{ "cells": [ { "cell_type": "markdown", "id": "5ad7b5a0", "metadata": {}, "source": [ "# Relaxation in complex sequences: RECRR" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "id": "d02b5a3f", "metadata": {}, "source": [ "A challenge in acquiring $R_{1\\rho}$ relaxation rate constants is that coherent oscillation is present at the beginning of the $R_{1\\rho}$ period, which distorts the signal decay. While we could wait until oscillation is subsided, we lose significant signal. The beginning of the relaxation period is also particularly important, because $R_{1\\rho}$ relaxation is multiexponential. The initial slope of decay gives the averaged rate constant, which is what we would like to acquire. However, after time, the faster relaxing components have decayed more than the slower components, so that the slope no longer correctly represents the correct average.\n", "\n", "Keeler et al. propose a solution to suppress oscillation at the beginning of the $R_{1\\rho}$ period, referred to as the REfocused CSA Rotating-frame Relaxation experiment (RECRR). In this experiment, the spin-locks (CW$_{\\pm x}$) are switched 180$^\\circ$ in phase, and $\\pi$-pulses are inserted to invert the magnetization, as follows:$^1$ \n", "\n", "CW$_x$ $-$ $\\pi_y$ $-$ CW$_x$ $-$ CW$_{-x}$ $-$ $\\pi_{-y}$ $-$ CW$_{-x}$\n", "\n", "The spin-locks each have an integer number of rotor periods.\n", "\n", "We will investigate the RECRR here and compare its performance to the standard $R_{1\\rho}$ experiment\n", "\n", "[1] E.G. Keeler, K.J. Fritzsching, A.E. McDermott. [*J. Magn. Reson.*](https://doi.org/10.1016/j.jmr.2018.09.004), **2018**, 296, 130-137." ] }, { "cell_type": "markdown", "id": "63a740e0", "metadata": {}, "source": [ "## Setup" ] } , { "cell_type": "code", "execution_count": 0, "metadata": {"tags": [ "remove-cell" ]}, "outputs": [], "source": [ "# SETUP SLEEPY\n", "import sys\n", "if 'google.colab' in sys.modules:\n", " !pip install sleepy-nmr" ] }, { "cell_type": "code", "execution_count": 2, "id": "df921dbb", "metadata": {}, "outputs": [], "source": [ "import SLEEPY as sl\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "e768b26c", "metadata": {}, "source": [ "## Build the system and Liouvillian" ] }, { "cell_type": "code", "execution_count": 3, "id": "c94277dd", "metadata": {}, "outputs": [], "source": [ "ex0=sl.ExpSys(v0H=600,Nucs=['15N','1H'],vr=16000,pwdavg=sl.PowderAvg(),n_gamma=50)\n", "ex0.set_inter('dipole',i0=0,i1=1,delta=44000)\n", "ex0.set_inter('CSA',i=0,delta=113,euler=[0,23*np.pi/180,0])\n", "ex1=ex0.copy()\n", "ex1.set_inter('dipole',i0=0,i1=1,delta=44000,euler=[0,15*np.pi/180,0])\n", "ex1.set_inter('CSA',i=0,delta=113,euler=[[0,23*np.pi/180,0],[0,15*np.pi/180,0]])\n", "\n", "L=sl.Liouvillian(ex0,ex1)\n", "L.kex=sl.Tools.twoSite_kex(tc=200e-6)" ] }, { "cell_type": "markdown", "id": "e176483b", "metadata": {}, "source": [ "## Build the propagators and density matrices\n", "We construct the simulation by building two sequences that contain the $y$ and $-y$ $\\pi$-pulses (seqA,seqB), which are two rotor periods each, and then two sequences that contain the $x$ and $-x$ spin-locks (seqx,seqmx). From these, we can construct propagators, and multiply them in the correct order for each time step in the RECRR sequence. We may also use the $x$-propagator for the $R_{1\\rho}$ experiment.\n", "\n", "The density matrices for $R_{1\\rho}$ (`R1p`) and RECRR (`RECRR`) sequences are also created below, including a basis set reduction for propagators and density matrices." ] }, { "cell_type": "code", "execution_count": 4, "id": "fe32a420", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State-space reduction: 32->16\n" ] } ], "source": [ "v1=25000\n", "v1pi=60000\n", "pi2=1/v1pi/2\n", "\n", "seqx=L.Sequence().add_channel('15N',v1=v1) #Spin-lock on xs\n", "seqmx=L.Sequence().add_channel('15N',v1=v1,phase=np.pi) #Spin-lock on -x\n", "\n", "t=[0,L.taur-pi2/2,L.taur+pi2/2,2*L.taur]\n", "#First refocusing period\n", "seqA=L.Sequence().add_channel('15N',t=t,v1=[v1,v1pi,v1],phase=[0,np.pi/2,0])\n", "#Second refocusing period\n", "seqB=L.Sequence().add_channel('15N',t=t,v1=[v1,v1pi,v1],phase=[np.pi,3*np.pi/2,np.pi])\n", "\n", "R1p=sl.Rho('15Nx','15Nx')\n", "\n", "R1p,seqx,seqmx,seqA,seqB=R1p.ReducedSetup(seqx,seqmx,seqA,seqB)\n", "RECRR=R1p.copy_reduced()" ] }, { "cell_type": "markdown", "id": "de407ef3", "metadata": {}, "source": [ "Below, we plot components of the RECRR sequence. `seqx` and `seqmx` will be appended to these sequences to increase the spin-lock length by a total of four rotor periods at a time." ] }, { "cell_type": "code", "execution_count": 5, "id": "1a46a827", "metadata": {}, "outputs": [ { "data": { "image/png": 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fgLPPPrviSqS8/m2v2rlk57dpe5LKYZarVDmz1RxXqXJnTPET9LFjx1ZdglSJfV96qa3bk1QOs1ylypmt5rhKlTtjip+gv/e97626BKkS73xxdVu3J6kcZrlKlTNbzXGVKnfGdPsc9IiYHxHHb7Dsqp40FhF9IuJXEXFj/f6uETEvIh6o/71LT9YnSZK6zyyXJKm19eQicfsCn42Iv+q0bEIP2/sEsLTT/YuA+Sml/YH59ftZXXPNNVxzzTW5m5Uqd/PQvbh56F5t256kjTLLpTaSM1vNcZUqd8b0ZIL+AnAUsEdE/DgidupJQxExDDgBuLrT4pOAa+u3rwX+qCfrbITx48czfvz43M1KlRv14mpGZTxcLXd7kjbqBcxyqW3kzFZzXKXKnTE9OQc9UkqvA/8jIqYCtwE9OYztm8BngB07LdsjpbQcIKW0PCIG92B9DWGgq1T7r84bsrnbk7RRZrnURnJmqzmuUuXOmJ58g/5/O26klK4BzgFu6c4LI2IKsCKltKhH1a2/jvMjYmFELHzmmWe2dDVvs27dOtatW9ew9Um9xRv1P+3anqSNqizLm5XjYJarXDmz1RxXqXJnzGa/QY+IfwBS/fbfb/Bwd39v4f3AifUL02wHDIyIHwJPR8SQ+ifuQ4AVXa0gpXQVcBXAhAkTUjfb3awf/OAHAEydOrVRq5R6hX+rn0d2QZu2J+ktrZDlzcpxMMtVrpzZao6rVLkzpjuHuC/sdPtS4K+6emJXUkoXAxcDRMQk4NMppY9FxFepfXp/Wf3vOT1d99Y6+OCDczcptYR3rnqxrduTtB6zXGpDObPVHFepcmfMZifoKaWOC78QEZ/sfL8BLgNmRcS5wGPAqQ1cd7cceOCBuZuUWsJ+L3X3S7Pe2Z6kt5jlUnvKma3muEqVO2N6cpE4qB8etzVSSguABfXbz1G7mmxl1q5dC0C/fv2qLEPK7vWItm5PUpfMcqlN5MxWc1ylyp0xPZ2gt53p06cDnrem8szbawgA+7Vpe5LKYZarVDmz1RxXqXJnTHcuErea2qftAWwfER0noASQUkoDm1hf002YMKHqEqRKvGvVqrZuT9JbzHKpPeXMVnNcpcqdMd05B33HzT2nNxs3blzVJUiV2Pell9u6PUlvMcul9pQzW81xlSp3xnT7d9Aj4r0bWfbhxpaT35o1a1izZk3VZUjZvbbNNry2Tbd3Ab2uPUlvZ5ZL7SVntprjKlXujOnJVvbtiHh3x52IOAP4fONLymvmzJnMnDmz6jKk7OYP2ZP5Q/Zs2/YkbZRZLrWRnNlqjqtUuTOmJxeJOwWYHRFnAocDZwPHNqWqjA455JCqS5AqccALec8ly92epI0yy6U2kjNbzXGVKnfGdHuCnlJ6KCJOB/4VWAYcm1J6tVmF5TJmzJiqS5Aqsc/Lec8ly92epLczy6X2kjNbzXGVKnfGdOcq7r9h/d9M3RXoA9wZEaSU8v5ye4O98sorAPTv37/iSqS81mQ+jyx3e5LeYpZL7SlntprjKlXujOnON+hTml5FhWbNmgX426kqz8/q55GNbtP2JK3HLJfaUM5sNcdVqtwZ052fWXs0RyFVOeyww6ouQarEuJUvtHV7kt5ilkvtKWe2muMqVe6M6clF4trS6NF+DqgyDa8frtOu7Ukqh1muUuXMVnNcpcqdMcVP0F966SUABgwYUHElUl6v9OnT1u1JKodZrlLlzFZzXKXKnTHduUjcYcAdKaW0uef2RrNnzwY8b03l+Y899wAg13Upc7cn6S1mudSecmarOa5S5c6Y7nyDfg5wRUT8DpgLzE0pPdXcsvI5/PDDqy5BqsS7V65s6/Ykrccsl9pQzmw1x1Wq3BnTnYvEXQAQEe8CPgRcExE7AT+jFvI/Tymta2qVTTRq1KiqS5AqMeyVvD99nLs9SW8xy6X2lDNbzXGVKnfGdPsc9JTSfcB9wDciYnvgSOBU4OvAhOaU13yrVq0CYKeddqq4Eimvl/vmPZcsd3uS3s4sl9pLzmw1x1Wq3BmzRReJSym9CtxU/9OrXX/99YDnrak8t+5RO5fsgDZtT9KmmeVS75czW81xlSp3xhR/Ffcjjjii6hKkSrzn+bznkuVuT1I5zHKVKme2muMqVe6MKX6CPnLkyKpLkCqx16t5zyXL3Z6kcpjlKlXObDXHVarcGVP8BH1l/YqUu+yyS8WVSHmt7pt388/dnqRymOUqVc5sNcdVqtwZs83WriAiPtuIQqoyZ84c5syZU3UZUna37TGY2/YY3LbtSeo+s1zqnXJmqzmuUuXOmB5/FBYRszrfBcYDf9uognKbNGlS1SVIlTjouefbuj1JXTPLpfaQM1vNcZUqd8ZsybEqL6aUzuu4ExH/1MB6shsxYkTVJUiV2HPNmrZuT9ImmeVSG8iZrea4SpU7Y7o9QY+IXwCfB760wUOXNLSizO778pd57b8eYqe1a6suRcpqxbJlvCPjRS9W9evH7x96CM46O1ubUqsYOGUKu/zxaVWXYZZLbSZnlpvjKtWqfv0YMGkSI88+K0t7PTkH/XzgQuA7EXFYx8KUUq8+3uXWdev4xeDdqy5Dym7RoYdw17vela29u971LhYdeki29qRWsea++3jxxhurLqODWS61kZxZbo6rVLcN2IFb7v1ttva6/Q16SmkJ8NGIOBj43xEB8PmU0uIm1ZbFh/7kTwAYPnx4xZVIeZ2wbFnW9o4743TAbU3lebSFvm0yy6X2kjPLzXGVauLHPw4Zf2ZwS67i/iDwReBxYGFjy8lv+PDh3drR3HzzzVxyySW88cYbGaqSmq+7Y39TerJduK1JLaXILN8S7pPUynKOfbczlWrwmt8zeM3vN/u8Ro3jbk/QI+LfI2IZsAj4HLASmLpVrbeAFStWsGLFCgDmzp3L6NGjGTVqFJdddtl6z7v11luZOHEit99+exVlSg3Xeex/61vfYty4cYwdO5ZvfvObbz5nU9sE9Gy7cFuTqldClk+bNo3Bgwczbty49Z7zjW98g7FjxzJu3DjOOOMM1tQveNXI/ZyUW8fYX7ZsGUceeSRjxoxh7NixfOtb3wLg/vvvZ/z48W/+GThw4Js539Ox73amUq3cdltWbrstkOf/sD35Bv3TwDtTSvunlE5KKV2cUvrhVrXeAm666SZuuukm1q1bx4UXXsjNN9/Mvffey4wZM7j33nvffF6fPn2YPn06Y8aMqbBaqXE6xv6SJUv49re/zV133cWvf/1rbrzxRh544IHNbhPQs+3CbU1qCW2d5QBTp05l7ty56z3+xBNP8Pd///csXLiQJUuWsG7dOmbOnNnw/ZyUW8fY79u3L3/3d3/H0qVLueOOO7jiiiu49957GT16NIsXL2bx4sUsWrSI/v3785GPfGSLxr7bmUp1x+6DuGP3Qdn+D9uTc9Dv3qqWWtQxxxwDwF133cWoUaMYWb8S5umnn86cOXM44IADAPjSlza84K3Uu3WM/V/84hcceuih9O/fH4APfvCDXH/99XzgAx/Y5DYBPdsu3Nak6rV7lgMcccQRPPLII297zuuvv86rr75Kv379eOWVV9hrr702uz8C90lqbR1jf8iQIQwZMgSAHXfckTFjxvDEE0+sN5bnz5/Pfvvtxz777MPtt9/e47HvdqZSTXz2OSDf/2G35Bz0tjJ06FCGDh3KE088sd55NcOGDeOJJ56osDKpuTrG/rhx47j11lt57rnneOWVV7jppptYtmxZw7cJtzVJzdKxf9nU45/+9KfZe++9GTJkCDvttBPHHnus+yP1ehsb+4888gi/+tWvOOSQ9a+4PnPmTM444wyALRr7bmcq1aDf/55Bv/99trGcbYIeEcMj4mcRsTQifhsRn6gv3zUi5kXEA/W/d8lVE8BTTz3FU089RUppYzXnLEXKqmPsjxkzhs9+9rMcc8wxTJ48mfe85z307du34duE25rUu7VqjsNb+5eurFy5kjlz5vDwww/z5JNP8vLLL/PDH/7Q/ZF6vQ3H/ksvvcRHP/pRvvnNbzJw4MA3l7/22mvccMMNnHrqqQBbNPbdzlSq57bdlue23TbbWM75DfrrwKdSSmOAQ4ELI+IA4CJgfkppf2B+/X42c+fOZe7cuQwbNoxlnX6q4vHHH2evvfbKWYqUVcfYBzj33HO5++67ufXWW9l1113Zf//9G75NuK1JvV5L5jisvz/bmJ/+9Kfsu+++7L777vTr14+TTz6ZX/ziF+6P1Ot1Hvtr167lox/9KGeeeSYnn3zyes+7+eabOfjgg9ljjz0Atmjsu52pVHftPoi7dh+UbSx3+xz0rZVSWg4sr99eHRFLgaHAScCk+tOuBRYAn81V1+TJkwEYNGgQDzzwAA8//DBDhw5l5syZ/OhHP8pVhpRdx9iH2pVZBw8ezGOPPcZ1113H7bffzo477tjQbcJtTerdWjXHYf392cbsvffe3HHHHbzyyitsv/32zJ8/nwkTJjBx4kT3R+rVOsZ+Solzzz2XMWPG8Bd/8Rdve96MGTPePLwd2KKx73amUv3BM88CcGCmsZxtgt5ZRIwADgLuBPaohz4ppeURMbiL15wPnA+1HUCj7Lnnnm/evvzyyznuuONYt24d06ZNY+zYsQ1rR2o1ncf+Rz/6UZ577jn69evHFVdcwS671I5QbeQ24bYmtY9WynFYf/9yxhlnsGDBAp599lmGDRvGpZdeyrnnnsspp5zCwQcfTN++fTnooIM4//zz6du3r/sj9WodY/+2227jBz/4Ae9+97sZP348AF/5ylc4/vjjeeWVV5g3bx5XXnnlm6/bkrHvdqZS7fbaa8CWbTdbIjZ2LH0zRcQA4D+AL6eUrouIF1JKO3d6fGVKaZPnr02YMCEtXLiwIfV0nNi/qYteSO0o99h3W1OpHj3rbAD2+cH3G7bOiFiUUprQsBX2rO2WynFw/6Jy5Rz7bmcq1aLzPg7Ae6/+dkPX21WWZ72Ke0T0A/4FmJ5Suq6++OmIGFJ/fAiwImdN8+bNY968eTmblFpC7rHvtib1fq2Y4+D+ReXKOfbdzlSqXw7ajV8O2i1be9kOcY/aJe6+AyxNKX2900M3AOcAl9X/npOrJoDjjz8+Z3NSy8g99t3WpN6tVXMc3L+oXDnHvtuZSnVo/Rz0XHKeg/5+4CzgNxGxuL7sc9QCfVZEnAs8BpyasSYGD97oqXJS28s99t3WpF6vJXMc3L+oXDnHvtuZSrVL/Rz0XHJexf02oKsfijsqVx0b6rhUfucfnZdKkHvsu61JvVur5ji4f1G5co59tzOVasV27wBgn0ztZT0HvRXNnz+f+fPnV12GlF3use+2JqlZ3L+oVDnHvtuZSrVot91YtFsbnoPeqqZMmVJ1CVIlco99tzVJzeL+RaXKOfbdzlSq9614Jmt7xU/QBw0aVHUJUiVyj323NUnN4v5Fpco59t3OVKqd1q7N2l7xE/RHHnkEgBEjRlRah5Rb7rHvtiapWdy/qFQ5x77bmUr11HbbAZ6Dns2CBQtYsGBB1WVI2eUe+25rkprF/YtKlXPsu52pVL/abVd+tduu2dor/hv0k046qeoSpErkHvtua5Kaxf2LSpVz7LudqVSHP70ia3vFT9B32WWXqkuQKpF77LutSWoW9y8qVc6x73amUu34+utZ2yt+gv7QQw8BMHLkyIorkfLKPfbd1iQ1i/sXlSrn2Hc7U6me3H57IN856MVP0G+99VbAnY3Kk3vsu61Jahb3LypVzrHvdqZS/XrX2tEjh2Vqr/gJ+kc+8pGqS5AqkXvsu61Jahb3LypVzrHvdqZSHfH001nbK36CvtNOO1VdglSJ3GPfbU1Ss7h/Ualyjn23M5Vqh9fXZW2v+An6gw8+CMCoUaMqrkTKK/fYd1uT1CzuX1SqnGPf7Uylery/56BnddtttwHubFSe3GPfbU1Ss7h/Ualyjn23M5XqN/VfMHh/pva2ydROyzrllFM45ZRTmDt3LqNHj2bUqFFcdtllG33u1KlTmT179tuWT5o0iYULF755/5FHHmHcuHFNq1lqhI6x367tSSqHWa5S5cxWc1yl+uBTT/PBp/Kdh178N+gDBgxg3bp1XHjhhcybN49hw4YxceJETjzxRA444ICqy5OaZsCAAW3dnqRymOUqVc5sNcdVqv7r8p6DXvw36Pfffz///M//zKhRoxg5ciTbbrstp59+OnPmzNnk677whS8wdepU3njjjU0+77zzzmP8+PGMHz+e3XffnUsvvbSR5Utb7P777+f+++9v2/YklcMsV6lyZqs5rlIt69+fZf37Z2uv+G/Qb7/9dn75y18yfPjwN5cNGzaMO++8s8vXfOYzn2HVqlV873vfIyIAOPPMM9m+/iP2r732GttsU/vs4+qrrwbg0Ucf5bjjjmPq1KlNeidSz9x+++0AjB49ui3bk1QOs1ylypmt5rhKtWSXnQE4PFN7xU/QTzvtNPr27cuCBQvWW94R1hv64he/yCGHHMJVV1213vLp06czYcIEoHbe2pQpU958bM2aNZx66qlcfvnl7LNPruv/SZt22mmntXV7ksphlqtUObPVHFepjlz+VNb2ij/EvX///uy3334sW7bszWWPP/44e+2110afP3HiRBYtWsTzzz/f7TYuuOACTj75ZI4++uitrldqlP79+9M/4+E6uduTVA6zXKXKma3muEq13RtvsN1mToVqpOIn6EuXLmXAgAE88MADPPzww7z22mvMnDmTE088caPPnzx5MhdddBEnnHACq1ev3uz6r7jiClavXs1FF13U6NKlrbJ06VKWLl3atu1JKodZrlLlzFZzXKV6dIcdeHSHHbK1V/wh7h3np11++eUcd9xxrFu3jmnTpjF27NguX3PqqaeyevVqTjzxRG666aZNrv9rX/sa/fr1Y/z48UDtE/gLLrigYfVLW6pj7I8ZM6Yt25NUDrNcpcqZrea4SnXvzjsBcESm9iKllKmpxpkwYULq/FulW2PNmjUAbLfddg1Zn9Rb5B77bmsq1aNnnQ3APj/4fsPWGRGLUkoTGrbCzBqZ4+D+ReXKOfbdzlSqB86ZCsD+117T0PV2leXFf4PuTkalyj323dYkNYv7F5Uq59h3O1Opts14/jk4QWfJkiUAjBs3ruJKpLxyj323NUnN4v5Fpco59t3OVKqHB9TOP8/1+x3FT9A7DrFzZ6PS5B77bmuSmsX9i0qVc+y7nalU9+1UOwd9Uqb2ip+gn3nmmVWXIFUi99h3W5PULO5fVKqcY9/tTKU65snlWdsrfoLer1+/qkuQKpF77LutSWoW9y8qVc6x73amUvXNfFH14ifo99xzDwAHHnhgxZVIeeUe+25rkprF/YtKlXPsu52pVP81YADgOejZ3H333YA7G5Un99h3W5PULO5fVKqcY9/tTKX63U4DAfjDTO0VP0E/66yzqi5BqkTuse+2JqlZ3L+oVDnHvtuZSnXcE09mbW+brK11ISImR8T9EfFgRFyUs+0+ffrQp0+fnE1KLSH32Hdbk9qbWS7ll3Psu52pVNuQd9Jc+QQ9IvoAVwAfAg4AzoiIA3K1v3jxYhYvXpyrOall5B77bmtS+zLLpWrkHPtuZyrVAzvuyAM77pitvVY4xP0PgAdTSg8BRMRM4CTg3hyNz549m5deeskdjoozfvx4gGxjP3d7UqtYs/Q+Dth1F75bdSHNZZZLFciZrea4SnXgO9/JDv36cXSm9iJlvmz82wqIOAWYnFI6r37/LOCQlNKfbvC884Hz63dHA/c3sIxBwLMNXF9vZT/YBx3sB/ugg/3Qmn2wT0pp96qL6NCdLG9yjkNr/jvlZh/U2A/2QQf7wT7o0Ir9sNEsb4Vv0GMjy972qUFK6SrgqqYUELEwpTShGevuTewH+6CD/WAfdLAf7INu2myWNzPHwX8nsA862A/2QQf7wT7o0Jv6ofJz0IHHgeGd7g8D8l4qT5IkbQ2zXJKkBmiFCfovgf0jYt+I2BY4Hbih4pokSVL3meWSJDVA5Ye4p5Rej4g/Bf4N6AN8N6X028xlNO2Qu17GfrAPOtgP9kEH+8E+2CyzvGXYBzX2g33QwX6wDzr0mn6o/CJxkiRJkiSpNQ5xlyRJkiSpeE7QJUmSJElqAcVP0CNickTcHxEPRsRFVdeTQ0QMj4ifRcTSiPhtRHyivnzXiJgXEQ/U/96l6lqbLSL6RMSvIuLG+v0S+2DniJgdEffVx8RhpfVDRPx5fVtYEhEzImK7EvogIr4bESsiYkmnZV2+74i4uL6vvD8ijqum6sbroh++Wt8m7omI6yNi506PtWU/9FYl5jiY5Z2Z5WY5mOUlZ3m75XjRE/SI6ANcAXwIOAA4IyIOqLaqLF4HPpVSGgMcClxYf98XAfNTSvsD8+v3290ngKWd7pfYB98C5qaU3gW8h1p/FNMPETEU+DNgQkppHLULXJ1OGX1wDTB5g2Ubfd/1fcTpwNj6a/6xvg9tB9fw9n6YB4xLKR0I/A64GNq+H3qdgnMczPLOzHKz3CxfX2lZfg1tlONFT9CBPwAeTCk9lFJ6DZgJnFRxTU2XUlqeUrq7fns1tZ34UGrv/dr6064F/qiSAjOJiGHACcDVnRaX1gcDgSOA7wCklF5LKb1AYf1A7Rctto+IvkB/ar/f3PZ9kFK6FXh+g8Vdve+TgJkppd+nlB4GHqS2D+31NtYPKaVbUkqv1+/eQe13vaGN+6GXKjLHwSzvYJab5Z2Y5W8pKsvbLcdLn6APBZZ1uv94fVkxImIEcBBwJ7BHSmk51IIfGFxhaTl8E/gM8EanZaX1wUjgGeB79cMDr46IHSioH1JKTwBfAx4DlgOrUkq3UFAfbKCr913y/nIacHP9dsn90Ir898Asxyw3y83yDZnl6+tVOV76BD02sqyY352LiAHAvwCfTCm9WHU9OUXEFGBFSmlR1bVUrC9wMPBPKaWDgJdpz8O/ulQ/L+skYF9gL2CHiPhYtVW1pCL3lxFxCbVDiad3LNrI09q+H1pY8f8eZrlZjllulndfcfvM3pjjpU/QHweGd7o/jNrhMG0vIvpRC/TpKaXr6oufjogh9ceHACuqqi+D9wMnRsQj1A6J/MOI+CFl9QHUtoHHU0p31u/PphbyJfXD0cDDKaVnUkprgeuA91FWH3TW1fsubn8ZEecAU4AzU0od4V1cP7S4ov89zHKzvM4sN8s3ZJbTe3O89An6L4H9I2LfiNiW2gUDbqi4pqaLiKB2ntLSlNLXOz10A3BO/fY5wJzcteWSUro4pTQspTSC2r/7v6eUPkZBfQCQUnoKWBYRo+uLjgLupax+eAw4NCL617eNo6idy1lSH3TW1fu+ATg9It4REfsC+wN3VVBfFhExGfgscGJK6ZVODxXVD71AkTkOZjmY5R3McsAs31DxWd6bczze+jChTBFxPLXzl/oA300pfbnaipovIg4H/hP4DW+ds/U5aueuzQL2prajOzWltOFFJ9pOREwCPp1SmhIRu1FYH0TEeGoX19kWeAj4E2of3hXTDxFxKfDH1A6B+hVwHjCANu+DiJgBTAIGAU8DfwX8K1287/phYtOo9dMnU0o3v32tvU8X/XAx8A7gufrT7kgpXVB/flv2Q29VYo6DWb4hs9wsN8vLzfJ2y/HiJ+iSJEmSJLWC0g9xlyRJkiSpJThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBThBlyRJkiSpBfStuoAtMWjQoDRixIiqy5AkqRKLFi16NqW0e9V1bClzXJJUuq6yvFdO0EeMGMHChQsbsq6f/vSnABx99NENWZ8kSc0WEY9WXcPWaGSOg1kuSep9usryXjlBb6RXX3216hIkSdJWMMslSe2i+An6hz/84apLkCRJW8EslyS1Cy8SJ0mSJElSCyh+gn7LLbdwyy23VF2GJEnaQma5JKldFH+I+9q1a6suQZIkbQWzXJLULoqfoJ9wwglVlyBJkraCWS5JahfFH+IuSZIkSVIryDpBj4idI2J2RNwXEUsj4rCI2DUi5kXEA/W/d8lZ09y5c5k7d27OJiVJ6pVaMcfBLJcktY/c36B/C5ibUnoX8B5gKXARMD+ltD8wv34/u2nTpjF48GDGjRv35rKpU6cye/bs9Z43YMCA3KVJktQqWjbHwSyXJPV+2c5Bj4iBwBHAVICU0mvAaxFxEjCp/rRrgQXAZ3PVNXnyZAD69+/Pn/7pn3L22WfnalqSpF6jVXMczHJJUvvI+Q36SOAZ4HsR8auIuDoidgD2SCktB6j/PXhjL46I8yNiYUQsfOaZZxpe3BFHHMGuu+7a8PVKktQmWjrHwSyXJPV+OSfofYGDgX9KKR0EvEwPDoNLKV2VUpqQUpqw++67N6yon/zkJ/zkJz/p8vG//Mu/ZPz48W/+kSSpUC2Z42CWS5LaR86fWXsceDyldGf9/mxqwf50RAxJKS2PiCHAiow10a9fv00+/tWvfpVTTjnlzfuetyZJKlRL5jiY5ZKk9pFtgp5SeioilkXE6JTS/cBRwL31P+cAl9X/npOrJoBjjz02Z3OSJPVKrZrjYJZLktpHzm/QAf4nMD0itgUeAv6E2mH2syLiXOAx4NTMNUmSpO4xxyVJaqKsE/SU0mJgwkYeOipnHZ39+Mc/BuBHP/oRCxYs4Nlnn2XYsGFceumlVZUkSVJLasUcB7NcktQ+cn+D3nK23357AGbMmPG2x84999y3LXvppZeaXpMkSeo+s1yS1C6Kn6AfffTRVZcgSZK2glkuSWoXOX9mTZIkSZIkdaH4CfqcOXOYMyf7BWclSVKDmOWSpHZR/CHuAwcOrLoESZK0FcxySVK7KH6CfuSRR1ZdgiRJ2gpmuSSpXRR/iLskSZIkSa2g+An6ddddx3XXXVd1GZIkaQuZ5ZKkdlH8Ie677bZb1SVIkqStYJZLktpF8RP0D37wg1WXIEmStoJZLklqF8Uf4i5JkiRJUisofoI+e/ZsZs+eXXUZkiRpC5nlkqR2Ufwh7nvuuWfVJUiSpK1glkuS2kXxE/TDDz+86hIkSdJWMMslSe2i+EPcJUmSJElqBcVP0GfNmsWsWbOqLkOSJG0hs1yS1C6KP8R92LBhVZcgSZK2glkuSWoXxU/Q3/e+91VdgiRJ2gpmuSSpXRR/iLskSZIkSa2g+An6jBkzmDFjRtVlSJKkLWSWS5LaRfGHuO+7775VlyBJkraCWS5JahfFT9APPfTQqkuQJElbwSyXJLWL4g9xlyRJkiSpFRQ/QZ8+fTrTp0+vugxJkrSFzHJJUrso/hD3d77znVWXIEmStoJZLklqF8VP0CdOnFh1CZIkaSuY5ZKkdlH8Ie6SJEmSJLWC4ifo3//+9/n+979fdRmSJGkLmeWSpHZR/CHuY8eOrboESZK0FcxySVK7KH6C/t73vrfqEiRJ0lYwyyVJ7aLbh7hHxPyIOH6DZVf1pLGI6BMRv4qIG+v3d42IeRHxQP3vXXqyPkmS1H1muSRJra0n56DvC3w2Iv6q07IJPWzvE8DSTvcvAuanlPYH5tfvZ3XNNddwzTXX5G5WkqQqmOWSJLWwnkzQXwCOAvaIiB9HxE49aSgihgEnAFd3WnwScG399rXAH/VknY0wfvx4xo8fn7tZSZKq8AJmuSRJLasn56BHSul14H9ExFTgNqAnh7F9E/gMsGOnZXuklJYDpJSWR8TgLhuPOB84H2DvvffuQbObZqBLkgpSWZY3K8fBLJcktY+efIP+fztupJSuAc4BbunOCyNiCrAipbSoR9V1klK6KqU0IaU0Yffdd9/S1bzNunXrWLduXcPWJ0lSC6ssy5uV42CWS5Lax2a/QY+IfwBS/fbfb/DwS91s5/3AifUL02wHDIyIHwJPR8SQ+ifuQ4AV3S+9MX7wgx8AMHXq1NxNS5KUhVkuSVLv0J1D3Bd2un0p8FddPbErKaWLgYsBImIS8OmU0sci4qvUPr2/rP73nJ6ue2sdfPDBuZuUJCk3s1ySpF5gsxP0lFLHhV+IiE92vt8AlwGzIuJc4DHg1Aauu1sOPPDA3E1KkpSVWS5JUu/Qk4vEQf3wuK2RUloALKjffo7a1WQrs3btWgD69etXZRmSJOVilkuS1KJ6cpG4tjR9+nSmT59edRmSJGkLmeWSpHbRnYvErab2aXsA20fEix0PASmlNLCJ9TXdhAkTqi5BkqSmMsslSeodunMO+o6be05vNm7cuKpLkCSpqcxySZJ6h24f4h4R793Isg83tpz81qxZw5o1a6ouQ5KkpjPLJUlqbT05B/3bEfHujjsRcQbw+caXlNfMmTOZOXNm1WVIkpSDWS5JUgvryVXcTwFmR8SZwOHA2cCxTakqo0MOOaTqEiRJysUslySphXV7gp5SeigiTgf+FVgGHJtSerVZheUyZsyYqkuQJCkLs1ySpNbWnau4/4b1fzN1V6APcGdEkFI6sFnF5fDKK68A0L9//4orkSSpOcxySZJ6h+58gz6l6VVUaNasWQBMnTq12kIkSWoes1ySpF6gOz+z9miOQqpy2GGHVV2CJElNZZZLktQ79OQicW1p9OjRVZcgSZK2glkuSWoXPfmZtbb00ksv8dJLL1VdhiRJ2kJmuSSpXWx2gh4Rh0VE5CimCrNnz2b27NlVlyFJUtOY5ZIk9Q7dOcT9HOCKiPgdMBeYm1J6qrll5XP44YdXXYIkSc1mlkuS1At05yJxFwBExLuADwHXRMROwM+ohfzPU0rrmlplE40aNarqEiRJaiqzXJKk3qHb56CnlO5LKX0jpTQZ+EPgNuBU4M5mFZfDqlWrWLVqVdVlSJLUdGa5JEmtbYuu4p5SehW4qf6nV7v++usBfztVklQWs1ySpNZT/M+sHXHEEVWXIEmStoJZLklqF8VP0EeOHFl1CZIkaSuY5ZKkdlH876CvXLmSlStXVl2GJEnaQma5JKldbPUEPSI+24hCqjJnzhzmzJlTdRmSJFXGLJckqTX0+BD3iJjV+S4wHvjbRhWU26RJk6ouQZKkrMxySZJa05acg/5iSum8jjsR8U8NrCe7ESNGVF2CJEm5meWSJLWgbh/iHhG/iIg/BL60wUOXNLakvJ599lmeffbZqsuQJKnpzHJJklpbT85BPx+4EPhORBzWsTCl9HzDq8roxhtv5MYbb6y6DEmScjDLJUlqYd0+xD2ltAT4aEQcDPzviAD4fEppcZNqy+Koo46qugRJkrIwyyVJam1bchX3B4EvAo8DCxtbTn7Dhw9n+PDhm33ezTffzCWXXMIbb7yRoSpJkprKLJckqQX15Bz0f4+IZcAi4HPASmBqk+rKZsWKFaxYsQKAuXPnMnr0aEaNGsVll1223vNuvfVWJk6cyO23315FmZIkbTWz3CyXJLW2nlzF/dPA0pTSq80qpgo33XQTAGeddRYXXngh8+bNY9iwYUycOJETTzyRAw44AIA+ffowffp0rrzyyirLlSRpa5jlZrkkqYX15Bz0u5tZSFWOOeYYAO666y5GjRrFyJEjATj99NOZM2fOm6H+pS9teMFbSZJ6F7PcLJcktbYtOQd9i0TE8Ij4WUQsjYjfRsQn6st3jYh5EfFA/e9dctUEMHToUIYOHcoTTzyx3vlrw4YN44knnshZiiRJLatVcxzMcklS+8g2QQdeBz6VUhoDHApcGBEHABcB81NK+wPz6/ezeeqpp3jqqadIKb3tsfrVbSVJUovmOJjlkqT20ZNz0LdKSmk5sLx+e3VELAWGAicBk+pPuxZYAHw2V11z584FYPTo0SxbtuzN5Y8//jh77bVXrjIkSWpprZrjYJZLktpHtgl6ZxExAjgIuBPYox76pJSWR8TgLl5zPnA+wN57792wWiZPngzAoEGDeOCBB3j44YcZOnQoM2fO5Ec/+lHD2pEkqV20Uo6DWS5Jah/ZJ+gRMQD4F+CTKaUXu3voWUrpKuAqgAkTJrz9GLYttOeee755+/LLL+e4445j3bp1TJs2jbFjxzaqGUmS2kKr5TiY5ZKk9pF1gh4R/aiF+vSU0nX1xU9HxJD6p+5DgBU5a+q4eMzQoUM5/vjjOf7443M2L0lSr9GKOQ5muSSpfeS8insA36H2+6tf7/TQDcA59dvnAHNy1QQwb9485s2bl7NJSZJ6nVbNcTDLJUntI+c36O8HzgJ+ExGL68s+B1wGzIqIc4HHgFMz1uSn7JIkdU9L5jiY5ZKk9pHzKu63AV2dqHZUrjo2NHjwRq9lI0mSOmnVHAezXJLUPnL+DnpLWrZs2Xo/ySJJknoXs1yS1C6Kn6DPnz+f+fPnV12GJEnaQma5JKldVPI76K1kypQpVZcgSZK2glkuSWoXxU/QBw0aVHUJkiRpK5jlkqR2Ufwh7o888giPPPJI1WVIkqQtZJZLktpF8RP0BQsWsGDBgqrLkCRJW8gslyS1i+IPcT/ppJOqLkGSJG0Fs1yS1C6Kn6DvsssuVZcgSZK2glkuSWoXxR/i/tBDD/HQQw9VXYYkSdpCZrkkqV0U/w36rbfeCsDIkSMrrkSSJG0Js1yS1C6Kn6B/5CMfqboESZK0FcxySVK7KH6CvtNOO1VdgiRJ2gpmuSSpXRR/DvqDDz7Igw8+WHUZkiRpC5nlkqR2Ufw36LfddhsAo0aNqrgSSZK0JcxySVK7KP4b9FNOOYVTTjmFuXPnMnr0aEaNGsVll1220edOnTqV2bNnv235pEmTWLhw4Zv3H3nkEcaNG9e0miVJ0lvMcklSuyh+gj5gwAC23357LrzwQm6++WbuvfdeZsyYwb333lt1aZIkqRvMcklSuyh+gn7//ffzz//8z4waNYqRI0ey7bbbcvrppzNnzpxNvu4LX/gCU6dO5Y033tjk88477zzGjx/P+PHj2X333bn00ksbWb4kScUzyyVJ7aL4c9Bvv/12fvnLXzJ8+PA3lw0bNow777yzy9d85jOfYdWqVXzve98jIgA488wz2X777QF47bXX2Gab2mcfV199NQCPPvooxx13HFOnTm3SO5EkqUxmuSSpXRT/Dfppp53GYYcd9rblHWG9oS9+8Yu88MILXHnlles9Z/r06SxevJjFixdz0003rfeaNWvWcOqpp3L55Zezzz77NPYNSJJUOLNcktQuip+g9+/fn/32249ly5a9uezxxx9nr7322ujzJ06cyKJFi3j++ee73cYFF1zAySefzNFHH73V9UqSpPWZ5ZKkdlH8BH3p0qUMGDCABx54gIcffpjXXnuNmTNncuKJJ270+ZMnT+aiiy7ihBNOYPXq1Ztd/xVXXMHq1au56KKLGl26JEnCLJcktY/iz0HvOD/t8ssv57jjjmPdunVMmzaNsWPHdvmaU089ldWrV3PiiSe+7RC4DX3ta1+jX79+jB8/Hqh9An/BBRc0rH5JkkpnlkuS2kWklKquoccmTJiQOv9W6dZYs2YNANttt11D1idJUrNFxKKU0oSq69hSjcxxMMslSb1PV1le/DfohrkkSb2bWS5JahfFn4O+ZMkSlixZUnUZkiRpC5nlkqR2Ufw36B2H2I0bN67iSiRJ0pYwyyVJ7aL4CfqZZ55ZdQmSJGkrmOWSpHZR/AS9X79+VZcgSZK2glkuSWoXxZ+Dfs8993DPPfdUXYYkSdpCZrkkqV0U/w363XffDcCBBx5YcSWSJGlLmOWSpHZR/AT9rLPOqroESZK0FcxySVK7aIlD3CNickTcHxEPRsRFOdvu06cPffr0ydmkJEltxyyXJGnrVT5Bj4g+wBXAh4ADgDMi4oBc7S9evJjFixfnak6SpLZjlkuS1BitcIj7HwAPppQeAoiImcBJwL05Gp/1ve/x0quvctecG3I0J0kq0LtH7ce3f/7zqstoJrNcktS2cuZ4K0zQhwLLOt1/HDhkwydFxPnA+fW7L0XE/Q2sYRDwbAPX11vZD/ZBB/vBPuhgPzSgD+5c8TRXRzSoHAD2aeTKGmCzWd7kHAfHKtgHHewH+6CD/WAfdNiqfmhCjkMXWd4KE/SNvdP0tgUpXQVc1ZQCIhamlCY0Y929if1gH3SwH+yDDvaDfdBNm83yZuY4+O8E9kEH+8E+6GA/2AcdelM/VH4OOrVP2Yd3uj8MeLKiWiRJUs+Z5ZIkNUArTNB/CewfEftGxLbA6YAnkUmS1HuY5ZIkNUDlh7inlF6PiD8F/g3oA3w3pfTbzGU07ZC7XsZ+sA862A/2QQf7wT7YLLO8ZdgHNfaDfdDBfrAPOvSafoiU3na6tyRJkiRJyqwVDnGXJEmSJKl4TtAlSZIkSWoBxU/QI2JyRNwfEQ9GxEVV15NDRAyPiJ9FxNKI+G1EfKK+fNeImBcRD9T/3qXqWpstIvpExK8i4sb6/RL7YOeImB0R99XHxGGl9UNE/Hl9W1gSETMiYrsS+iAivhsRKyJiSadlXb7viLi4vq+8PyKOq6bqxuuiH75a3ybuiYjrI2LnTo+1ZT/0ViXmOJjlnZnlZjmY5SVnebvleNET9IjoA1wBfAg4ADgjIg6otqosXgc+lVIaAxwKXFh/3xcB81NK+wPz6/fb3SeApZ3ul9gH3wLmppTeBbyHWn8U0w8RMRT4M2BCSmkctQtcnU4ZfXANMHmDZRt93/V9xOnA2Ppr/rG+D20H1/D2fpgHjEspHQj8DrgY2r4fep2CcxzM8s7McrPcLF9faVl+DW2U40VP0IE/AB5MKT2UUnoNmAmcVHFNTZdSWp5Surt+ezW1nfhQau/92vrTrgX+qJICM4mIYcAJwNWdFpfWBwOBI4DvAKSUXkspvUBh/UDtFy22j4i+QH9qv9/c9n2QUroVeH6DxV2975OAmSml36eUHgYepLYP7fU21g8ppVtSSq/X795B7Xe9oY37oZcqMsfBLO9glpvlnZjlbykqy9stx0ufoA8FlnW6/3h9WTEiYgRwEHAnsEdKaTnUgh8YXGFpOXwT+AzwRqdlpfXBSOAZ4Hv1wwOvjogdKKgfUkpPAF8DHgOWA6tSSrdQUB9soKv3XfL+chpwc/12yf3Qivz3wCzHLDfLzfINmeXr61U5XvoEPTayrJjfnYuIAcC/AJ9MKb1YdT05RcQUYEVKaVHVtVSsL3Aw8E8ppYOAl2nPw7+6VD8v6yRgX2AvYIeI+Fi1VbWkIveXEXEJtUOJp3cs2sjT2r4fWljx/x5muVmOWW6Wd19x+8zemOOlT9AfB4Z3uj+M2uEwbS8i+lEL9Okppevqi5+OiCH1x4cAK6qqL4P3AydGxCPUDon8w4j4IWX1AdS2gcdTSnfW78+mFvIl9cPRwMMppWdSSmuB64D3UVYfdNbV+y5ufxkR5wBTgDNTSh3hXVw/tLii/z3McrO8ziw3yzdkltN7c7z0Cfovgf0jYt+I2JbaBQNuqLimpouIoHae0tKU0tc7PXQDcE799jnAnNy15ZJSujilNCylNILav/u/p5Q+RkF9AJBSegpYFhGj64uOAu6lrH54DDg0IvrXt42jqJ3LWVIfdNbV+74BOD0i3hER+wL7A3dVUF8WETEZ+CxwYkrplU4PFdUPvUCROQ5mOZjlHcxywCzfUPFZ3ptzPN76MKFMEXE8tfOX+gDfTSl9udqKmi8iDgf+E/gNb52z9Tlq567NAvamtqM7NaW04UUn2k5ETAI+nVKaEhG7UVgfRMR4ahfX2RZ4CPgTah/eFdMPEXEp8MfUDoH6FXAeMIA274OImAFMAgYBTwN/BfwrXbzv+mFi06j10ydTSje/fa29Txf9cDHwDuC5+tPuSCldUH9+W/ZDb1VijoNZviGz3Cw3y8vN8nbL8eIn6JIkSZIktYLSD3GXJEmSJKklOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXChcRO0fE/9jMc66MiPfnqkmSJHWfWS61DyfoknYGNhnqwCHAHc0vRZIkbYGdMcultuAEXdJlwH4RsTgivrrhgxExBvhdSmndBssXRMTo+u3dImJJ/fYOEfGTiPh1RCyJiD/O8SYkSSqYWS61ib5VFyCpchcB41JK47t4/EPA3I0sHwU8UL99IPCb+u3JwJMppRMAImKnxpUqSZI2wiyX2oTfoEvanOPYINQjYh/giZTSG/VFBwL31G//Bjg6Iv42Ij6QUlqVr1RJkrQRZrnUSzhBl9SliOgP7JxSenKDh8bzVogDvLfjfkrpd/X7vwH+JiL+V4ZSJUnSRpjlUu/iBF3SamDHLh47EvjZRpa/B9gOICL2B06iflhcROwFvJJS+iHwNeDgRhcsSZLWY5ZLbcIJulS4lNJzwM/rF4HZ8MIyXZ2zNh7YJiJ+DfwvYClwTv2xdwN3RcRi4BLgS82oW5Ik1ZjlUvuIlFLVNUhqURFxN3BISmntBssfBA5KKa2upjJJktQdZrnUu3gVd0ldSim97ZC2iNgReMNAlySp9ZnlUu/iN+iSJEmSJLUAz0GXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkFOEGXJEmSJKkF/P+IPkcewvrJmQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=plt.subplots(2,2,figsize=[14,5])[1].T\n", "seqA.plot(ax=ax[0])\n", "ax[0][0].set_title('Sequence part A')\n", "seqB.plot(ax=ax[1])\n", "ax[1][0].set_title('Sequence part B')\n", "ax[0,0].figure.tight_layout()" ] }, { "cell_type": "markdown", "id": "e4a72884", "metadata": {}, "source": [ "## Propagation and plotting\n", "We start with the standard $R_{1\\rho}$ experiment\n", "\n", "The basic $R_{1\\rho}$ experiment only requires repetition of the `Ux` propagator, so we can simply use the `DetProp` function.\n", "\n", "Note that we can extract the purely decaying (non-oscillating components) using the `extract_decay_rates` function of a density matrix object (`rho`). This is used to quantify the fraction of the signal that can be fitted to a decay curve, and also to construct a curve with purely decaying components (no oscillation), which we overlay with the total signal." ] }, { "cell_type": "code", "execution_count": 6, "id": "362755f4", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "R1p.clear(data_only=True)\n", "Ux=seqx.U() #Propagator for R1p\n", "\n", "#Extract decay rates and their corresponding weights\n", "# Includes powder average weighting in 'wt_rates' mode\n", "r1p,A=R1p.extract_decay_rates(Ux,mode='wt_rates') \n", "\n", "R1p.DetProp(Ux,n=800) #Propagate\n", "\n", "#Build decay-only curve\n", "I=np.sum([A0*np.exp(-r1p0*R1p.t_axis) for r1p0,A0 in zip(r1p,A)],axis=0)\n", "sc=A.sum()\n", "\n", "# Plotting\n", "ax=R1p.plot()\n", "ax.plot(R1p.t_axis*1e3,I,color='black',linestyle=':')\n", "_=ax.legend((r'$R_{1\\rho}$ decay','Oscillation removed'))" ] }, { "cell_type": "code", "execution_count": 7, "id": "5a6fb2ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "52% of the signal is non-oscillating\n" ] } ], "source": [ "print(f'{sc*100:.0f}% of the signal is non-oscillating')" ] }, { "cell_type": "markdown", "id": "7eb685d5", "metadata": {}, "source": [ "At the beginning of the decay, we observe a loss of almost half of the signal, due to coherent oscillation.\n", "\n", "We also calculate the RECRR sequence. Since additional rotor periods must be inserted into each of four spin-lock blocks, we cannot use the `DetProp` function. We do accelerate the calculation by building up the $x$ and $-x$ spin locks at each loop step, instead of recalculating `Ux**k` and `Umx**k` at every step." ] }, { "cell_type": "code", "execution_count": 8, "id": "8c57cc11", "metadata": {}, "outputs": [], "source": [ "Ux=seqx.U()\n", "Umx=seqmx.U()\n", "UA=seqA.U() #First half of sequence\n", "UB=seqB.U() #Second half of sequence\n", "\n", "RECRR()\n", "for n in range(200):\n", " RECRR.reset() #Reset density matrix\n", " UB*UA*RECRR #Propagate by both first and second parts of sequence\n", " RECRR() #Detect\n", " UA=Ux*UA*Ux #Add 1 rotor period to each side of UA (x)\n", " UB=Umx*UB*Umx #Add 1 rotor period to each side of UB (-x)" ] }, { "cell_type": "code", "execution_count": 9, "id": "1d40e982", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_=RECRR.plot()" ] }, { "cell_type": "markdown", "id": "682717cf", "metadata": {}, "source": [ "Indeed, oscillations at the beginning of the decay curve have been almost entirely removed. However, it is worth noting that the decay rate at the beginning of the curve appears to be faster than with the standard $R_{1\\rho}$ experiment. We overlay the two curves, scaling the RECRR curve to match the beginning of the non-coherent decay of the $R_{1\\rho}$ curve." ] }, { "cell_type": "code", "execution_count": 10, "id": "6511a712", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax=R1p.plot()\n", "ax.plot(RECRR.t_axis*1e3,RECRR.I[0].real*sc)\n", "_=ax.legend((r'$R_{1\\rho}$','RECRR'))" ] }, { "cell_type": "markdown", "id": "a558bd1e", "metadata": {}, "source": [ "We clearly see that the RECRR curve is relaxing more quickly at the beginning.\n", "\n", "We can investigate this effect based on analysis of a single orientation (single crystal), where the $R_{1\\rho}$ experiment should be closer to monoexponential." ] }, { "cell_type": "markdown", "id": "fc875e95", "metadata": {}, "source": [ "## Single crystal behavior\n", "We simulate both sequences for a single crystal to better see the differences between the sequences. We sweep the correlation time and observe that at shorter correlation times, the relaxation behavior is very similar between the two sequences. However, at longer correlation times, a fast decaying component emerges in the RECRR that is not present in the standard $R_{1\\rho}$ experiment. This is likely because the RECRR experiment relies on a refocusing of the CSA (and dipole) by cycling the phases, where if the frequency of the phase change matches the rate of motion, we interfere with this refocusing, and therefore obtain an additional relaxation mechanism that is not present in the $R_{1\\rho}$ experiment. Since the frequency of the phase change is varying throughout the RECRR experiment, the timescale sensitivity is also varying depending on what time point in the RECRR experiment is currently being acquired.\n", "\n", "We plot the $R_{1\\rho}$ curves at the top, and RECRR curves at the bottom. We calculate the $R_{1\\rho}$ decay without oscillation as well (dashed lines). This curve is overlayed over the RECRR curve with a scaling factor. We do this to show that the relaxation at longer times is very similar to the $R_{1\\rho}$ behavior. For slower motion, it takes longer for the two curves to line up, since we are further into the sequence before the interference between motion and phase changes is fully mitigated." ] }, { "cell_type": "code", "execution_count": 11, "id": "9704fe6a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Use just one orientation\n", "# We generate the JCP59 powder average with q=2\n", "# Indexing powder average returns single orientation\n", "ex0.pwdavg=sl.PowderAvg(3)[10]\n", "\n", "fig,ax0=plt.subplots(2,5,figsize=[12,5],sharex=True,sharey=True)\n", "for tc,ax,sc in zip([1e-6,1e-5,1e-4,1e-3,1e-2],ax0.T,[1,1,.55,.5,0]):\n", " L.kex=sl.Tools.twoSite_kex(tc=tc)\n", "\n", " Ux=seqx.U()\n", " Umx=seqmx.U()\n", " UA=seqA.U()\n", " UB=seqB.U()\n", "\n", " R1p.clear(data_only=True) #This keeps the Liouvillian in R1p\n", " #Without this, we would have to re-determine how R1p is block diagonal\n", " RECRR.clear(data_only=True)\n", "\n", " # R1p calculation\n", " r1p,A=R1p.extract_decay_rates(Ux,mode='rates')\n", " A,r1p=A[0],r1p[0] #Index runs over the powder average, but we just have one element\n", " R1p.DetProp(Ux,n=800)\n", "\n", " R1p.plot(ax=ax[0])\n", "\n", " # Here we calculate the oscillation-free decay from R1p\n", " I=np.sum([A0*np.exp(-r1p0*R1p.t_axis) for r1p0,A0 in zip(r1p,A)],axis=0)\n", "\n", " ax[0].plot(R1p.t_axis*1e3,I,linestyle=':',color='black')\n", " ax[0].set_title(fr'$\\tau_c$ = {tc*1e6:.0f} $\\mu$s')\n", " \n", " # RECRR calculation\n", " RECRR()\n", " for k in range(200):\n", " RECRR.reset()\n", " (UB*UA*RECRR)()\n", " UA=Ux*UA*Ux\n", " UB=Umx*UB*Umx\n", " RECRR.plot(ax=ax[1])\n", " ax[1].plot(R1p.t_axis*1e3,I/I[0]*sc,linestyle=':',color='black')\n", " for a in ax:\n", " a.set_ylim([0,1])\n", " if not(a.is_first_col()):a.set_ylabel('')\n", " if not(a.is_last_row()):a.set_xlabel('')\n", "ax0[0][2].set_title(r'$R_{1\\rho}$'+'\\n'+ax0[0][2].get_title())\n", "ax0[1][2].set_title(r'RECRR')\n", "fig.tight_layout()\n", "_=ax0[0,0].legend((r'$R_{1\\rho}$',r'Oscillation Removed'))" ] }, { "cell_type": "markdown", "id": "e6e2bd86", "metadata": {}, "source": [ "Then, while the RECRR pulse sequence presents some significant advantages over the $R_{1\\rho}$ sequence, because of the more complex relaxation behavior, it becomes necessary to use simulation to fit the curves, rather than relying on simple mono-exponential or bi-exponential fitting. This is especially important at slower correlation times, where a second relaxation mechanism emerges, and the sensitivity of this experiment to correlation time varies throughout the duration of the experiment." ] } ], "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": 5 }