y1tbWYm5tzOgwi283NzaG2ttbWazK52Ki5uRkAay6VqqGhAdeuXXM6DCLbXbt2DQ0NDbZek8nFRmvXrsWWLVtYc6lQTU1NmJqawsTEBGZnZ9lERmVNVTE7O4uJiQlMTU3Zvrw/hyLbjLP0K1d9fT3a2towOTmJ06dPY35+3umQiApSW1uLhoYGtLW1ob6+3tZrM7nYrKWlhcmlgtXX16O1tTXRv0ZE2bFZzGatra1sFiOiqsfkYjOrWYzt8URUzUqiWUxEPAA6AcQAuAHEVDW8zDkuAD0AhgFMAmgC4Acwsty5xdTS0oLZ2VnE43E0NjY6FQYRkaMcTy4i4gYQVNWupG1DIhJT1dgSpzYBCJoPAIgDOOJkYgFSZ+kzuRBRtSqFZjE/gPT7eIZwJ2kspQtAI4B2VW1U1WG7g8sXb3dMRFQayaUbQDRt26i5fVmqGl+mhrOquL4YEZHDycXsN3HD6DNJUNW4ud/tRFyF4PpiRETO97k0AXeSSRZuGJ38i3GLiFXDaQIwuVTTmIj0wBgEgLa2tvyjzcGmTZuwfv16NosRUVVzOrkUcpu4SQBITibmQAAslmBUtR9APwB0dnYWZaywiHCWPhFVvRU1i4nIJhHZLyK7RGST3UHlwuxr6U/bnOtAgKJqaWlhzYWIqlpONRcROQLAB2MuisJoqrLuJeoWkUZz2yCAYVU9nU8QIuJaomksHzEzHruutyKtra04ceKEUy9PROS4RWsuZu3kr0Xk32EkFJ+qNqnqFlU9oKofMR97rG0AXgHwjIgMisgTOby+1Z+Sshyn2dGfvD9bfL1ZNlsDAxwdCMD1xYio2mWtuYjI+2F0fPep6qlcL6aqzwN43rzGERHxqOrfLHF8XERiyOx7aQKw6BBja+KliAynHWMlKUeHJre2tiIej2NmZsb2lUaJiMpBRs1FRHYDcKvq5/JJLOlUdQDAgIh8cplDwzCa25J5zO2LXTsGwJ8l+XgBRJ1sEgM4kZKIKCO5qOopVf2uHRdX1auq+r1lDgvA6M9J5je3AzCayURkzBxKbJlMngdjNqX5ARwpMOyCMbkQUbXLayiyiOxX1eN2BmA2jQVEJAjgGIz+kmCWWklT2nnDItJtznPZAqNpzVcKs/WZXIio2uU7z8UP4HPJG0RkM4z+mZGVJh5VjSJzCZjk/XEYa4ilb3d8LbFsrCVgmFyIqFotOc9FRN4SkWMi8leLjf4ym76+DGBLjiPEKt62bdsgIkwuRFS1lptE6YMx+usjMDrYe8xk86yIPJE8gdIcKVbIjPuKUVdXh61bt3I4MhFVrSWbxVT1FRhzVwAAIvITACMwlroPAFARicJYxThibl+uA78qcJY+EVWzfJd/ianql83JkzUADgD4DowO9Y8A+Gu7AyxXTC5EVM3y7dAfSn6yXEd8NWttbcWbb77pdBhERI7Iq+Zi9qtQDqyai2pRFl8mIippWWfo5zCrPifm+mSfteNa5aalpQUzMzOIxx1dLICIyBFZZ+gDOCUi/0dEdq30wuZKykdV9e9XHl754kRKIqpmWZvFzFFizwB4SkT+XUQ+m8t9W8x7vHzDXEl5TFWP2hxv2WByIaJqtmiHvqpehZFgICJ/AODvRcQDY/n9OO4sb98OY/Z8DMaQ5JCZnKoaZ+kTUTXLabSYuZBlYjFLc8kXN8wkYyYiSsKaCxFVs3yHIgNI1GqqvnaylM2bN6O+vp6z9ImoKuU7iZJyJCKcSElEVYvJpYiYXIioWq04uYjIJ6t1DkuumFyIqFrllVyShhpbN/VqFJFRc07M/uKEWL5aW1uZXIioKi3boW/Ob/EDOAxgDEC/qj6VdMiXReT9MObEdAAYNI+5VoyAy0lLSwsuX76Mubk51NXVOR0OEdGqWbTmIiJ/YC6x/zyAKVXtVNXD2dYXU9VXVPUpVT0A4CqA/2dOvrRlGZlyZQ1HvnTpksOREBGtrqzJRUS+AaATgF9VD+SzhIuqDqhqJ4CnAHxARAbtCbX8cK4LEVWrrM1iac1eK2KuUfZModcpZ0wuRFStbBmKXMgCl5WMS8AQUbWya57LlLWwpYhsznWhy0rX3NwMAJylT0RVx67k0gjggIhsMpeGGULaXSurUX19PRobG1lzIaKqs6K1xbIYUdX7zFqLVWPZYtO1yxonUhJRNbKr5tIvIvvNWosA6ABw0KZrlzUmFyKqRkvNc9mV60VU9csATpl/XzX/5s3jwVn6RFSdlqq5BPO5UPI9XcxhyLLSoCpJS0sLxsfHocpcS0TVY6nk4hORb4vIf1/JyC/eQMzQ0tKC6elp3Lhxw+lQiIhWzXJ9Lh+BcQfKKRE5aS5QuaJkU604kZKIqtFSyWVYVZsA7AHwORh3njyMLMlmFeIsW0wuRFSNlkoukwCgqjFV7VfVQ2ayaUdashGRKyLyePHDLT+cpU9E1WjR5LLY+mKqeipLsvl7AGERubdIcZYtq+bCWfpEVE0KnudiJpsAgAMA+goPqbI0NTVhzZo1rLkQUVWxaxIlVDUKYNSu61WKmpoaNDc3M7kQUVUpOLmIyCeTbnHMyRxZcJY+EVUbO9YW6wPQKCJHYNyFktK0trbiwoULTodBRLRq7GgW64BxU7CYqg7YcL2KY83SJyKqFgXXXMyZ+EwqS2hpacGlS5cwPz+P2tpap8MhIio62zr0aXEtLS1YWFjAxMSE06EQEa2KrMlFRP6niDxR6MVFZL+I/I9Cr1PuOEufiKrNYjWXYQCHzCVens1n+X0R2WQmp1EAfgDPFx5meWNyIaJqk7XPxVwy/ykAEJE/gHEzMAUQUtXvZTvHPM4PYzjykKp2Fifk8mMtAcNOfSKqFst26Kvqd2GsH7YbgF9E+gCMAAgBiMNIQgcBhAH4zcRESZqbmwGw5kJE1SPn0WJm0ngGwDMichDA/4JRS+lX1WeKFF9F2LhxIxoaGphciKhqrGgosqo+D/al5IWz9ImomnAo8iphciGiasLkskpaW1uZXIioajC5rBIuAUNE1YTJZZW0tLTg2rVrmJ6edjoUIqKiY3JZJdZEynfeecfhSIiIio/JZZVwlj4RVRMml1VizdJnciGiasDkskqsmgs79YmoGjC5rJJt27ahpqaGNRciqgpMLquktrYW27ZtY3IhoqrA5LKKONeFiKoFk8sq2r59Oy5cuOB0GERERcfksop27NiB8+fPOx0GEVHRrWhVZLuJiAdAJ4AYADeAmKqGi3WeU3bu3InLly/j1q1bWLdundPhEBEVjePJRUTcAIKq2pW0bUhEYqoas/s8J+3YsQMA8Pbbb8PtdjscDRFR8ZRCs5gfxl0tk4UABIt0nmOs5HLu3DmHIyEiKq5SSC7dAKJp20bN7cU4zzFWcmG/CxFVOkeTi4i4YPSVTCZvV9W4uT9r29FKz3MakwsRVQunay5NwJ2kkMViSWKl5znqrrvugsvlYnIhoorndHJxreZ5ItIjIqMiMnr58uUVvnRhOByZiKqB08llValqv6p2qmrntm3bHIlhx44d7NAnoopXEsnF7ENZtfOctHPnTtZciKjiOZ1crPkoTckbk5LGYvNVVnqe43bs2IF33nkHs7OzTodCRFQ0jiYXs0M+hsw+lCYA8cUmQ670vFKQPJGSiKhSOV1zAYAwjCVcknnM7cU4z1GcSElE1aAUkksAgC9tm9/cDsBo7hKRMRHpyee8UsS5LkRUDRxfW0xV4yISEJEggGMw5qgEszRtNa3wvJKyc+dOAEwuRFTZHE8uAKCqUWQu5ZK8Pw6gMd/zSlFDQwM2b96MM2fOOB0KEVHRlEKzWNXZvXs3Tp065XQYRERFw+TiALfbzeRCRBWNycUBVnJZWFhwOhQioqJgcnGA2+3GrVu3cPHiRadDISIqCiYXB+zevRsAEIuV9MA2IqIVY3JxgHWLYyYXIqpUTC4OuPfeeyEi7NQnoorF5OKA+vp67NixgzUXIqpYTC4OcbvdTC5EVLGYXByye/duJhciqlhMLg5xu914++23cfPmTadDISKyHZOLQ+6//34AwMmTJx2OhIjIfkwuDtm7dy8A4MSJEw5HQkRkPyYXh9x///2oqalhciGiisTk4pD6+nq0t7czuRBRRWJycdDevXvxxhtvOB0GEZHtmFwctHfvXrz55puYm5tzOhQiIlsxuTjogQcewO3bt/HWW285HQoRka2YXBy0b98+AMCvfvUrhyMhIrIXk4uD9u3bh7Vr1yISiTgdChGRrZhcHFRfX4/3vve9GB0ddToUIiJbMbk4rKOjA5FIhLc8JqKKwuTisM7OTly9epWd+kRUUZhcHPahD30IAPDCCy84HAkRkX2YXBz2wAMPoLm5GT/96U+dDoWIyDZMLg4TETz++OP46U9/ClV1OhwiIlswuZSAJ554AuPj45zvQkQVg8mlBHziE59ATU0NhoaGnA6FiMgWTC4loLm5GY8//jgGBwfZNEZEFYHJpUR8+tOfxsmTJzEyMuJ0KEREBWNyKRGf+tSnsH37dnzpS19i7YWIyh6TS4mor6/HF7/4RfzsZz/DV77ylcR2VcUrr7yCL3zhCzhw4AB2796NRx55BH/xF3+BixcvOhgxEdHipFp/JXd2dmqprem1sLCAT37yk/iXf/kX/N7v/R6amprwwgsv4MyZM6ipqcGjjz6KtrY2jI2N4cUXX8Rdd92FP//zP8fTTz+Nmhr+TiCi4hORiKp2Lnsck0tpmZmZwV/+5V/im9/8Jm7duoUDBw7g4x//OH7/938f27ZtSxz35ptv4vOf/zx+8IMf4KMf/Sj+4R/+AXfffbeDkRNRNWByWUapJpd8qCr6+/vxp3/6p2hqasI//uM/4uDBg06HRUQVLNfkwraUMiYi8Pv9+OUvf4nNmzejq6sLzzzzDGZnZ50OjYiqHJNLBXjf+96H0dFRfPazn0UwGMTevXutiaMeAAAK8klEQVQxPDzMZfyJyDFMLhVi48aN6O/vx49+9COsW7cOPp8P7e3t+NKXvoRXX32Vw5uJaFUxuVSYj33sYzh+/Di+/e1vw+1248/+7M+wf/9+7Ny5Ez09Pfj+97+P6elpp8MkogrHDv0KNz4+jh//+Mf4t3/7N/zkJz/B9evXsW7dOni9XnziE5/Ak08+iZaWFqfDJKIywdFiyygkuTz23GMZ2w7tO4Q/OvBHmJ6bxu9+83cz9n9m/2fwmf2fwcT0BLq/052x/3Odn8PhBw/j3NVz+MP/+4cZ+z//yOfx5G89id9M/Ab+H/gz9n/xt78Ir9uL4xeP4+kfP52x/68O/hU6mzvx9e9/HX/zyt9gYmICMzMzAICGTQ34TPNn4PuwD5OuSfxd5O8yzg99PITf2vpb+OcT/4y/ffFvsbCwkGhqU1V85Xe+gpYNLfjX2L/in379Tyn7bt++jS/c9wXITcEP3/4h/vPqf+L27duYn5/H/Pw8VBUfu/Ix1C7U4vWNr+PU+lNQKJD00ey60AVVxQnXCVzYeMHYb1qzsAa/c/53AACvb30d72x4JyX2+vl6fHj8wwCA41uPY2LdRMr+DfMb8Og7jwIARreOYrJ+MmX/ptlNePjywwCAl7a9hGt111L2N840onPC+Lf28+afY3pNas1w662t2D+xHwDwQusLmK1NHXDRPN2MB688CAD4j+3/gds1t1P2b7+xHe+ZfA8A4Pm251PKBQB2Xt+J+6buw225jRd2Zt50bld8F3Zf3Y2Z2hn8YscvMva3T7Zj57WdmF4zjZd3vJxStgBw/8T9uOf6Pbi+9joi2yMZr/+eS+9B87vNiK+L49XWVzOu/+A7D2LL9BZc2XAFrzW/lrH/fePvg+uWC+9sfAe/vvvXGfvff+H9aJhpwHjDOE5uO5mxv/NcJzbMbcD5zecR2xLL2P/BMx/E2ttrcabxDM42nc3Y/0jsEazRNYhtieGC60LG/g+PGZ+dk9tO4uKm1InLtQu1eCT2CADg182/xuWGyyn7195eiw+e/iAA4PXW1zG5MfWztX52PTrPGp+d/9r+X7i6/uqdnQrcNXMX9p8zPjvHdx7HjfobKedvvrkZD114CAAQuTeCm3U3U/Y3vduEveN7AQAv734Zs7WzePStR/G1r30N27dvz3ivucg1uaxZ0dWpLK1duxYf+MAHsOf6HuzZswfvvvsuJiYmMDExga9+9av46he+CriB2sdrsaZuDUQEuqBYWFhAx//uwMzbM7jtvg18KPPaH+z9IHANwD4ABzL3dx/tBqYB7DcfAKRGUFtbC4Hghz/6IWrmazC9bxo33TchIndOFuDnP/85RARX913FuzveheDOfpkXRKNRqCquPHgFN1uMf2DWl2TtTC1efvllY//7r+DW1lspsU1PT+MXvzC+dCc6JzDblPrlf/PaTfziJWP/5YcvY27TXMr+makZvDT6knH+f5vA7Y2pyWH28ixmjxvXnPrtKSzUpw60uH3xNm69ZsR0teEqtDb12/v8hfOY/rWRsG40pn65AMD5c+fx7lvvYqF24c7+pOI7d/4crp+6jttrbyf2J5ffuXPncPXcVcytn8O7je9mXP/c2XOIj8cx0zCDaVdmk+q5c+cwdWkKNzffxPTmzP1nzpzB5SuXMb1lGtMNmftPnTqF9VfX48bdNzB913RK7ABw+tRp1N+ox7XWa8b+NLFYDGtvrsXVHVcxvSFz/9jYGNbMrkF8Vxw319/Men7NfA2uLFzBzfrM/dYtyCdkIuPLW+YFY2NjEBFMrZ3CrTWpn6252TnEYkbCi6+P41ZN6v75m/OJ/dfuuoZbSN2vNxSnT58GAFx3XceMzqS+/jVJ7L+x5Qbm1qd+Nq9evZrYP333NG6vvY3Tp09jbi71uGJgzYUAABcvXkQ0GsWrr76K8fFxTE1NYX5+HvX19aivr8f69etTHuvWrUNtbS1qamogIqipqUk8kp+vWbMGmzZtQkNDAzZt2pR4NDQ0oK6uzum3TUR5YrPYMphciIjyx0mURETkGCYXIiKyHZMLERHZjsmFiIhsx+RCRES2Y3IhIiLbMbkQEZHtmFyIiMh2VTuJUkQuAzizwtO3AphY9iiysLzyw/LKD8srP4WW172qum25g6o2uRRCREZzmaFKBpZXflhe+WF55We1yovNYkREZDsmFyIish2Ty8r0Ox1AmWF55YfllR+WV35WpbzY50JERLZjzYWIiGzH5EJERLZjciEiItutcTqAciEiHgCdAGIA3ABiqhp2NqrSIiLdAOLZyoXll8osKzeAdvO/IVUdTjuGZWYSES+ALgBXYJRZRFX7045heWUhIi4AQVX1p20vankxueRARNww/ud0JW0bEpGYqsYcDK1kmP/4BwD4suxj+SUxE0vMSibmP/6IiDRZX5gsszvMzxZUNZC0LSIiLlXtM5+zvBYXBNCUvGE1yovNYrnxAwilbQvB+J9W1UTELSIhGL98Jhc5jOWXyq2qUeuJqsZhlEVyGbHM7vBn2RZO287yysJMIk1ZdhW9vJhcctMNIJq2bdTcXtVUNaaq/vQmijQsP5NZSzls/jdZ2NzvNp+zzFJ1ZdkWT/qb5ZWdF8BIlu1FLy8ml2WYXwIZv8rNX5vJXwaUBcsvlfm+3eYjK5ZZKlX1JTeJmboBDAIsr8WYzYnfybJ9VcqLyWV5TcCdgs+iKj+4eWD5pVHVxuRmMZMXxmCIGFhmSxKRHgBRq78FLK/FuBYpk1UpL3boLy+9+YLyw/LLjR/As+bfLLMszIEQXYBRm0naxfJKIyLd6aMPk6xKeTG5EDnM/CU+mfRLnLIwvyyHRcQlIhEAR7LUAKue2ey1WK1k1bBZLEdZOmApDyy/7Mz2bX/ykNCkfSyzLMzmnBCA55O3s7wSDuUyX6XY5cXksjxrzHf6OHFX2n7KjuW3tCCAg2nbWGbLCwNwmZ3WLC+TOTFydJnDVqW82Cy2DFWNi0gMme2UTbjTAUuLYPktzpwfFEjvWGWZ3WHW7CIADi7SBOZieaXoBNAuIoeTtnkAuEUkCOCYqg6vRnkxueQmDON/WvKH22Nup+Wx/NKY/SzB5H/I1q9wcxvLzOCC8Us6/QvPGtFklQ/LC0C2+WYi0gvgQNpw7qKXF5vFchNA5rImfnM73dGE7CNRWH5JzFFPgNGs4zEfXgC+pGTDMgNg1lYGs+wKAOhjeeVkS5ZtRS8v3iwsR2Zb5mEAx2D8aopyUbxEO+1RGGXSDeMXZhjASPJQSJafwSyvqUV2x1S1PelYlpnJrOm1Y/mFK1leJrNJMQDgEIwfff0wFkiNmvuLWl5MLkREZDs2ixERke2YXIiIyHZMLkREZDsmFyIish2TCxER2Y7JhYiIbMfkQkREtmNyISIi2zG5EBGR7ZhciEqMudbYmNNxEBWCyYWo9BxGCdxJkKgQTC5EpceLKlsqnioPkwtR6fEAGHE6CKJCMLkQlQAR8YpISESspOIzn3scDYxohbjkPlEJMe8aeFhVO5yOhagQrLkQlZYusL+FKgCTC1Fp8YL9LVQBmFyISkRS/8qoo4EQ2YDJhah0eGHcxzwOACLicjgeohVjciEqHQeQWmvpcSoQokIxuRCVlghgDE0GO/apjDG5EJWOZwF0iUg3AKhq1OF4iFaM81yIiMh2rLkQEZHtmFyIiMh2TC5ERGQ7JhciIrIdkwsREdmOyYWIiGzH5EJERLZjciEiItsxuRARke3+PydFfMKJm1ClAAAAAElFTkSuQmCC\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "jmax = (N/2)\n", "j2max = N/2*(N/2+1)\n", "\n", "fig1 = plt.figure(1)\n", "plt.plot(t, jzt_tot/jmax, 'k-', label='time evolution')\n", "plt.plot(t, t*0+jz_ss/jmax, 'g--', label='steady state')\n", "plt.title('Total inversion', fontsize = label_size)\n", "plt.xlabel(r'$t$', fontsize = label_size)\n", "plt.ylabel(r'$\\langle J_z\\rangle (t)$', fontsize = label_size)\n", "plt.legend(fontsize = label_size)\n", "plt.show()\n", "plt.close()\n", "\n", "fig2 = plt.figure(2)\n", "plt.plot(t, jpjmt_tot/j2max, 'k-', label='time evolution')\n", "plt.plot(t, t*0+jpjm_ss/j2max, 'g--', label='steady state')\n", "plt.xlabel(r'$t$', fontsize = label_size)\n", "plt.ylabel(r'$\\langle J_{+}J_{-}\\rangle (t)$', fontsize = label_size)\n", "plt.title('Light emission', fontsize = label_size)\n", "plt.xlabel(r'$t$', fontsize = label_size)\n", "plt.legend(fontsize = label_size)\n", "plt.show()\n", "plt.close()\n", "\n", "fig3 = plt.figure(3)\n", "plt.plot(t, adagat_tot, 'k-', label='time evolution')\n", "plt.plot(t, t*0 + nphot_ss, 'g--', label='steady state')\n", "plt.title('Cavity photons', fontsize = label_size)\n", "plt.xlabel(r'$t$', fontsize = label_size)\n", "plt.ylabel(r'$\\langle a^\\dagger a \\rangle (t)$', fontsize = label_size)\n", "\n", "plt.legend(fontsize = label_size)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "[1] E.G. Dalla Torre *et al.*, *Phys Rev. A* **94**, 061802(R) (2016)\n", "\n", "[2] P. Kirton and J. Keeling, , *Phys. Rev. Lett.* **118**, 123602 (2017)\n", "\n", "[3] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, *to be submitted*.\n", "\n", "[4] J. R. Johansson, P. D. Nation, and F. Nori, *Comp. Phys. Comm.* **183**, 1760 (2012). http://qutip.org\n" ] }, { "cell_type": "code", "execution_count": 9, "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: 1.14.2\n", "Scipy Version: 1.1.0\n", "Cython Version: 0.28.5\n", "Matplotlib Version: 2.2.3\n", "Python Version: 3.6.7\n", "Number of CPUs: 2\n", "BLAS Info: INTEL MKL\n", "OPENMP Installed: False\n", "INTEL MKL Ext: True\n", "Platform Info: Darwin (x86_64)\n", "Installation path: /Users/nathanshammah/miniconda3/lib/python3.6/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()" ] } ], "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }