{ "cells": [ { "cell_type": "markdown", "id": "4dda497a-9c6c-4dc9-97cc-a3986ad3c919", "metadata": {}, "source": [ "# Integrating the Bloch Hamiltonian" ] }, { "cell_type": "markdown", "id": "f5132bb1-051e-4b65-830b-254d3159da21", "metadata": {}, "source": [ "**What you'll learn:**\n", "- How to integrate the Bloch Hamiltonian to simulate Bragg diffraction pulses\n", "- How to reproduce adiabatic rapid passage results from Kovachy (2012)\n", "- How to simulate Bloch oscillations with a swept lattice\n", "- How to include single-photon scattering via density matrix integration" ] }, { "cell_type": "markdown", "id": "01949504-c062-4d6d-b21c-c0626af37177", "metadata": {}, "source": [ "## Adiabatic Bragg pulse" ] }, { "cell_type": "markdown", "id": "66f348c6-dccd-48ec-b636-96e876ae05a8", "metadata": {}, "source": [ "First lets simulate the adiabatic Bragg pulse from [Adiabatic-rapid-passage multiphoton Bragg atom optics](https://doi.org/10.1103/PhysRevA.86.011606) by Kovachy." ] }, { "cell_type": "code", "execution_count": 1, "id": "268a23b4-eeb3-4373-a6ba-31367da6cc37", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mwave.integrate import propagate, make_kvec, make_phi\n", "from numba import jit\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "# Define pulse parameters\n", "n0, nf = 0, 5\n", "omega = 30\n", "delta = 4*(n0 + nf)\n", "\n", "# Compute tfinal and t0 from sigma\n", "tfinal = 8*2*np.pi\n", "t0 = tfinal/2\n", "\n", "# Compute detuning ramp rate as 2*omega_r/(tfinal/2)\n", "rate = 2/(tfinal/2)\n", "\n", "# Define pulse profile used in Kovachy (2012)\n", "@jit(nopython=True)\n", "def omega_fnc(t, args):\n", " omega = args[0]\n", " return omega*np.tanh(8*t/tfinal)*np.tanh(8*(1 - t/tfinal))\n", "\n", "# Define the phase used in Kovachy (2012)\n", "@jit(nopython=True)\n", "def phase_fnc(t, args):\n", " tcurrent = (t-tfinal/2)\n", " return rate/2*(tcurrent**2) # The phase is the integral of the time dependent frequency over time\n", "\n", "# Write out a function for the detuning vs time\n", "def delta_fnc(t):\n", " tcurrent = (t-tfinal/2)\n", " return rate*tcurrent\n", "\n", "# Define the initial state and the kvec array\n", "kvec, n0_idx, nf_idx = make_kvec(n0, nf)\n", "phi0 = make_phi(kvec, n0)\n", "\n", "# Integrate the pulse\n", "result = propagate(kvec, phi0, tfinal, delta, omega_fnc, np.array([omega]), phase_fnc, np.array([]))\n", "sol = result.scipy_sol\n", "\n", "# Determine the minimum and maximum indicies\n", "n_max = max(n0_idx, nf_idx)\n", "n_min = min(n0_idx, nf_idx)\n", "\n", "# Plot\n", "fig, [ax1, ax2, ax3] = plt.subplots(nrows = 3, sharex=True, gridspec_kw={'height_ratios': [2, 1, 1]})\n", "ax1.plot(sol.t, np.abs(sol.y.T[:,n_min-2:n_max+2])**2, label=[r\"$%i\\hbar k$\" % k for k in kvec[n_min-2:n_max+2]])\n", "ax2.plot(sol.t, [omega_fnc(t, np.array([omega])) for t in sol.t])\n", "ax3.plot(sol.t, [delta_fnc(t) for t in sol.t])\n", "ax1.legend(bbox_to_anchor=(1.05, 0.95))\n", "ax1.set_ylabel(r'population')\n", "ax2.set_ylabel(r'$\\Omega(t)$')\n", "ax3.set_ylabel(r'$\\delta(t)$')\n", "ax3.set_xlabel(r'time [$\\omega_r$]')\n", "fig.suptitle(r'$n_\\text{bragg}=5$, $\\Omega(t)=\\Omega\\tanh(8t/t_f)\\tanh(8(1-t/t_f))$, $t_f=2\\pi %0.1f$' % (tfinal/2/np.pi))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e87a6945-79be-4c55-ae39-23a3d0336b88", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "The two lower subplots are equivalent to Fig. 1a and b from the paper." ] }, { "cell_type": "markdown", "id": "26f80fd9-860a-418a-956b-4d2231224245", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Next lets replicate Fig. 2a" ] }, { "cell_type": "code", "execution_count": 2, "id": "da4a2f63-2103-469b-8c85-f6eb9264f44d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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ZMGGC9OnTR/r166fnsFE1MWr0lDJ+/HgJDw/XnYKV0aNH6xFWPXv21HPiHDlyRNfmqPstIQfAlSssNsmSXxP09t0DGP4NwLEYGm7GjBkjqampMmvWLElKSpIePXrImjVrrJ2M4+Pjy9XUPPnkk+Lm5qavExMTJSQkRAeb//u//zNwLwDns3Z/il79O7iht9zQpeJmYgCwV25mF2vPUaOl1JDwjIwMOhcDlRi/aKtsOJQqUwe3k0dv7MRxAmC4mnx/0wMXQDnxZ3N0sFHG9qVJCoDjIdwAKOeTX0uGf1/dPlhaNvXn6ABwOIQbAFYFRSZZtq20I3H/VhwZAA6JcAPA6rvfkyTtQoE0a+Qj13VuxpEB4JAINwAumZH4zr6R4uXBrwcAjonfXgC0o6kXJO7YWXF3ExnTj47EABwX4QaA9smWklqbIR2bSXiQH0cFgMMi3ACQvMJi+WzHKX0k7mIdKQAOjnADQFbvPSPpOYXSItBXBnekIzEAx0a4ASCLS5uk7uzXUjxUpxsAcGCEG8DFHUrOkl9PnNehZkzfSKOLAwBXjHADuDjLpH3XdWomoQG+RhcHAK4Y4QZwYcUms6zcdVpv39E7wujiAIBNEG4AF/bLkTRJycqXIH8vPQQcAJwB4QZwYV/sTNTXo6Kbi7cnvw4AOAd+mwEuKju/SNbsTdLbt/eiSQqA8yDcAC7q231JkltYLG2CG0jPyCCjiwMANkO4AVy8SerWHuHi5sbcNgCcB+EGcEHJmXm6M7FyW89wo4sDADZFuAFc0MpdiWIyi/Rp1VhaNvU3ujgAYFOEG8AFLd9R0iR1Wy9qbQA4H8IN4GJ+P50pB5KyxNvDXUZ1b2F0cQDA5gg3gIv5YucpfT20UzMJ9PcyujgAYHOEG8BFl1ugSQqAsyLcAC6E5RYAuALCDeBCWG4BgCsg3AAuuNzCbT1ZbgGA8yLcAC623ELrpv7SqyXLLQBwXoQbwNWWW+jJcgsAnBvhBnCx5RZup0kKgJMj3AAugOUWALgSwg3gAlhuAYArIdwATm7/GZZbAOBaCDeAi3QkZrkFAK6CcAM4+XILK0rDDcstAHAVhBvAibHcAgBXRLgBnNiKXSW1NqOim4u3Jx93AK6B33aAk8orLJbv9iXr7Vt7hBtdHACoN4QbwEmtP5gqF/KLpEWgr/Rq2djo4gBAvSHcAE7qq99O6+tRMS3E3d3N6OIAQL0h3ABOSNXYrD1Q0iQ1OrqF0cUBgHpFuAGc0Nr9yZJXaJI2wQ2kW3iA0cUBgHpFuAGc0Je7SpqkRkc3Fzc3mqQAuBbCDeBk0nMKZMPhVL09OoYmKQCuh3ADOJlv9yVJYbFZOoU1kvahjYwuDgDUO8IN4GS++u2MvqbWBoCrItwATiQlK082HU3T24ySAuCqCDeAE1m9J0lMZpGYyCBp2dTf6OIAgCEIN4ATTtx3Mx2JAbgwwg3gJBLTc2XbyfOiRn6P7N7c6OIAgGEIN4CT+Lq01qZf6yYSFuhrdHEAwDCEG8BJfLW7tEmqB3PbAHBthBvACRxLvSB7EzPFw91NbupGkxQA10a4AZxobpurooKlSQNvo4sDAIYi3AAOzmw2y5e/JeptRkkBAOEGcHgHkrLkaGq2eHu6y/VdQ40uDgAYzvCam/nz50vr1q3F19dX+vfvL1u3bq3y+enp6XL//fdL8+bNxcfHRzp06CDffPNNvZUXsDdflo6SGtIxRAJ8vYwuDgAYztPIf3zp0qUyffp0WbhwoQ428+bNk+HDh8vBgwelWbNmlzy/oKBArr/+ev3YZ599JuHh4XLy5EkJCgoypPyAPTRJWSbuYy0pALCDcDN37lyZNGmSTJw4Ud9WIWfVqlWyaNEieeyxxy55vrr/3LlzsmnTJvHyKvkLVdX6AK5qV0K6nDqfK/7eHnJdJ5qkAMDQZilVC7N9+3YZNmyY9T53d3d9Oy4ursLXfPnllxIbG6ubpUJDQ6Vbt27y3HPPSXFxcaX/Tn5+vmRmZpa7AM42Sur6LqHi5+1hdHEAwLXDTVpamg4lKqSUpW4nJSVV+Jpjx47p5ij1OtXPZubMmfLKK6/Iv/71r0r/nTlz5khgYKD1EhkZafN9AYxQbDLL16UT97ECOABcYbhJTk6WcePGSYsWLcTT01M8PDzKXeqKyWTS/W3efvtt6d27t4wZM0aeeOIJ3ZxVmRkzZkhGRob1kpCQUGflA+rT1uPnJCUrXwJ8PeWaDiEcfAC4kj43f/3rXyU+Pl7XnKhRS25qpb4aCg4O1kFIBaWy1O2wsLAKX6P+LdXXpmyA6ty5s67pUc1c3t6XTl6mRlSpC+Csyy2oGYnVMHAAwBWEm40bN8rPP/8sPXr0kNpSQUTVvqxdu1ZuvfVWa82Muv3AAw9U+JpBgwbJ4sWL9fNU/xzl0KFDOvRUFGwAZ1VYbJLVe0r624yKYbkFACirVn/uqX4ragjqlVLDwN955x358MMPZf/+/TJ16lTJzs62jp4aP368blayUI+r0VIPP/ywDjVqZJXqUKw6GAOu5JcjaXI+p1CCG3pLbNumRhcHABy/5kbNR6OGar/11ltXNBRb9ZlJTU2VWbNm6aYlVRO0Zs0aaydj1fRlqaGxhKpvv/1Wpk2bJtHR0XqeGxV0Hn300VqXAXDkUVIjujcXTw+apACgLDdzLapgGjduLDk5OVJUVCT+/v7WOWcsVO2KvVJDwdWoKdW5OCAgwOjiADWWV1gsff/1g2TlF8myKbHSt3UTjiIAp5dZg+/vWtfcADDGhkOpOtiEBfhK75aNOQ0AYItwM2HChNq8DIANfLW7tCNxdHNxd6/5SEUAcHa1Xn5BTaS3YsUK3RFY6dq1q9x88811Os8N4OpyCorkh99Lpk9gLSkAsGG4OXLkiIwYMUISExOlY8eO1pmAVYdfNYKpXbt2tXlbAJexdn+K5BYWS8sm/hIdEcjxAoAK1GqYxUMPPaQDjJrtd8eOHfqiRja1adNGPwagbliWW1BNUrWZPBMAXEGtam5++ukn2bx5szRp8scojaZNm8rzzz+vJ9oDYHuZeYWy7mCq3qZJCgBsXHOjljPIysq65P4LFy4wUzBQR77flywFRSaJatZQOoU14jgDgC3DzahRo2Ty5MmyZcsWPVOxuqianClTpuhOxQDqbi0ptQI4TVIAYONw8/rrr+s+N7GxseLr66svqjkqKipKXnvttdq8JYAqnM8ukI2H0/Q2a0kBQB30uQkKCpKVK1fK4cOH5cCBA9bVuVW4AWB7a/YlSZHJLF2aB0i7kIYcYgCoi3lulPbt2+sLgLr11W+lTVIxLTjUAGCrcKNW8H722WelQYMGersqc+fOre7bAriMlMw8iTt21joEHABgo3Czc+dOKSwstG4DqB/f7Dkjannbni2DJLKJP4cdAGwVbtatW1fhNoD6WkuKJikAqLPRUvfcc0+F89xkZ2frxwDYRmJ6rmw/eV7UZMQju9MkBQB1Fm4+/PBDyc3NveR+dd9HH31Um7cEUIFVpXPb9GvdRMICfTlGAGDr0VKZmZnWSftUzY2a36bsKuHffPONNGvWrCZvCaAKX/1W0iTFKCkAqKNwo+a3UTOjqkuHDh0ueVzd//TTT9fkLQFU4nhatuxJzBAPdze5qVsYxwkA6iLcqI7EqtZm6NCh8vnnn5dbONPb21tatWolLVrQ6RGwha9L57YZ2K6pNG3ow0EFgLoIN9dee62+Pn78uERGRoq7e6267ACohq9LR0nRJAUA9TBDsaqhUXJyciQ+Pl4KCgrKPR4dHV2btwVQ6mBSlhxMzhIvDzcZ3pUmKQCo83CTmpoqEydOlNWrV1f4uOpcDKD2vi4dJXVthxAJ9PPiUAJADdSqXemRRx6R9PR02bJli/j5+cmaNWv08HC1ztSXX35Zm7cEUEr1a2MtKQCo55qbH3/8Ua8K3qdPH93vRjVTXX/99RIQECBz5syRkSNHXkGRANe2+1SGnDibI75e7nJd51CjiwMArlFzo2Yitsxn07hxY91MpXTv3l127Nhh2xICLmbFrkR9fX2XMGnoU6u/PwDApdUq3HTs2FEOHjyot2NiYuStt96SxMREWbhwoTRvzhTxQG0Vm1STVMkoqVtimFYBAGqjVn8WPvzww3LmTMkv4NmzZ8uNN94o//3vf/VcNx988EGtCgJAZNPRNEm7kC9B/l5yTYcQDgkA1Fe4+ctf/mLd7t27t5w8eVIOHDggLVu2lODg4Nq8JQDVJLWzZJSUWiTT25N5pACgNmzSoO/v7y+9evWyxVsBLiuvsFi+3Zekt2/pEW50cQDA+cPN9OnTq/2mc+fOrW15AJe1dn+KXMgvkvAgP+nTqrHRxQEA5w83O3furNbz1OKZAGo/SurmHi3E3Z3PEQDUebhRi2YCqBsZOYWy/mCK3r6lB6OkAOBK0GMRsAPf7D0jhcVm6RTWSDqFBRhdHABwvQ7FQ4YMqbL5Sc1gDKD6VpY2SdGRGAAMCjc9evQod7uwsFB27dole/fulQkTJtigWIDrOJORK1uOn9Pbo2OYBBMADAk3r776aoX3P/XUU3LhwoUrLRPgUr7cdVrMZpF+rZtIRGN/o4sDAA7Ppn1u1OR+ixYtsuVbAk5v5a6Siftu6UlHYgCwu3ATFxcnvr6+tnxLwKkdTs6S389kiqe7m4zoRpMUABjWLHX77beXu202m/VaU9u2bZOZM2fapGCAK81tM7hjiDRu4G10cQDAdcNNYGBgudvu7u56pfBnnnlGbrjhBluVDXBq6o8Ca5MUyy0AgLHh5v3337ddCQAXtSP+vJw6nysNvD1kWOdQo4sDAE7jihbOVM1Q+/fv19tdunTRK4QDqNkK4MO7homftweHDQCMDDenTp2SsWPHyi+//CJBQUH6vvT0dBk4cKAsWbJEIiIibFU+wCkVFptk1Z4zevuWnqwADgCGj5a677779MR9qtbm3Llz+qK2TSaTfgxA1TYeTpNz2QUS3NBbBrVryuECAKNrbn766SfZtGmT7kRsobbfeOMNufrqq21ZPsCpR0mNim4hnh4s8QYAtlSr36qRkZG65uZixcXF0qIFE5EBVckpKJLv9iXrbVYABwA7CTcvvfSSPPjgg7pDsYXafvjhh+Xll1+2ZfkAp/P978mSW1gsrZr6S4/Ikj5rAADbcTOryTZqqHHjxpKTkyNFRUXi6VnSsmXZbtCgQbnnqv449iQzM1PP05ORkSEBAQFGFwcuaOL7W2XdwVR5aGiUTL/hj6ZdAIBtvr9r1edm3rx5tXkZ4PLOXsiXnw+n6eNwMxP3AUCdqFW4mTBhgu1LArgANSNxkcks3cMDJapZQ6OLAwBOqdaT+KnOwytWrLBO4te1a1e5+eabxcODyciAyizbfkpf/7kPc0EBgF2FmyNHjsiIESMkMTHROhx8zpw5ehTVqlWrpF27drYuJ+Dw9iZmyP4zmeLt4S43xzCqEADsarTUQw89pANMQkKC7NixQ1/i4+OlTZs2+jEAl/qstNbm+q6hEuTPCuAAYHeT+G3evFmaNGliva9p06by/PPPy6BBg2xZPsAp5BcVWyfu+1NvmqQAwO5qbnx8fCQrK+uS+y9cuCDe3vxFClzsx/0pkp5TKKEBPnJN+xAOEADYW7gZNWqUTJ48WbZs2SJqmhx1UTU5U6ZM0Z2KAVTckfj2XhHi4e7G4QEAews3r7/+uu5zExsbK76+vvqiVgSPioqS1157zfalBBxYSmaerD+Yorf/TJMUANhnuAkKCpKVK1fKoUOHZNmyZfqitr/44gs9e2BNzZ8/X1q3bq1DUv/+/WXr1q3Vet2SJUvEzc1Nbr311lrsBVA/lu9MFJNZpHerxtI2hLltAKCu1Xo54vfee0+Hij//+c/6orbffffdGr/P0qVLZfr06TJ79mw96iomJkaGDx8uKSklf+lW5sSJE/L3v/+dVchh11ST7bJtCXqbWhsAsONwM2vWLL1I5ujRo601N2p72rRp+rGamDt3rkyaNEkmTpwoXbp0kYULF4q/v78sWrSoygkE7777bnn66aelbdu2tdkFoF7sTEiXo6nZ4uvlLiOjm3PUAcBeh4IvWLBA3nnnHRk7dqz1PtWRODo6Wq8W/swzz1TrfQoKCmT79u0yY8YM633u7u4ybNgwiYuLq/R16v2bNWsm9957r/z8889V/hv5+fn6UnbhLaC+57YZ0a25NPL14sADgL3W3BQWFkqfPn0uub937956dfDqSktL07UwoaGh5e5Xt5OSkip8zcaNG3WTmApX1aFmTlb9gCwXNYsyUB/yCovlq99O6+0/sdwCANh3uBk3bpyuvbnY22+/rZuL6oqaW0f92yrYBAcHV+s1qlZILY9uuahZlYH68O2+JMnKK5KIxn4yoE1TDjoA2PvCmar25LvvvpMBAwbo22rOG7UEw/jx43UH4bJ9aiqjAopaaDM5Obnc/ep2WFjYJc8/evSo7kis+vdYmEymkh3x9JSDBw9esq6VmnBQXYD6tmxbSZPUHb0ixJ25bQDAvsPN3r17pVevXtbAYQkq6qIes1DDtKuiZjNWTVlr1661DudWYUXdfuCBBy55fqdOnWTPnj3l7nvyySd1jY6aX4cmJ9iLxPRc+eVomt5muQUAcIBws27dOpsVQNXyTJgwQffh6devn8ybN0+ys7P16ClF1QSFh4frvjNqHpxu3bpdMueOcvH9gJE+335KzGaR2LZNJbKJPycDAByhWcpWxowZI6mpqXoIuepE3KNHD1mzZo21k7Fq6lIjqABHYTKZraOk/kxHYgCod25mNcuYC1FDwdWoKdW5OCAgwOjiwAltOXZWxry9WRr6eMqvTwwTP28Po4sEAC71/U2VCFBHi2SOim5OsAEAAxBuABvKzi+Sb/ac0ds0SQGAMQg3gA2t2nNGcgqKpW1wA+nVsjHHFgAMQLgBbOgzy9w2vSMuOxUCAKBuEG4AGzmRli1bT5wTNV+fmrgPAGAMwg1gI5/8Gq+vr24fImGBvhxXADAI4Qaw0SKZn/5asm7ZXwa04pgCgIEIN4ANfL37jJzPKZTwID8Z2qkZxxQADES4AWzgo7gT+vruAS3Fg0UyAcBQhBvgCu1KSJfdpzLE28NdxvSJ5HgCgMEIN4CNam3UjMRNG/pwPAHAYIQb4Aqcyy7Q/W2U8QNbcywBwA4QboArsPTXBCkoMkl0RKD0iAziWAKAHSDcALVUbDLLx5tP6u1xDP8GALtBuAFq6ccDKZKYnitB/l4yOqYFxxEA7AThBrjCjsRqhJSvlwfHEQDsBOEGqIVjqRfk58NpotbGZEZiALAvhBugFj7eXLKO1JCOzSSyiT/HEADsCOEGqKGcgiJZtr1kHanxsawjBQD2hnAD1NDKXaclK69IWjf1l2vah3D8AMDOEG6AGjCbzfLhppKOxKqvjTvrSAGA3SHcADWw7eR5OZCUJb5e7vLn3qwjBQD2iHAD1MBHcSWT9t0SEy6B/l4cOwCwQ4QboJpSsvJkzd6SdaTG0ZEYAOwW4QaopiVbE6Sw2Cy9WgZJt/BAjhsA2CnCDVANhcUm+e+Wkiap8bGs/g0A9oxwA1TD978nS3JmvgQ39JabuodxzADAjhFugGoM/357wzG9fWffluLjyTpSAGDPCDfAZcQdOyu7EtLFx9NdJgykSQoA7B3hBriMBeuP6usxfSMlpJEPxwsA7BzhBqjCbwnpevVvD3c3mXR1W44VADgAwg1QhX+vP6Kvb+nRgtW/AcBBEG6AShxOzpJv9yWLm5vI3wa34zgBgIMg3ACVWPBTSV+b4V3CJKpZI44TADgIwg1QgYRzObJy12m9/bch1NoAgCMh3AAVUPPaFJvMcnX7YImOCOIYAYADIdwAFSyQuXRbgt7+2+Aojg8AOBjCDXCRRRtPSEGRSXq2DJIBbZtwfADAwRBugDIycgvl480lC2TePzhK3NRQKQCAQyHcAGX8J+6EXMgvkk5hjWRop2YcGwBwQIQboFROQZEs+uWE3p46uJ24u1NrAwCOiHADlFqyNUHOZRdIyyb+MrJ7c44LADgowg0gojsQv/PzMX0splzbTjw9+GgAgKPiNzggIit2JsqZjDxp1shH7ugdzjEBAAdGuIHLU5P1WZZamHxNW/Hx9HD5YwIAjoxwA5e3eu8ZOZ6WLUH+XjK2X0uXPx4A4OgINxBXr7V5Y+0Rvf3Xga2lgY+n0UUCAFwhwg1c2ufbT8nB5CwJ9POSiQPbGF0cAIANEG7g0vPavPzdQb394NAoCfT3MrpIAAAbINzAZb3783FJycqXyCZ+Mi62ldHFAQDYCOEGLrvy98LSEVL/HN6JEVIA4EQIN3BJ8344LDkFxdIjMkhGRTMbMQA4E8INXM7h5CxZsjVebz8xsjMrfwOAkyHcwOU8v/qAmMwiw7uGSt/WTYwuDgDAxgg3cCmbjqbJ2gMp4unuJo/e2Mno4gAA6gDhBi7DZDLLc9/s19t3928pbUMaGl0kAEAdINzAZaz8LVH2JmZKIx9Peei69kYXBwDgzOFm/vz50rp1a/H19ZX+/fvL1q1bK33uO++8I1dffbU0btxYX4YNG1bl8wElr7BYXv72kN6eMridNG3ow4EBACdleLhZunSpTJ8+XWbPni07duyQmJgYGT58uKSkpFT4/PXr18vYsWNl3bp1EhcXJ5GRkXLDDTdIYmJivZcdjuP9X05IYnquNA/0lXuvYpkFAHBmbmaz2WxkAVRNTd++feXNN9/Ut00mkw4sDz74oDz22GOXfX1xcbGuwVGvHz9+/CWP5+fn64tFZmamfv+MjAwJCAiw8d7AHp3LLpBrX1wnWflF8sqfY+SO3hFGFwkAUEPq+zswMLBa39+G1twUFBTI9u3bddOStUDu7vq2qpWpjpycHCksLJQmTSoe0jtnzhx9MCwXFWzgWl5fe1gHmy7NA+S2nuFGFwcAUMcMDTdpaWm65iU0NLTc/ep2UlJStd7j0UcflRYtWpQLSGXNmDFDpzzLJSEhwSZlh2M4npYtH28+aZ2wz93dzegiAQDqmKc4sOeff16WLFmi++GozsgV8fHx0Re4phdWH5Aik1mGdAyRQVHBRhcHAODs4SY4OFg8PDwkOTm53P3qdlhYWJWvffnll3W4+eGHHyQ6OrqOSwpH9MPvybJmX5KoypoZIzobXRwAgCs0S3l7e0vv3r1l7dq11vtUh2J1OzY2ttLXvfjii/Lss8/KmjVrpE+fPvVUWjiSjJxCefyLPXp70tVtpUNoI6OLBABwlWYpNQx8woQJOqT069dP5s2bJ9nZ2TJx4kT9uBoBFR4erjsGKy+88ILMmjVLFi9erOfGsfTNadiwob4AyrOrfpeUrHxpG9xApl3fgYMCAC7E8HAzZswYSU1N1YFFBZUePXroGhlLJ+P4+Hg9gspiwYIFepTVn/70p3Lvo+bJeeqpp+q9/LA/6w6myGfbT4mbm8iLf4oWXy8Po4sEAHCleW7seZw8HE9WXqHc8OoGOZORJxMHtZbZo7saXSQAgCvNcwPY2nPfHNDBpmUTf/nH8I4cYABwQYQbOI1fjqTJJ1vj9fYLd0SLv7fhra4AAAMQbuAUsvOL5NHPd+vtcQNaSWy7pkYXCQBgEMINnMILaw7IqfO5Eh7kJ4/e1Mno4gAADES4gcPbfOysfBRXssTC83d0l4Y+NEcBgCsj3MCh5RYUW5uj7uwbKVe3DzG6SAAAgxFu4NBe/u6gnDybI80DfeXxkSyxAAAg3MCBbT95Thb9clxvP3d7dwnw9TK6SAAAO0DNDRy2Oeofn+0WNQXlHb0iZEjHZkYXCQBgJwg3cDhqUu3Hlu+WY6nZEtLIR2aOojkKAPAHwg0cznsbj8vKXafF091N3hjbU4L8vY0uEgDAjhBu4FA2HUmTOasP6O0nR3aWAW2ZrA8AUB7hBg7j1PkcuX/xDik2meX2XuEyYWBro4sEALBDhBs4TAfi//nPdjmfUyjdwwPludu6i5ubm9HFAgDYIcINHKID8Yzlu2Xf6Uxp0sBbFo7rLb5eHkYXCwBgpwg3sHvv/3JCVuw6LR7ubjL/rl56/SgAACpDuIFd23Q0Tf7vm/16+4kRnVntGwBwWYQb2K3E9Fx5YPFO3YH4tp7hMnEQHYgBAJdHuIFdyisslin/2S7nsguka4sAOhADAKqNcAO77ED8+Bd7ZE9ihjT295K3xvUWP286EAMAqodwA7vz2trDsnxHorUDcURjf6OLBABwIIQb2JXX1x6WeT8c1tuzRnWRgVHBRhcJAOBgCDewG/PXHZG53x/S2zNu6sQMxACAWiHcwC4sWH9UXvr2oN7+540d5X+ubWd0kQAADopwA8O99dNReWFNyWKY/xjeUf42OMroIgEAHBjhBoZ69+dj1lW+p1/fQe4fQrABAFwZwg0M897G4/KvVSWzDz98XXt56Lr2nA0AwBUj3MAQ7/9yXJ79+ne9/dDQKHlkGMEGAGAbhBvUu4/iTsjTX5UEm/uHtJNp13cQNzc3zgQAwCY8bfM2QPVmHn5rwzF5vrSPzdTB7eTvN3Qk2AAAbIpwg3qRW1Asj36+W7787bS+/T/XtJV/DifYAABsj3CDOnfqfI5M/mi7/H4mUzzd3WTW6C4ybkAramwAAHWCcIM6telomjyweKde3btpA2+Zf3cvGdC2KUcdAFBnCDeos/41H2w6oYd6F5vM0i08QN4a10fCg/w44gCAOkW4gc3lFRbLE1/slc93nNK3b+sZLnNu7y6+Xh4cbQBAnSPcwKbOZOTKlP9sl99OZYiHu5s8PqKz3DOoNf1rAAD1hnADm4k7elYe/GSnpF3IlyB/L5l/Vy8ZFBXMEQYA1CvCDa5YRk6hzFm9X5b8mqBvdwprJO+M7yORTfw5ugCAeke4wRV1Gv5q9xl55qt9knahQN83tl+kzBzVRfy9+dECABiDbyDUSsK5HHlyxV756VCqvh3VrKE8d1t36demCUcUAGAowg1qpLDYJIs2HpdXfzgkeYUm8fZwlweGRsn/XNtWfDwZDQUAMB7hBtW2KyFdZizfI/vPZOrbA9o20bU1bUMachQBAHaDcIPLOp2eK/PXHZHFW+PFbBY9EuqJEZ3lT70jGOINALA7hBtU6uTZbFmw/qiejK+w2Kzvu71nuDwxsrM0bejDkQMA2CXCDS5xJCVL5q87Kit3JYqpJNNIbNum8vCw9qwLBQCwe4QbWO07naGbn1bvTdLNT8rgjiHywJAo6dOaUVAAAMdAuHFxaq6aHfHn5d/rjsraAynW+4d3DZUHhrSX7hGBhpYPAICaIty48BpQX+xMlOU7EuVIygV9n7ubyKjoFnL/kCjpGNbI6CICAFArhBsXklNQJGv2JulA88vRNGvTk4+nu9wc00KmDm7HsG4AgMMj3Dg5k8ksm4+flc+3J8rqvWckp6DY+piaTfiOXuEyontzaeTrZWg5AQCwFcKNE8rMK5RNR87Kz4dTZd2BFDmdkWd9rFVTf7m9Z4Tc1jNcWjZlYUsAgPMh3DiBYpNZdp9Kl58Pp8mGQ6myMyFd32fRyNdTRkU3lzt6RUjvVo2ZeA8A4NQINw5IBZfjaRdk+8nzsuFQmmw8kiYZuYXlntM2uIFc0yFErm4fLIOigsXXi3WfAACugXDjAEO1T5zN0TUze05lyO7EDNmXmCHZZfrOWGpnBrULtgaayCY0OQEAXBPhxo5k5BTK8bPZulbmYNIF2ZOYLrtPZUhWXtElz/Xz8pBu4QEyUAeaYImJCBJPD3dDyg0AgD0h3NSz7PwiSTifI8dTs+VYmgoyf1zOZRdU+BpvT3fp2iJAosMDpXtEkERHBEq7kIbioSamAQAA9hdu5s+fLy+99JIkJSVJTEyMvPHGG9KvX79Kn79s2TKZOXOmnDhxQtq3by8vvPCCjBgxQowecp2WnS/JGfl6grzkzDxJUpeMfOt2ckaeZOVfWgtTVmiAj7QJbqDDS3cdZgKlQ2gj8aJWBgAAxwg3S5culenTp8vChQulf//+Mm/ePBk+fLgcPHhQmjVrdsnzN23aJGPHjpU5c+bIqFGjZPHixXLrrbfKjh07pFu3bmIU1al3/KKt1XpuoJ+XDjCq06+6bhNSct26aQNp4GP4KQEAwKG5mVWPVQOpQNO3b19588039W2TySSRkZHy4IMPymOPPXbJ88eMGSPZ2dny9ddfW+8bMGCA9OjRQweky8nMzJTAwEDJyMiQgIAAm+3H4eQsGT5vg4Q08pGwAF8JDfCVsMDS67Lbgb7SkAADAECN1OT729BqgoKCAtm+fbvMmDHDep+7u7sMGzZM4uLiKnyNul/V9JSlanpWrFhR4fPz8/P1pezBqQuqGenQv26iUy8AAAYzdHhNWlqaFBcXS2hoaLn71W3V/6Yi6v6aPF81X6mkZ7moWqG64O7uRrABAMAOOP3YYVUrpKqwLJeEhASjiwQAAOqQoc1SwcHB4uHhIcnJyeXuV7fDwsIqfI26vybP9/Hx0RcAAOAaDK258fb2lt69e8vatWut96kOxep2bGxsha9R95d9vvL9999X+nwAAOBaDB93rDoHT5gwQfr06aPntlFDwdVoqIkTJ+rHx48fL+Hh4brvjPLwww/LtddeK6+88oqMHDlSlixZItu2bZO3337b4D0BAAD2wPBwo4Z2p6amyqxZs3SnYDWke82aNdZOw/Hx8XoElcXAgQP13DZPPvmkPP7443oSPzVSysg5bgAAgP0wfJ6b+lZX89wAAAD7+P52+tFSAADAtRBuAACAUyHcAAAAp0K4AQAAToVwAwAAnArhBgAAOBXCDQAAcCqGT+JX3yzT+qjx8gAAwDFYvrerMz2fy4WbrKwsfR0ZGWl0UQAAQC2+x9VkflVxuRmK1cKcp0+flkaNGombm5vNU6UKTQkJCU45+7Gz758r7CP75/g4h47N2c9fXe6jiisq2LRo0aLcskwVcbmaG3VAIiIi6vTfUCfTWX9oXWH/XGEf2T/Hxzl0bM5+/upqHy9XY2NBh2IAAOBUCDcAAMCpEG5syMfHR2bPnq2vnZGz758r7CP75/g4h47N2c+fveyjy3UoBgAAzo2aGwAA4FQINwAAwKkQbgAAgFMh3AAAAKdCuKnEhg0bZPTo0XomRDWT8YoVK8o9rvphz5o1S5o3by5+fn4ybNgwOXz48GUP+Pz586V169bi6+sr/fv3l61bt4q97V9hYaE8+uij0r17d2nQoIF+zvjx4/XMzlV56qmn9HuVvXTq1Ens9Rz+9a9/vaS8N954o1OcQ+XifbNcXnrpJYc4h3PmzJG+ffvq2cSbNWsmt956qxw8eLDcc/Ly8uT++++Xpk2bSsOGDeWOO+6Q5OTkKt+3tp/d+t6/c+fOyYMPPigdO3bU5WzZsqU89NBDkpGRUeX71vbn2qhzOHjw4EvKO2XKFKc4hydOnKj0c7hs2TK7P4cLFiyQ6Oho62R8sbGxsnr1aof4/BFuKpGdnS0xMTH6i6wiL774orz++uuycOFC2bJliw4Bw4cP1ye7MkuXLpXp06frIXI7duzQ769ek5KSIva0fzk5Obp8M2fO1NfLly/XH9ibb775su/btWtXOXPmjPWyceNGsddzqKhfGGXL+8knn1T5no5yDpWy+6UuixYt0r8k1S8gRziHP/30k/7FuXnzZvn+++916L7hhhv0fltMmzZNvvrqK/1FoZ6vAvjtt99e5fvW5rNrxP6pfVGXl19+Wfbu3SsffPCBrFmzRu69997LvndNf66NPIfKpEmTypVXnSNnOIdqCYKLP4dPP/20DgI33XST3Z/DiIgIef7552X79u2ybds2GTp0qNxyyy2yb98++//8qaHgqJo6TF988YX1tslkMoeFhZlfeukl633p6elmHx8f8yeffFLp+/Tr1898//33W28XFxebW7RoYZ4zZ45d7V9Ftm7dqp938uTJSp8ze/Zsc0xMjNkeVbSPEyZMMN9yyy01eh9HPodqX4cOHVrlc+z5HKakpOj9/Omnn6yfOS8vL/OyZcusz9m/f79+TlxcXIXvUdvPrhH7V5FPP/3U7O3tbS4sLKz0ObX5uTZyH6+99lrzww8/XO33cPRz2KNHD/M999xT5fvY8zls3Lix+d1337X7zx81N7Vw/PhxSUpK0tVpZde7UE0UcXFxFb6moKBAp9+yr1HrXKnblb3GnqiqcPVXf1BQUJXPU9WLqpmkbdu2cvfdd0t8fLzYs/Xr1+vqZFX1P3XqVDl79mylz3Xkc6iqiletWlWtv/rt9RxammOaNGmir9W5UH8plz0fqglNNd9Udj5q89k1av8qe45qHvD09LTZz7U97ON///tfCQ4Olm7dusmMGTN07XFlHPkcqp/ZXbt2VetzaG/nsLi4WJYsWaJrpVTzlL1//lxu4UxbUCdHCQ0NLXe/um157GJpaWn6h6Oi1xw4cEDsmaouVH1wxo4dW+UiaOoHVFWdqw+jpfr16quv1lXqqk3a3qhqX1WF2qZNGzl69Kg8/vjjuqpYfcg8PDyc6hx++OGH+hxcrsrYXs+hyWSSRx55RAYNGqS/ABX1WfP29r4kcFf1OazNZ9eo/avo5+/ZZ5+VyZMn2/Tn2uh9vOuuu6RVq1Y6UO/evVv/rlHN4Ko53NnO4XvvvSedO3eWgQMHOsw53LNnjw4z6ntANad98cUX0qVLFx3S7PnzR7hBlVQy/3//7//pTmCqc1lVyrYhq05o6otS/dL69NNPq/WXSn278847rduq87Qqc7t27fRfTNddd504E9XfRtXCqE7QjngOVb8GFbCM7MNl5P5lZmbKyJEj9ZeK6vTtiD/Xle1j2bCmyqs6mqpyqi91VW5nOYe5ubmyePFi3ZfxcuzpHHbs2FEHGVUr9dlnn8mECRN0/xp7R7NULYSFhenri3uFq9uWxy6mqlxV4q7Ja+wl2Jw8eVJ3lqvp0vUq0Xfo0EGOHDkijkA1w6jzVFl5HfEcKj///LP+S/i+++6r8Wvt4Rw+8MAD8vXXX8u6det0B0cLdcxVU2F6enq1z0dtPrtG7Z9FVlaW/kte1Zypv5q9vLxs+nNtD/tYlgrUSmXldcRzqKhgoJrb1MjTmjLyHHp7e0tUVJT07t1bjw5Tgxhee+01u//8EW5qQVUVqhOxdu3acn9ZqZ7fqvqush8Q9cNR9jWqGlPdruw19hBsVP+LH374QQ/1q6kLFy7ov77UX2KO4NSpU7pdu7LyOto5LFsVrsqtfik50jlUtYXqS0N9of/444/6c1eW2if1RV/2fKgQp/oIVXY+avPZNWr/LGVTo2/Uz96XX3552Zq32vxcG72PF1O1BEpl5XW0c1j2c6hGnIaEhDjUObyY+p2Xn59v/58/m3ZPdiJZWVnmnTt36os6THPnztXbltFCzz//vDkoKMi8cuVK8+7du3XP9jZt2phzc3Ot76FGprzxxhvW20uWLNG9wj/44APz77//bp48ebJ+j6SkJLvav4KCAvPNN99sjoiIMO/atct85swZ6yU/P7/S/fvf//1f8/r1683Hjx83//LLL+Zhw4aZg4OD9QgCI1S1j+qxv//977pXvyrvDz/8YO7Vq5e5ffv25ry8PIc/hxYZGRlmf39/84IFCyp8D3s+h1OnTjUHBgbq8pT9GczJybE+Z8qUKeaWLVuaf/zxR/O2bdvMsbGx+lJWx44dzcuXL7fers5n1x72T527/v37m7t3724+cuRIuecUFRVVuH/V/bm2l31U+/XMM8/oc6fKq85J27Ztzddcc41TnEOLw4cPm93c3MyrV6+u8H3s9Rw+9thjeuSXKoc6zuq22o/vvvvO7j9/hJtKrFu3Tn9hXHxRQ/QsQ9pmzpxpDg0N1V921113nfngwYPl3qNVq1Z6aG1Z6otE/TCo4ZxqWPHmzZvN9rZ/6ge5osfURb2usv0bM2aMuXnz5nrfwsPD9W31y8soVe2j+uVzww03mENCQvRwRrUvkyZNuiSkOOo5tHjrrbfMfn5+erhlRez5HFb2M/j+++9bn6N+If7tb3/Tw1NViLvtttv0l8vF71P2NdX57NrD/lV2ftVFfUYr2r/q/lzbyz7Gx8frINOkSRN9LqKiosz/+Mc/dLBzhnNoMWPGDHNkZKSeOqKy97HHc3jPPffof1/9PlDlUcfZEmzs/fPnVvqPAwAAOAX63AAAAKdCuAEAAE6FcAMAAJwK4QYAADgVwg0AAHAqhBsAAOBUCDcAAMCpEG4AAIBTIdwAAACnQrgB4PB2794tt99+u17gVS0u2bVrV3nppZekqKjI6KIBMADhBoBD27BhgwwYMED8/Pxk5cqV8ttvv8mjjz4qc+fO1YFHrWIMwLWwthQAh1VcXCwdOnSQ2NhY+fjjj8s9duDAAYmOjpYFCxbIvffea1gZAdQ/wg0AhxUXFycDBw6UXbt2SUxMzCWP33bbbZKdnS3fffedIeUDYAyapQA4rOPHj+vr9u3bV/i4uv/kyZP1XCoARiPcAHBYAQEB+vrcuXMVPn7+/HnrcwC4DsINAIel+tp4eXnJV199VWF/nG+//VauuuoqQ8oGwDiEGwAOSw39fuihh+Rf//qXnD59utxjr776qq7RmTZtmmHlA2AMwg0Ah3XhwgUdblq3bi1DhgyRHTt26PvVHDePP/64vPHGG+Lt7a1rcQC4DkZLAXBYTz31lDz99NPW2xMmTJAPPvhA3NzcLul4rAIQANdAuAEAAE6FZikAAOBUCDcAAMCpEG4AAIBTIdwAAACnQrgBAABOhXADAACcCuEGAAA4FcINAABwKoQbAADgVAg3AADAqRBuAACAOJP/Dy6bH2qEIb05AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define a function to compute the population in the final state as a function of the drive\n", "fpop = lambda omega: propagate(kvec, phi0, tfinal, delta, omega_fnc, np.array([omega]), phase_fnc, np.array([]), atol=1e-6, rtol=1e-6).population(2*nf)\n", "\n", "# Compute along an array of omega values\n", "omegas = np.linspace(10,30)\n", "pops = np.full_like(omegas, np.nan)\n", "for i in range(len(omegas)):\n", " pops[i] = fpop(omegas[i])\n", "\n", "# Plot\n", "fig, ax1 = plt.subplots()\n", "ax1.plot(omegas, pops)\n", "ax1.set_ylabel(r'population')\n", "ax1.set_xlabel(r'$\\Omega$')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "3fc63522-e812-4338-8a51-87c6ef04eef7", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Bloch oscillations" ] }, { "cell_type": "markdown", "id": "e946c826-9da0-473c-aca8-8fcde53e2d73", "metadata": {}, "source": [ "The lattice velocity should initially be that of the atoms and should be swept at rate $\\alpha$ until the lattice velocity reaches our target velocity. Mathematically this works out to be\n", "$$\\delta_0=8n_0\\omega_r$$\n", "$$\\delta(t)=\\delta_0+\\alpha t$$\n", "$$\\delta_f=8n_f\\omega_r$$\n", "The phase of the drive is therefore\n", "$$\\theta(t)=\\delta_0t+\\frac{1}{2}\\alpha t^2$$\n", "The sweep should be stopped at\n", "$$t_f=(\\delta_f-\\delta_0)/\\alpha=8(n_f-n_0)\\omega_r/\\alpha$$\n", "Lets try this out with fifth order Bloch" ] }, { "cell_type": "code", "execution_count": 3, "id": "2dd75163-d41d-4b57-a0ca-78284191e9a3", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mwave.integrate import propagate, make_kvec, make_phi\n", "from numba import jit\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "# Define pulse parameters\n", "n0, nf = 0, 5\n", "omega = 2\n", "alpha = 1\n", "\n", "# Compute parameters\n", "delta0 = 8*n0\n", "deltaf = 8*nf\n", "tfinal = (deltaf-delta0)/alpha\n", "\n", "# Define a constant pulse profile\n", "@jit(nopython=True)\n", "def omega_fnc(t, args):\n", " omega = args[0]\n", " return omega\n", "\n", "# Define a quadratically ramped phase\n", "@jit(nopython=True)\n", "def phase_fnc(t, args):\n", " return delta0*t+0.5*alpha*t**2 # The phase is the integral of the time dependent frequency over time\n", "\n", "# Write out a function for the detuning vs time (this is just for plotting)\n", "def delta_fnc(t):\n", " return delta0+alpha*t\n", "\n", "# Define the initial state and the kvec array\n", "kvec, n0_idx, nf_idx = make_kvec(n0, nf)\n", "phi0 = make_phi(kvec, n0)\n", "\n", "# Integrate the pulse\n", "result = propagate(kvec, phi0, tfinal, 0, omega_fnc, np.array([omega]), phase_fnc, np.array([]))\n", "sol = result.scipy_sol\n", "\n", "# Determine the minimum and maximum indicies\n", "n_max = max(n0_idx, nf_idx)\n", "n_min = min(n0_idx, nf_idx)\n", "\n", "# Plot\n", "fig, [ax1, ax2, ax3] = plt.subplots(nrows = 3, sharex=True, gridspec_kw={'height_ratios': [2, 1, 1]})\n", "ax1.plot(sol.t, np.abs(sol.y.T[:,n_min-2:n_max+2])**2, label=[r\"$%i\\hbar k$\" % k for k in kvec[n_min-2:n_max+2]])\n", "ax2.plot(sol.t, [omega_fnc(t, np.array([omega])) for t in sol.t])\n", "ax3.plot(sol.t, [delta_fnc(t) for t in sol.t])\n", "ax1.legend(bbox_to_anchor=(1.05, 0.95))\n", "ax1.set_ylabel(r'population')\n", "ax2.set_ylabel(r'$\\Omega(t)$')\n", "ax3.set_ylabel(r'$\\delta(t)$')\n", "ax3.set_xlabel(r'time [$\\omega_r$]')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4fea2f3a-a818-4007-9800-a4a6639c47a3", "metadata": { "editable": true, "raw_mimetype": "text/restructuredtext", "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "There we go! Note that this simulation does not include any effect of loading the lattice, etc.\n", "\n", "We can easily account for single photon scattering by including the `Gamma_sps` parameter in our call to the :py:func:`mwave.integrate.propagate` function. This causes :py:func:`mwave.integrate.propagate` to integrate the density matrix instead of the wavefunction." ] }, { "cell_type": "code", "execution_count": 4, "id": "5b4674e6", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mwave.integrate import propagate, make_kvec, make_phi\n", "from numba import jit\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "# Define pulse parameters\n", "n0, nf = 0, 5\n", "omega = 2\n", "alpha = 1\n", "Gamma_sps = 0.5\n", "\n", "# Compute parameters\n", "delta0 = 8*n0\n", "deltaf = 8*nf\n", "tfinal = (deltaf-delta0)/alpha\n", "\n", "# Define a constant pulse profile\n", "@jit(nopython=True)\n", "def omega_fnc(t, args):\n", " omega = args[0]\n", " return omega\n", "\n", "# Define a quadratically ramped phase\n", "@jit(nopython=True)\n", "def phase_fnc(t, args):\n", " return delta0*t+0.5*alpha*t**2 # The phase is the integral of the time dependent frequency over time\n", "\n", "# Write out a function for the detuning vs time\n", "def delta_fnc(t):\n", " return delta0+alpha*t\n", "\n", "# Define the initial state and the kvec array\n", "kvec, n0_idx, nf_idx = make_kvec(n0, nf)\n", "phi0 = make_phi(kvec, n0)\n", "\n", "# Integrate the pulse. Passing Gamma_sps switches propagate to density-matrix\n", "# evolution, so result.scipy_sol.y has shape (N, N, len(t)).\n", "result = propagate(kvec, phi0, tfinal, 0, omega_fnc, np.array([omega]), phase_fnc, np.array([]), Gamma_sps=Gamma_sps)\n", "sol = result.scipy_sol\n", "pops = np.diagonal(sol.y)\n", "\n", "# Determine the minimum and maximum indicies\n", "n_max = max(n0_idx, nf_idx)\n", "n_min = min(n0_idx, nf_idx)\n", "\n", "# Plot\n", "fig, [ax1, ax2, ax3] = plt.subplots(nrows = 3, sharex=True, gridspec_kw={'height_ratios': [2, 1, 1]})\n", "ax1.plot(sol.t, np.real(pops[:,n_min-2:n_max+2]), label=[r\"$%i\\hbar k$\" % k for k in kvec[n_min-2:n_max+2]])\n", "ax2.plot(sol.t, [omega_fnc(t, np.array([omega])) for t in sol.t])\n", "ax3.plot(sol.t, [delta_fnc(t) for t in sol.t])\n", "ax1.legend(bbox_to_anchor=(1.05, 0.95))\n", "ax1.set_ylabel(r'population')\n", "ax2.set_ylabel(r'$\\Omega(t)$')\n", "ax3.set_ylabel(r'$\\delta(t)$')\n", "ax3.set_xlabel(r'time [$\\omega_r$]')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.12" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }