{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Boundary time crystals\n", "\n", "Notebook author: Nathan Shammah (nathan.shammah at gmail.com)\n", "\n", "We apply the Permutational Invariant Quantum Solver (PIQS) [1], imported in QuTiP as $\\texttt{qutip.piqs}$ to the study of the following driven-dissipative dynamics\n", "\\begin{eqnarray}\n", "\\dot{\\rho} = \\mathcal{D}_\\text{TLS}(\\rho) &=& \n", "-\\frac{i}{\\hbar}\\lbrack H,\\rho \\rbrack\n", "+\\frac{\\gamma_\\text{CE}}{2}\\mathcal{L}_{J_{-}}[\\rho]\n", "\\nonumber\\\\\n", "&&+\\sum_{n=1}^{N}\\left(\n", "\\frac{\\gamma_\\text{E}}{2}\\mathcal{L}_{J_{-,n}}[\\rho]\n", "+\\frac{\\gamma_\\text{D}}{2}\\mathcal{L}_{J_{z,n}}[\\rho]\\right)\n", "\\end{eqnarray}\n", "\n", "where $J_{\\alpha,n}=\\frac{1}{2}\\sigma_{\\alpha,n}$ are SU(2) Pauli spin operators, with ${\\alpha=x,y,z}$ and $J_{\\pm,n}=\\sigma_{\\pm,n}$. The collective spin operators are $J_{\\alpha} = \\sum_{n}J_{\\alpha,n}$. The Lindblad super-operators are $\\mathcal{L}_{A} = 2A\\rho A^\\dagger - A^\\dagger A \\rho - \\rho A^\\dagger A$.\n", "\n", "Here the rates $\\gamma_\\text{CE}$ (gCE), $\\gamma_\\text{E}$ (gE) and $\\gamma_\\text{D}$ quantify collective emission, local emission and local dephasing. \n", "\n", "Here we study the Hamiltonian $H=\\hbar\\omega_x J_x$, which has been studied in the context of quantum optics in Refs. [2,3].\n", "\n", "The collective driven-dissipative dynamics has been studied in the regime $\\gamma_\\text{E}=\\gamma_\\text{D}=0$ and in the context of quantum phase transitions (QPTs) in Ref. [4].\n", "\n", "Below we will study the spectrum of the Liouvillian [5] in the two parameter regimes found in Ref. [4], that of strong and of weak dissipation. If only collective processes are present, one can efficiently study the system's dynamics in the reduced symmetric space, whose Hilbert space dimension is only (N+1). We will do so using QuTiP's jmat() functions [6]. \n", "\n", "We then generalize the study of the collective dynamics to include local terms. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from time import clock\n", "from scipy.io import mmwrite\n", "import matplotlib.pyplot as plt\n", "\n", "from qutip import *\n", "from qutip.piqs import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spectrum of the Liouvillian - Strong dissipation limit $\\omega_{0} = 0.5 \\kappa$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "nnn = 10\n", "N = nnn\n", "jj_mat = nnn/2\n", "[jx_mat, jy_mat, jz_mat] = jmat(jj_mat)\n", "jp_mat = jx_mat + 1j * jy_mat\n", "jm_mat = jx_mat - 1j * jy_mat" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "w0 = 1\n", "kappa = 2 * w0 \n", "gg = kappa/ jj_mat\n", "ham = w0 * jx_mat\n", "c_ops = [np.sqrt(gg) * jm_mat]\n", "liouv_mat = liouvillian(ham, c_ops)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(121, 121)\n" ] } ], "source": [ "print(liouv_mat.shape)\n", "eig_mat = liouv_mat.eigenenergies()\n", "re_eigmat = np.real(eig_mat)\n", "imag_eigmat = np.imag(eig_mat)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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FSANmz55d6qSv9gyZSFT1JDIGGmnPUE8qaXdtU6Iws1nAemBHMmmhu++sMEsiTau1Z9RKFEXtGSp5SCdom0ABTAM2uvvyqjMiMlpl2zPySh4KFNJu2ilQAJyblCx2uPuFVWdGZDTKtGfUSh67du3CzOjp6Rmn3ImU105tFNuA5e6+EDjMzOZVnSGRsTZ79mxWr15Nd3c3Q0NDLFu2LNpWofYMqULblCiS9ojrk7dbgVnZNGa2BFgCMHPmzPHLnMgYGhgYYGhoiKGhoWj1k9ozpCptU6LIlCBOAvqzadx9rbv3unvvjBkzxi9zImOo7I18ZXtSqdQhrdY2JQpgm5mtJzRq3+Xud1WdIZHxULbhu6enh66uLty9MKCo1CFjoW0ChbtvAxZWnQ+RKtRr+O7r62PZsmXs3buXrq4uVq9enZs+XerYtWsXK1euZOXKlQoWMiptU/UkIsVqAWBoaAh3Z2BgIDddrRqrq6uLoaEhNm7cyNy5c1UNJaOiQCHSAcq2Y9SqsebNm7cvWOjOcBmttql6EpFiZdsxagMRLliwgNtuu60ld4ZrcENRoBDpEGXaMdIn/dWrVzMwMBA9wa9bt45nnnkGd8/tmqvGcQFVPYlMGNnuswMDA6xYsSJa+rjyyitxdwAmTZo0ouShhzUJKFCITBiNPlhp8+bN7N27FwAz421ve9uIoJJuHNcQIwcuBQqRCaLWjvGhD32osK0h3WidDiwHHXQQixYtyl2nhhgRtVGITCBF7RhFbQ31Gsj7+vrYsGEDe/fuHfUQI2oU71wKFCIHgKLhzGMN5LUT/65duxgaGqKrqytapRVrGFejeGdT1ZPIAaDR9gsYfpNfV1cX8+bNKzzB12sYz7tjXNVTnUOBQuQAEGu/KGpXSAeXqVOnRocCqdcwrjvGO5y7d+TrxBNPdBEZnS1btvjBBx/s3d3dfvDBB/uWLVtGzF+1alXd6fXWU0szf/587+rqcsC7u7t91apVhfnK266MHtDvDZ5v1UYhcgCr9yjWvDaMZhrGG7ljXI3i7UeBQuQAVqsSqjfUR1qjDeON3jGuRvH2ozYKkQPYaNsuyt7YV/aOcTWKtyeVKEQOcI1UL9XSF1Uz5VULxUot2fRlG8VrXXY3btzIbbfdpsEMx5gChYiM0Mq2i6LAkpc+G1TSd4vXTvyrV69mw4YNbNy4sfAmwFigUwBpnAKFiIzQyrYLyA8seelXrFhRKqisXr26sFG8r6+PlStX7it1pPOiNo7mKFCIyAh5pYB6V+J5wSW2TFEwKhNUBgYGogGl6G7yvDYOPSq2hEb707bLS/dRiIyfMvdJ1NLV7n8oe29F9n6Movs28taVTb9q1Srv7u52wLu6unz+/PnD1lVbT+1ejq6urtJ5myho4j6Kyk/4zb4UKETGT/oEHLtRbjTLNHrzX1762Dpqy69Zs6bwxr90mjKBqRM1EyhU9SQidaWribq7u3nooYfo6+uLVtk02s7RaAN6q9s40mnMjKGhoRHPHJ8zZw579uxh8uTJI/I3kbXVfRRmdqmZrTezi6rOi4jsV2uzWLx4MWbGFVdcUXespuw9GkD0WRV592fEnm9RlD6vTaSojSN9/0g6zdDQEN3d3cPWvW7dOnbv3r3vRsB169aNyNNEfR5H6RKFmb0MeBVwBHAQsAO4D9ji7v892oyY2QkA7r4wCRiz3H3baNcrIq1RO5kODg4WXvXnLVO2t1G2AR2ILtNI+jKlm2ya2h3kPT09bN68mUcffTR6fCZ0l9xYvRQwC/gI8AiwF9gDbAceBn4NDAGDwCbgT4GuRuu+Utu6CJiX/H8usCSWXm0UIuOvbKN21ni0cdRLX6ahPdYOMmXKFJ88ebKbmU+dOnXEvi9dutTNLLfdo5ljNlZoZRuFmf0L8GbgduCDwBbgB+6+N5VmOnAS8Drgw8BKM7vA3W9vImb1EEopADuT9YpIG6ldxedVu8Sk76gu++ztRpeplz7dxnHJJZcUdpMtqrICOPvss3n66adZsGDBiBv8skOP7Ny5k9e97nUccsghw6q91q1bx7p16/aVUI444ggWLVpUWNJYu3YtGzZsYMaMGWzfvp0FCxawZMmSuscvT1IldkTDCxZFEOCTwFFlIw6hveN84PxGo1Wy/BrghOT/ecClsfQqUYhUo9kr5DVr1vjkyZOjXVJHu0zZ9GW7yW7ZssWnTJniZuaTJk3yqVOn5u73qlWr9q3LzPzUU091YN9r8uTJw0ol6XlAbgmltj/ZtICvWbOm7rEr2udw2m/s/FzYmO3u73T3nzYQcIbc/Tp3v658mBrmAUJVF8A0YCCbwMyWmFm/mfVv3769yc2IyGjk9TYqY2BgILcnUSuX+e53v8vg4GDd9LNnz2b16tXMmjVrXw+novRmBoSL6j179uTud09PD0NDQ/vSPf7448PWcfTRRzN37lzOOussBgcHR2yjaNsbNmzIzX/R9Jja59aMdur1tJH91U1nJO+Hcfe17t7r7r0zZswY18yJSNDT00NXV1fdZ2i3YrlGlqk38mw27bJly9i2bVu4Yi5Yf63xvnZlbWaYGd3d3cPSDgwM0NUVTqdmxvTp04et5/7772fTpk3ceOONTJo0ssa/aN8WLFiQm/+i6TG1qjlCqaQho76PwsymAcd5c+0S+7j7XWZ2vpmtB7a5+12jzZuItFbtBLt37166urpYvXp1qV48zSzX6DKb64w8m02bfR74ypUrgdB+UeudlL1/xN0ZGhraV8qomTNnDpMmTdrXffaOO+7goosu4u677+aQQw7hhhtu2Je3xYsXA5Rqo6i1RbSijaLWvnTyySc/0uiyjXSPfRZwbPI6LvW31jDS3ejGs9x9+WjXISJjJ32CNTMGBkbUELdsuTLLpLudxkaerZe2FiRiT+576KGHWLt27b4qqHTX4NmzZ/P2t7+dNWvW4O4MDg4ybdo0brrpJvr6+rjpppuG5auRLrJLlixpuvE6K9luvJ9vjlivp1nAYuDlhKDwgtos4OfAvcC/Jn/vaXTDItJ5Gr3bunZy7unpKbVc7GSeXSbvvoXYczLqpU33hKr1TqrNX7FiBWvXrt3XDjE0NDSiV9WiRYu45pprcgc5jD0mthPEShQ3AC8idI+9CViYTH+zu39jrDMmIu0l/TyI2KNM0+kbeQRqIyd+KB7CI2/deWmzgSdbzXTVVVcxODi4Ly+1dohadVW2hBMLCEWPie0YRd2hCDfYnZt6Px1YR7jp7pPAsxrtYtXKl7rHioyfZrrEjuUNc7E85Q3cl71x7pxzzsnt6lpbdunSpSPy0m43zjWLVo4eC/wxMCNn+unAjwjVT29sdIOteilQiIyfZu6sbnSY8XojvzZzJ/XSpUuHzVu6dKlPnTp13x3UsaCk0WNLBIroQjAZeB/wNPBV4Mhm1jOalwKFyPhp5nkUee/rrbMofdlAlU5HcvNbOr/15sf2ZaIYt0Cxb2E4Gvh34MnRrKeZlwKFyNhq5KRfm99I1UwjpZSyQaWWrqjEECtxHCiaCRSxXk9/BlzrqbGdcto37gfmm9mbkmWOBp7n7reVaR8RkfZUNBJqvfsYYs+TyCrq1ZQ30mrZkWLTY1GlG6MnUg+kShRFEOBu4EHgQ8ArIul6CIMH3gD8Cjiv0WjVzEslCpGx0+o2idgjTss0UGeXKXpCXWzdEtDqqifCIH+3E4YTfxK4A/g68EXgFuAnhN5R24HVwPMbzUCzLwUKkdao10uozGNJR7OutHSAMjNfunTpiPWXfea15Gt5oNiXCF4IXEgY4fUrhPsqPgesJIzLNLnRDY/2pUAhMnrNlgJG0xaxdOnSaAP3lClTCkdVTa+rq6vL58+fryDRoGYCRakhPNz9AcLoriIygcTaFYraJIqWKXqKW70b2bI3pmWHwkjnKW/oDbUzjL12Gj1WRMZZ3nOn0/KeAV30rOq5c+fy3ve+d8SztNPP2z7++OMLh+quWbRoEQcddFBunrLP4VaQGB8NjR5rZi8Gnk94ZvYw7n5jqzIlIq1XpjdRvfGR0j2LYuMk5fV4uuaaa9i1a9e+ITCKxnyq1zOp44fD6EClAoWZvYzQJvESwqCAWU4LRo8VkbFRdNKHxquY8pap9xjSomG9i074CgbtpWzV05WEMZ7+CHgx8HuZ16ziRUWkankn/XrSVUzd3d089NBDw6qU0mpPjOvu7mZoaIhly5YVVldNnTpVbQsdpmygeAlwsbt/w91/7O4/zb7GMpMiMjpFbRF5bRA16bYFM+OKK64Y0f6QFntsqdoWOlvZNorvADPHMiMiMnpFPY/y6v1j1VHp5TYnjwOtd8d1vedHqDqpc5UNFEuAz5nZ08CtwM5sAnd/upUZE5HG1DvxZ0/UZYfcqD232t2jDx3S8BgTV9lA8ThhOI91kTRqzBapULNjLRU1QEPjz61WqWFiKttG8VngtcA/AEuBt+e8RKRC2XaInp6ewvYHqN8ADcN7K7l76Wdky8RStkRxOrDY3a8dy8yISPPSVT89PT0sW7Ys2v4A+Q3QRXdVl3lGtkxMZUsUDxIeUiQiFYn1UKqZPXs2K1asYGBgoFR32Hp3Zqu3kkD5EsXfAB8ws7vd/cExzI+I5CjTQymd9qGHHmLSpPDzHm0DtNodpGyg+AChe+x9ZvYg+b2eXjWajJjZLGA9sCOZtNDdR2xH5ECUbqh+5plnWLduXe7JOx1Quru7Wbx4MYsWLVIDtIxK2UBxb/IaS9OAje6+fIy3I9Jx5syZQ3d3N3v37sXdueqqq3IDQDqgAMycOVNBQEat7DDjbxvrjCTOTUoWO9z9wnHapkjlim6Uq6k3/HaNGp9lLDQ0euwY2wYsd/frzWy9mc1z941VZ0pkrJVtf1i0aBHXXHNNNAjopjcZC4WBwsy2E0aFLcXdD29042Z2KWFAwa3u/mHg+mTWVnIGGjSzJYS7xJk5UyOKyMRQ9ka5skFAbQ7SarESxWU0ECiakW6PyJQgTgIuyUm/FlgL0NvbO6Z5ExkvZYfIAAUBqUZhoHD3leOYD4BtZrae0Kh9l7vfNc7bF2mpeu0OtTSNDJEhUoW2aaNw923AwqrzIdIKZdsd0kNkmJmGyJC2pGdmi4yBsg8KqndntEg7aJsShchEUrabqnopSScw985sE+7t7fX+/v6qsyFSqEwbhch4M7M73b23kWVUohBpQCMnf/VQkolCgUKkpEYG5hOZSNSYLVJS2QZqkYlGgUKkJPVQkgOVqp5ESlIPJTlQKVCINEAN1HIgUtWTiIhEKVCIiEiUAoWIiEQpUIiISJQChYiIRClQiIhIlAKFiIhEKVCIiEiUAoWIiEQpUIiISJQChYiIRClQiIhIlAKFiIhEVRoozGxN5v2lZrbezC6qKk8iIjJcJYHCzKYlQeK81LQTANx9IdBjZrOqyJuIiAxXSaBw953ufiGwLTV5HnBz8v/W5L2IiFSsndooeoAdyf87gRdWmBcREUm0U6CYVnUGRERkpHELFCUaqh8Aau0S04CBnHUsMbN+M+vfvn37WGVVRERSxi1QuPtyd1/o7h8uSLIROCn5/4zkfXYda9291917Z8yYMVZZFRGRlMqqnsxsPTArKWXMcve7UtN31t6LiEi1JlW14aQbbHba8iryIiIixdqpMVtERNqQAoWIiEQpUIiISJQChYiIRClQiIhIlAKFiIhEKVCIiEiUAoWIiEQpUIiISJQChYiIRClQiIhIlAKFiIhEKVCIiEiUAoWIiEQpUIiISJQChYiIRClQiIhIlAKFiIhEKVCIiEiUAoWIiEQpUIiISJQChYiIRFUWKMzsGDPrM7NdZvbXmXkPmtk9Zna3mfVXlUcREYFJFW57B/Au4JyC+ae7++PjmB8REclRWYnC3R9z963AnqryICIi9bVrG4UD/25md5rZkqozIyJyIKuy6inmFHd/xMwOB242s/909/+oOlMiIgeicS1RmNk7kgbqu83sd4rSufsjyd/HgC8Br0qWX2Jm/WbWv3379vHJtIjIAW5cA4W7X+buxyevR/LSmNmhZvbs2v/AfODeZPm17t7r7r0zZswYv4yLiBzAKqt6MrMjgH7gOcCQmS0DXgpMB75kZrX8Xevu/1ZVPkVEDnSVBQp3fxS9HQ/VAAAIy0lEQVQ4MmfWk8Arxjk7IiJSoF17PYmISJtQoBARkSgFChERiVKgEBGRKAUKERGJUqAQEZEoBQoREYlSoBARkSgFChERiVKgEBGRKAUKERGJUqAQEZEoBQoREYlSoBARkSgFChERiVKgEBGRKAUKERGJUqAQEZEoBQoREYlSoBARkSgFChERiVKgEBGRqMoChZm92cy+n7y2mNkrUvPONLP/MrP7zeziqvIoIiLVlih+Apzm7i8HPgSsBTCzbuAy4A+BlwJ/amYvrSyXIiIHuMoChbtvcff/Tt5+Gzgy+f9VwP3uvs3ddwOfB95QRR5FRKR92iguAL6R/P984GepeQ8n00REpAKTqs6AmZ1OCBSvqU3KSebjlyMREUkb10BhZu8AFidvzwKmA/8C/KG7DyTTHwZekFrsSOCRZPklwJJk+i4zu3fMM12d6cDjVWdiDGn/OttE3r+JvG8AL250AXOv5mLdzGYCtwCL3H1Lavok4D5gLvBzYCvwP939B5nl+929dxyzPK60f51N+9e5JvK+QXP7V2XV0/uAHuByMwMYdPdedx80s3cCNwHdwJXZICEiIuOnskDh7n8O/HnBvBuBG8c3RyIikqddej01Y23VGRhj2r/Opv3rXBN536CJ/ausjUJERDpDW5cozOwYM+szs11m9teZeQ+a2T1mdreZ9Rcsb2b2iWQokO+b2Qnjk/NyivbPzF5gZrea2Y/M7Adm9u6C5eeY2RPJMbjbzN43frkvz8zWZN5fambrzeyigvTR+dJ+OvkzS/J9s5ldWnVeWq1Vv7W2DhTADuBdwD8UzD/d3Y+PtOD/IfD7yWsJ8M+tz+KoFO3fIPB/3P0lwKuBd0SGMbktOQbHu/sHxzCvDTOzaUmQOC817QQAd18I9JjZrMwy0fntyMyWmNmdqddFmfmzkuk3J69pVeW1GfXy34mfWU3S5f4Sdz8DmJW9mOzkz66Vv7W2DhTu/pi7bwX2NLmKNwDrPPg2MM3Mnte6HI5O0f65+y/c/a7k/18BP6ID7053953ufiGwLTV5HnBz8v/W5D0NzG877r7W3U909xOBfuD6TJJpwEZ3PyN57Rz/XI5Kvfx33GeWsrH2WyPsQ/ais5M/u5b91to6UNThwL8n0X5JQZqOHw7EzH4XeCVwR0GS2Wb2PTP7hpkdO24Za14PoSQFsBN4YYPz25aZzQN2uvu2nNnnJkX8NTnzOkEs/x37mWU+q1qgz+rUz65lv7VODhSnuPsJhOqld5jZqTlpOno4EDN7FrABWObuT+YkuQs4yt1fAfwT8OXxzF+T6hXdO6Zon2O5uy/Pmb4tmbcQOCwJKJ2kXv47+TMD9lXDHJYqXdR08mfXst9a2wUKM3tHqnH2d4rSufsjyd/HgC8RRp3NKhwOpCpl98/MJhOCxL+6+xfz0rj7k+7+6+T/G4HJZjZ9TDJeUonGsQeAWl3oNGCgwfltIbufsbrrpAquVh21lf3717bS+1ci/x3xmdUUfHYXJsFgmE787FJa9ltru0Dh7pelGmdzT+pmdqiZPbv2PzAfyBv36avAoqT306uBJ9z9F2OW+RJK7p8BnwZ+5O4fLVqXmR2RpMXMXkX4PCv9kbr7cndf6O4fLkiyETgp+f+M5H0j89tCzn7OI5TwRshchZ5EfvVGW0nvX4n8d8RnVpPz2V2atKWN0ImfXUrLfmttFyjSkhPhw8BfAe8xs4fN7DnAbwO3m9n3gO8AX3f3f0uWWWpmS5NV3EgoOt4PXAH85bjvRERk/04B/gx4bar0cVayTHr/zgXuTY7DJ4A3eZvdGGNm6wm9Sdab2axa0T6ZvjP1/maAovkdYBbhCm2f2j4B25L9vxnY1kH7VJOb/wnwmZGUKualeqydm0zv+M+ulb813XAnIiJRbV2iEBGR6ilQiIhIlAKFiIhEKVCIiEiUAoWIiEQpUIhkmNlKM/PU61Ez+5qZvbzJ9VkyzMpbMtPfYGZDZvZDMzs6Z7nLzOzTze6HSKsoUIjkewKYnbyWAS8Cbjazw5pY13nAc4FrM9O/DbwpWffinOU+Arw5L4iIjCcFCpF8g+7+7eT1eWARcDhwZhPrehfwGXfPjhL8S3f/AnA7MKK04u4PJvP+ooltirSMAoVIOd9L/qbHDsPMXmNm3zSzp81swMyuqA0vk8w/GjiZkUOPp90HFI38u4FQqtBvVSqjL59IOTOTvz+pTTCzU4BNwKOE4VSWAWcBV6WWmws8xf5AM4yZzUiWfUEyfEvWFsKQNS8bZf5Fmjap6gyItCszq/0+jgI+CdwNfCWV5O+BLe5+fmqZnwObzOw4d7+X8IyDH7n7UMFm/pH9F2zHAn2Z+T8A9hJGR84NNiJjTSUKkXw9hCcP7iEMKvlK4I3uvgvAzA4hNHR/wcwm1V6ENoU9hAABcATweN4GzOx04M3JC3Kqn9x9kPBQmSNatF8iDVOgEMn3BGEI5lcDFwJTgGtTbQXPBbqBy9kfUPYAu4DJ7G/LOCiZNoyZTSE8w32tu38d+DlwXEFediXrEamEqp5E8g26e+3ZA3eY2W+AdcBC4DrCVb4DKwnD2WfVnjWyg/zSwMXAbyV/ITxPpahBexr7H1kpMu5UohAp57OE9oLlAO7+FOE+iBe7e3/OqxYo/gv4vfSKkp5QK4B3ufsTyeR7yClRJI3dhxB6RolUQoFCpITkgVCrgFea2dxk8kXAuWb2meQu69ea2VuTB928KEnzLWBmcsKvuRy4xd3Xp6bdCxyRc0NfL6HksqXlOyVSkgKFSHnXAT8mBAjc/XbgVGAG8BnghmTez4BfJstsJlQbnQlgZn9KuK8i+7TFe5K/2VLFmcA33b2tn0MtE5uecCcyxszs48DR7v76BpfrBn4KXOzunx2TzImUoBKFyNj7CDAnVR1V1kLgN8DnW58lkfIUKETGmLs/DFwAPK/BRQ24ILmXQqQyqnoSEZEolShERCRKgUJERKIUKEREJEqBQkREohQoREQkSoFCRESi/j8yJaYDP1fT8QAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig6 = plt.figure(6)\n", "plt.plot(re_eigmat/kappa, imag_eigmat/kappa, 'k.')\n", "label_size = 15\n", "label_size2 = 15\n", "label_size3 = 15\n", "plt.rc('text', usetex = True)\n", "plt.title(r'BTC - $\\mathcal{L}$ spectrum, strong dissipation limit QuTiP jmat',\n", " fontsize = label_size2)\n", "\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "plt.ylim([-20,15])\n", "plt.xlim([-15,0])\n", "\n", "plt.xlabel(r'$\\mathrm{Re}(\\lambda)$', fontsize = label_size3)\n", "plt.ylabel(r'$\\mathrm{Im}(\\lambda)$', fontsize = label_size3)\n", "\n", "fname = 'figures/btc_eig_N{}_strong_jmat.pdf'.format(N)\n", "savefile = False\n", "if savefile == True: \n", " plt.savefig(fname, bbox_inches='tight')\n", "plt.show()\n", "plt.close()\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#Saving for Mathematica\n", "liouvd_jmat =liouv_mat.full()\n", "liouvd_re_jmat = np.real(liouvd_jmat)\n", "liouvd_imag_jmat = np.imag(liouvd_jmat)\n", "#saveto_file_name2 = str(\"re_liouv_N={}\".format(N))\n", "#liouvd_re.astype('float32').tofile('{}.dat'.format(saveto_file_name2))\n", "#saveto_file_name3 = str(\"imag_liouv_N={}\".format(N))\n", "#liouvd_imag.astype('float32').tofile('{}.dat'.format(saveto_file_name3))\n", "#mmwrite('data/liouvrejmat.mtx', liouvd_re_jmat/kappa)\n", "#mmwrite('data/liouvimjmat.mtx', liouvd_imag_jmat/kappa)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig7 = plt.figure(7)\n", "plt.plot(re_eigmat/kappa, imag_eigmat/kappa, 'k.', re_eigmat/kappa, 0*imag_eigmat/kappa, '-', lw = 0.5)\n", "label_size = 15\n", "label_size2 = 15\n", "label_size3 = 15\n", "plt.title(r'BTC - $\\mathcal{L}$ spectrum, strong dissipation limit, Jmat', fontsize = label_size2)\n", "\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "plt.ylim([-1,1])\n", "plt.xlim([-4,0])\n", "\n", "\n", "plt.xlabel(r'$\\mathrm{Re}(\\lambda)$', fontsize = label_size3)\n", "plt.ylabel(r'$\\mathrm{Im}(\\lambda)$', fontsize = label_size3)\n", "\n", "fname = 'figures/btc_eig_inset_N{}_strong_jmat.pdf'.format(N)\n", "if savefile == True: \n", " plt.savefig(fname, bbox_inches='tight')\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Figure above reproduces qualitatively the study performed in Ref. [4]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spectrum of the Liouvillian - Weak dissipation limit $\\omega_{0} = 1.5 \\kappa$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "nnn = 36\n", "N = nnn\n", "jj_mat = nnn/2\n", "[jx_mat, jy_mat, jz_mat] = jmat(jj_mat)\n", "jp_mat = jx_mat + 1j * jy_mat\n", "jm_mat = jx_mat - 1j * jy_mat\n", "w0 = 1\n", "kappa = 2/3 * w0 \n", "gg = kappa/ jj_mat\n", "ham = w0 * jx_mat\n", "c_ops = [np.sqrt(gg) * jm_mat]\n", "liouv_mat = liouvillian(ham, c_ops)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1369, 1369)\n" ] } ], "source": [ "print(liouv_mat.shape)\n", "eig_mat = liouv_mat.eigenenergies()\n", "re_eigmat = np.real(eig_mat)\n", "imag_eigmat = np.imag(eig_mat)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig8 = plt.figure(8)\n", "plt.plot(re_eigmat/kappa, imag_eigmat/kappa, 'k.')\n", "label_size = 15\n", "label_size2 = 15\n", "label_size3 = 15\n", "plt.rc('text', usetex = True)\n", "plt.title(r'BTC - $\\mathcal{L}$ spectrum, weak dissipation limit QuTiP jmat', fontsize = label_size2)\n", "\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "plt.ylim([-50,35])\n", "plt.xlim([-15,0])\n", "\n", "plt.xlabel(r'$\\mathrm{Re}(\\lambda)$', fontsize = label_size3)\n", "plt.ylabel(r'$\\mathrm{Im}(\\lambda)$', fontsize = label_size3)\n", "\n", "fname = 'figures/btc_eig_N{}_weak_jmat.pdf'.format(N)\n", "if savefile == True: \n", " plt.savefig(fname, bbox_inches='tight')\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Figure above reproduces qualitatively the study performed in Ref. [4]." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig9 = plt.figure(9)\n", "plt.plot(re_eigmat/kappa, imag_eigmat/kappa, 'k.', re_eigmat/kappa, 0*imag_eigmat/kappa, '-', lw = 0.5)\n", "label_size = 15\n", "label_size2 = 15\n", "label_size3 = 15\n", "plt.title(r'BTC - $\\mathcal{L}$ spectrum, weak dissipation limit, Jmat', fontsize = label_size2)\n", "\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "plt.ylim([-5,5])\n", "plt.xlim([-0.4,0])\n", "\n", "plt.xlabel(r'$\\mathrm{Re}(\\lambda)$', fontsize = label_size3)\n", "plt.ylabel(r'$\\mathrm{Im}(\\lambda)$', fontsize = label_size3)\n", "\n", "fname = 'figures/btc_eig_inset_N{}_weak_jmat.pdf'.format(N)\n", "if savefile == True: \n", " plt.savefig(fname, bbox_inches='tight')\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Figure above reproduces qualitatively the study performed in Ref. [4]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Time evolution of collective operators, such as $\\langle J_z (t)\\rangle$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System size: N = 20 | nds = 121 | nds^2 = 14641 | 2^N = 1048576\n" ] } ], "source": [ "N = 20\n", "ntls = N\n", "nds = num_dicke_states(N)\n", "print(\"System size: N = \", N, \"| nds = \", nds, \"| nds^2 = \", nds**2, \"| 2^N = \", 2**N)\n", "[jx, jy, jz] = jspin(N)\n", "jp = jspin(N, \"+\")\n", "jm = jp.dag()\n", "jpjm = jp*jm" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "0.01\n", "0.1\n", "1\n" ] } ], "source": [ "w0 = 1\n", "kappa = 0.5 * w0\n", "gCE = 2*kappa/N\n", "gE = 0\n", "gP = 0\n", "gCD = 0\n", "gCP = 0\n", "h = w0 * jx\n", "\n", "nt = 1001\n", "td0 = kappa\n", "tmax = 200 * td0\n", "t = np.linspace(0, tmax, nt)\n", "rho0 = dicke(N, N/2, N/2)\n", "\n", "jzt_list = []\n", "jpjmt_list = []\n", "jz2t_list = []\n", "gD_list = [0, 0.01, 0.1, 1]\n", "for gD in gD_list:\n", " \n", " print(gD)\n", " system = Dicke(N=N)\n", " system.collective_emission = gCE\n", " system.emission = gE\n", " system.dephasing = gD\n", " system.pumping = gP\n", " system.collective_pumping = gCP\n", " system.collective_dephasing = gCD\n", " # energy / dynamics numerical\n", " system.hamiltonian = h\n", " liouv = system.liouvillian()\n", " result = mesolve(liouv, rho0, t, [], e_ops = [jz, jp*jm, jz*jz], options = Options(store_states=True))\n", " rhot = result.states\n", " jz_t = result.expect[0]\n", " jpjm_t = result.expect[1]\n", " jz2_t = result.expect[2]\n", " \n", " jzt_list.append(jz_t)\n", " jpjmt_list.append(jpjm_t)\n", " jz2t_list.append(jz2_t)\n", "# gD_list.append(gD)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rc('text', usetex = True)\n", "label_size = 20\n", "label_size2 = 20\n", "label_size3 = 20\n", "plt.rc('text', usetex = True)\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "lw = 1\n", "i = 0\n", "fig5 = plt.figure(figsize=(7,5))\n", "\n", "for gD in gD_list:\n", " plt.plot(w0*t, jzt_list[i]/(N/2), '-', \n", " label = r\"$\\gamma_\\phi/\\omega_x={}$\".format(gD), linewidth = 2*lw+0.4*i)\n", " i = i+1\n", "plt.ylim([-1,1])\n", "#plt.title(r'Total inversion', fontsize = label_size2)\n", "plt.xlabel(r'$\\omega_x t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\langle J_z \\rangle (t)$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size3*0.8)\n", "\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#cooperativity\n", "plt.rc('text', usetex = True)\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "fig8 = plt.figure(figsize=(7,5))\n", "i=0\n", "for gD in gD_list:\n", " plt.plot(w0*t, (jz2t_list[i] -jzt_list[i] + jpjmt_list[i])/((N/2*(N/2+1))), \n", " '-', label = r\"$\\gamma_\\phi/\\omega_x={}$\".format(gD), linewidth = 2*lw+0.4*i)\n", " i = i+1\n", "plt.ylim([0,2.])\n", "plt.xlabel(r'$\\omega_x t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\langle J^2 \\rangle (t)$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size3*0.8)\n", "\n", "plt.title(r'Cooperativity', fontsize = label_size2)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "\n", "fig6 = plt.figure(figsize=(8,6))\n", "i=0\n", "for gD in gD_list:\n", " plt.plot(w0*t, jpjmt_list[i]/(N/2)**2, label = r\"$\\gamma_\\phi/\\omega_x={}$\".format(gD), linewidth = 2*lw+0.4*i)\n", " i = i+1\n", "#plt.ylim([-1,1])\n", "plt.xlabel(r'$\\omega_x t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\langle J_{+}J_{-} \\rangle (t)$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size3*0.7)\n", "plt.title(r'Light emission', fontsize = label_size2)\n", "plt.show()\n", "plt.close()\n", "\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "\n", "fig7 = plt.figure(figsize=(7,5))\n", "i=0\n", "for gD in gD_list:\n", " plt.plot(w0*t, jz2t_list[i]/(N/2), '-', label = r\"$\\gamma_\\phi/\\omega_x={}$\".format(gD), linewidth = 2*lw+0.4*i)\n", " i = i+1\n", "#plt.ylim([-1,1])\n", "plt.xlabel(r'$\\omega_x t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\langle J_z^2 \\rangle (t)$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size3*0.7)\n", "plt.title(r'Second moment', fontsize = label_size2)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "20\n", "0\n", "0.01\n", "0.1\n", "1\n" ] } ], "source": [ "# Study of local incoherent losses\n", "N = 20\n", "print(N)\n", "w0 = 1\n", "kappa = 0.5 * w0\n", "gCE = 2*kappa /N\n", "gE = 0\n", "gP = 0\n", "gD = 0\n", "gCD = 0\n", "gCP = 0\n", "gD = 0\n", "h = w0 * jx\n", "\n", "nt = 1001\n", "td0 = kappa\n", "tmax = 200 * td0\n", "t = np.linspace(0, tmax, nt)\n", "rho0 = dicke(N, N/2, N/2)\n", "\n", "jzt_list = []\n", "jpjmt_list = []\n", "jz2t_list = []\n", "gE_list = [0, 0.01, 0.1, 1]\n", "for gE in gE_list:\n", " print(gE)\n", " system = Dicke(N=N)\n", " system.collective_emission = gCE\n", " system.emission = gE\n", " system.dephasing = gD\n", " system.pumping = gP\n", " system.collective_pumping = gCP\n", " system.collective_dephasing = gCD\n", " # energy / dynamics numerical\n", " system.hamiltonian = h\n", " liouv = system.liouvillian()\n", " result = mesolve(liouv, rho0, t, [], e_ops = [jz, jp*jm, jz*jz], options = Options(store_states=True))\n", " rhot = result.states\n", " jz_t = result.expect[0]\n", " jpjm_t = result.expect[1]\n", " jz2_t = result.expect[2]\n", " \n", " jzt_list.append(jz_t)\n", " jpjmt_list.append(jpjm_t)\n", " jz2t_list.append(jz2_t)\n", "# gD_list.append(gD)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rc('text', usetex = True)\n", "label_size = 20\n", "label_size2 = 20\n", "label_size3 = 20\n", "plt.rc('text', usetex = True)\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "lw = 1\n", "i = 0\n", "fig5 = plt.figure(figsize=(7,5))\n", "\n", "for gD in gD_list:\n", " plt.plot(w0*t, jzt_list[i]/(N/2), '-', label = r\"$\\gamma_\\downarrow/\\omega_x={}$\".format(gD), linewidth = 2*lw+0.4*i)\n", " i = i+1\n", "plt.ylim([-1,1])\n", "#plt.title(r'Total inversion', fontsize = label_size2)\n", "\n", "plt.xlabel(r'$\\omega_x t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\langle J_z \\rangle (t)$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size3*0.8)\n", "\n", "fname = 'figures/btc_jzt_N{}_gE.pdf'.format(N)\n", "if savefile == True: \n", " plt.savefig(fname, bbox_inches='tight')\n", "plt.show()\n", "plt.close()\n", "\n", "#cooperativity\n", "plt.rc('text', usetex = True)\n", "plt.rc('xtick', labelsize=label_size) \n", "plt.rc('ytick', labelsize=label_size)\n", "fig8 = plt.figure(figsize=(7,5))\n", "i=0\n", "for gD in gD_list:\n", " plt.plot(w0*t, (jz2t_list[i] -jzt_list[i] + jpjmt_list[i])/((N/2*(N/2+1))), \n", " '-', label = r\"$\\gamma_\\downarrow/\\omega_x={}$\".format(gD), linewidth = 2*lw+0.4*i)\n", " i = i+1\n", "plt.ylim([0,2.])\n", "plt.xlabel(r'$\\omega_x t$', fontsize = label_size3)\n", "plt.ylabel(r'$\\langle J^2 \\rangle (t)$', fontsize = label_size3)\n", "plt.legend(fontsize = label_size3*0.8)\n", "\n", "plt.title(r'Cooperativity', fontsize = label_size2)\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plots above integrate the study on the effect of local dissipation performed in Ref. [1]. The boundary time crystals were introduced in Ref. [4]. A study of the effect of inhomogenous broadening (non-identical two level systems) is performed in Ref. [7] with regard to boundary time crystals and in Ref. [8] with regards to Dicke superradiance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### References\n", "\n", "[1] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, \n", "Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance https://arxiv.org/abs/1805.05129\n", "\n", "The PIQS library can be found at https://github.com/nathanshammah/piqs/\n", "\n", "[2] R. Bonifacio and L. A. Lugiato, Optical bistability and cooperative effects in resonance fluorescence, *Phys. Rev. A* **18**, 1129 (1978)\n", "\n", "[3] S. Sarkar and J. S. Satchell, Optical bistability with small numbers of atoms, *Europhys. Lett.* **3**, 797 (1987)\n", "\n", "[4] F. Iemini, A. Russomanno, J. Keeling, M. Schirò€, M. Dalmonte, and R. Fazio, Boundary Time Crystals, arXiv:1708.05014 (2017)\n", "\n", "[5] V. V. Albert and L. Jiang, Symmetries and conserved quantities in Lindblad master equations, *Phys. Rev. A* **89**, 022118 (2014)\n", "\n", "[6] J.R. Johansson, P.D. Nation, and F. Nori, *Comp. Phys. Comm.* **183**, 1760 (2012) http://qutip.org\n", "\n", "[7] K. Tucker, B. Zhu, R. Lewis-Swan, J. Marino, F. Jimenez, J. Restrepo, and A. M. Rey, arXiv:1805.03343 (2018)\n", "\n", "[8] N. Lambert, Y. Matsuzaki, K. Kakuyanagi, N. Ishida, S. Saito, and F. Nori, *Phys. Rev. B* **94**, 224510 (2016)." ] }, { "cell_type": "code", "execution_count": 20, "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: 4.3.0\n", "Numpy Version: 1.13.3\n", "Scipy Version: 1.0.0\n", "Cython Version: 0.27.3\n", "Matplotlib Version: 2.1.1\n", "Python Version: 3.6.3\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/Downloads/Applications/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()" ] }, { "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }