{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# $F=0 \\rightarrow F'=1$ MOT capture\n", "\n", "This script shows examples about how to solve for the dynamics of a 1D MOT and\n", "calculate things like the capture velocity. We will deal specifically with a 1D MOT.\n", "We can compare results to those of 1 D. Haubrich, A. Höpe, and D. Meschede, “A simple model for optical capture of atoms in strong magnetic quadrupole fields” _Optics Communications_ __102__, 225 (1993). http://dx.doi.org/10.1016/0030-4018(93)90387-K\n", "\n", "In this example, we will mostly focus on the heuristic force equation for an $F=0\\rightarrow F'=1$ atom in a magnetic field:\n", "\n", "$$\n", "\\mathbf{f} = \\frac{\\hbar \\mathbf{k} \\Gamma}{2}\\sum_{q,i} \\frac{s_i (\\epsilon'_{q,i})^2}{1+\\sum_js_j + 4[\\Delta - \\mathbf{k}_i\\cdot \\mathbf{v} - q \\mu_B B(r)/\\hbar]^2/\\Gamma^2}\n", "$$\n", "\n", "where $\\mathbf{f}$ is the force, $\\Gamma$ is the decay, $q=-1,0,1$, $s_i$, $\\boldsymbol{\\epsilon}'_{q,i}$, and $\\mathbf{k}_i$ are the intensity, polarization (rotated along the local magnetic field) and wavevector of the $i$th laser beam, respectively. All laser parameters can can depend on time $t$ and position $\\mathbf{r}$. This equation is encoded in `pylcp.heuristiceq`. Of course, one can also switch to the rate equations by loading `pylcp.rateeq`.\n", "\n", "We'll use the standard 3D MOT quadrupole field,\n", "\n", "$$\n", "\\mathbf{B} = B'\\left(-\\frac{1}{2}(x\\hat{x} + y\\hat{y})+z\\hat{z}\\right)\n", "$$\n", "\n", "where $B'$ is the magnetic field gradient." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.constants as cts\n", "from scipy.optimize import bisect #For root finding\n", "import pylcp\n", "import pylcp.atom as atom\n", "from pylcp.common import progressBar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Choose the units:\n", "As with any problem in `pylcp`, the units that one chooses are arbitrary. For this example, we are going to get fancy and use a special unit system that is only possible with the heuristic equation or, when magnetic forces are not included, the rate equations. As in the documentation, we will denote all explicit units with a subscript and all quantities where we have removed the units with an overbar, e.g. $\\bar{x} = x/x_0$. Let's choose units where the heuristic force is given by (along the $\\hat{z}$ axis):\n", "\n", "$$\n", "\\bar{\\mathbf{f}} = \\frac{\\hat{\\mathbf{k}}}{2}\\sum_{q,i}\\frac{s_i (\\epsilon_{q,i}')^2}{1+\\sum_js_j + 4(\\delta - \\hat{\\mathbf{k}}_i\\cdot \\mathbf{\\bar{v}} - q \\bar{z})^2}\n", "$$\n", "\n", "where $\\delta = \\Delta/\\Gamma$. This is equivalent the above equation by setting $k/\\Gamma=1$ and $\\mu_B B'/(\\hbar \\Gamma)=1$. Or, in other words, we want a unit system that measures velocities in terms of $\\Gamma/k$, positions in terms of $\\hbar \\Gamma/\\mu_B B'$, and forces in terms of $\\hbar k \\Gamma$.\n", "\n", "Programmatically, it allows us to just specify the _unit_ vector for $\\mathbf{k}$ when we program `laserBeams`, set the magnetic field gradient parameter $\\alpha=1$, and set $\\Gamma=1$ ($\\hbar=1$ by default).\n", "\n", "So what are the length and time units of this system? Well, the length unit is given by $x_0 = \\hbar \\Gamma/\\mu_B B'$ and $t_0$ is defined such that\n", "\n", "$$\n", "\\bar{v} = \\frac{k v}{\\Gamma} = k \\frac{x_0}{\\Gamma t_0}\\bar{v}\n", "$$\n", "\n", "implying that\n", "\n", "$$\n", "t_0 = \\frac{k x_0}{\\Gamma}\n", "$$\n", "\n", "Finally, we need the mass, which is defined through the prefactor to the force equation. We'll factor out the magnitude of the $\\mathbf{k}$ vector because :\n", "\n", "$$\n", "\\ddot{\\mathbf{r}} = \\frac{\\mathbf{f}}{m} = \\frac{\\hbar k \\Gamma}{m}\\hat{\\mathbf{k}}\n", "$$\n", "\n", "Note that I neglected the sum, since that is dimensionless already. I can now put in the units explicitly:\n", "\n", "$$\n", "\\frac{x_0}{t_0^2} \\ddot{\\bar{\\mathbf{r}}} = \\frac{\\hbar k \\Gamma }{m}\\hat{\\mathbf{k}}\n", "$$\n", "\n", "Rearranging,\n", "\n", "$$\n", "\\ddot{\\bar{\\mathbf{r}}} = \\frac{\\hbar k \\Gamma t_0^2}{m x_0} \\hat{\\mathbf{k}} = \\frac{\\hbar k^2 t_0}{m}\\hat{\\mathbf{k}} = \\frac{\\bar{\\mathbf{f}}}{\\bar{m}}\n", "$$\n", "\n", "where $\\bar{m} = m/(\\hbar k^2 t_0)$.\n", "\n", "Note again that this unit system is effectively measuring lengths in two different ways - one in terms of $k$ and the other in terms of the magnetic field. This works because we have the mass term which we can adjust. However, if you wanted to include magnetic forces, or use the optical Bloch equations, this unit system will not work as the forces calculated in those schemes have quite a different constant.\n", "\n", "Plugging in the numbers, we find:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.2857142857142857 80553.65778435367 23015.33079552962 2.6525823848649224e-08 0.0006105006105006105\n", "0.03454474231473474\n" ] } ], "source": [ "x0 = (6/1.4/15) # cm\n", "k = 2*np.pi/780E-7 # cm^{-1}\n", "kbar = k*x0\n", "\n", "gamma = 2*np.pi*6e6\n", "t0 = k*x0/gamma\n", "print(x0, k, kbar, 1/gamma, t0)\n", "\n", "mass = 86.909180527*cts.value('atomic mass constant')/(cts.hbar*(k*1e2)**2*t0)\n", "print(mass)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the problem\n", "\n", "As always, we must define the laser beams, magnetic field and Hamiltonian." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "det = -1.5\n", "alpha = 1.0\n", "s = 1.0\n", "\n", "laserBeams = pylcp.laserBeams([\n", " {'kvec':np.array([0., 0., 1.]), 'pol':np.array([0., 0., 1.]), 's':s, 'delta':det},\n", " {'kvec':np.array([0., 0., -1.]), 'pol':np.array([1., 0., 0.]), 's':s, 'delta':det}],\n", " beam_type=pylcp.infinitePlaneWaveBeam\n", ")\n", "\n", "magField = pylcp.quadrupoleMagneticField(alpha)\n", "\n", "# Use the heuristic equation (or comment it out):\n", "eqn = pylcp.heuristiceq(laserBeams, magField, gamma=1, mass=mass)\n", "\n", "# Define the atomic Hamiltonian:\n", "# Hg, muqg = pylcp.hamiltonians.singleF(F=0, muB=1)\n", "# He, muqe = pylcp.hamiltonians.singleF(F=1, muB=1)\n", "\n", "# dq = pylcp.hamiltonians.dqij_two_bare_hyperfine(0, 1)\n", "\n", "# hamiltonian = pylcp.hamiltonian(Hg, He, muqg, muqe, dq, mass=mass)\n", "\n", "# eqn = pylcp.rateeq(laserBeams, magField, hamiltonian, include_mag_forces=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute equilibrium force\n", "\n", "As with the previous example, we will calculate over the 2D phase space defined by $z$ and $v_z$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 29.65 s. \n" ] } ], "source": [ "dz = 0.1\n", "dv = 0.1\n", "z = np.arange(-20, 20+dz, dz)\n", "v = np.arange(-20, 20+dv, dv)\n", "\n", "Z, V = np.meshgrid(z, v)\n", "\n", "Rfull = np.array([np.zeros(Z.shape), np.zeros(Z.shape), Z])\n", "Vfull = np.array([np.zeros(Z.shape), np.zeros(Z.shape), V])\n", "\n", "eqn.generate_force_profile([np.zeros(Z.shape), np.zeros(Z.shape), Z],\n", " [np.zeros(V.shape), np.zeros(V.shape), V],\n", " name='Fz', progress_bar=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot up the result:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "plt.imshow(eqn.profile['Fz'].F[2], origin='bottom',\n", " extent=(np.amin(z)-dz/2, np.amax(z)-dz/2,\n", " np.amin(v)-dv/2, np.amax(v)-dv/2),\n", " aspect='auto')\n", "cb1 = plt.colorbar()\n", "cb1.set_label('$f/(\\hbar k \\Gamma)$')\n", "ax.set_xlabel('$x/(\\hbar \\Gamma/\\mu_B B\\')$')\n", "ax.set_ylabel('$v/(\\Gamma/k)$')\n", "fig.subplots_adjust(left=0.12,right=0.9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Add trajectories in phase space\n", "\n", "We'll use the evolve motion method to evolve the particle and simulate capture. But we also need to define some stop conditions, either when the atom is captured at the origin or lost to \"$+\\infty$\"." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "v0s = np.arange(1, 15.5, 1)\n", "\n", "# See solve_ivp documentation for event function discussion:\n", "def captured_condition(t, y, threshold=1e-5):\n", " if(y[-4]20.:\n", " val = -1.\n", " else:\n", " val = 1.\n", " \n", " return val\n", "\n", "captured_condition.terminal=True\n", "lost_condition.terminal=True\n", "\n", "sols = []\n", "for v0 in v0s:\n", " eqn.set_initial_position_and_velocity(np.array([0., 0., z[0]]),\n", " np.array([0., 0., v0]))\n", " if isinstance(eqn, pylcp.rateeq):\n", " eqn.set_initial_pop(np.array([1., 0., 0., 0.]))\n", "\n", " eqn.evolve_motion([0., 100.], events=[captured_condition, lost_condition], max_step=0.1)\n", " \n", " sols.append(eqn.sol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, plot up the additional trajectories in white:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "plt.imshow(eqn.profile['Fz'].F[2], origin='bottom',\n", " extent=(np.amin(z)-dz/2, np.amax(z)-dz/2,\n", " np.amin(v)-dv/2, np.amax(v)-dv/2),\n", " aspect='auto')\n", "cb1 = plt.colorbar()\n", "cb1.set_label('$f/(\\hbar k \\Gamma)$')\n", "ax.set_xlabel('$x/(\\hbar \\Gamma/\\mu_B B\\')$')\n", "ax.set_ylabel('$v/(\\Gamma/k)$')\n", "\n", "fig.subplots_adjust(left=0.15, right=0.91, bottom=0.2)\n", "\n", "for sol in sols:\n", " ax.plot(sol.r[2], sol.v[2], 'w-', linewidth=0.375)\n", "\n", "ax.yaxis.set_ticks([-20, -10, 0, 10, 20])\n", "# Display the figure at the end of the thing.\n", "ax.set_xlim((-20, 20))\n", "ax.set_xlim((-20, 20));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By having two conditions, we can tell if the atom was lost or captured:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "captured\n", "captured\n", "captured\n", "captured\n", "captured\n", "captured\n", "lost\n", "lost\n", "lost\n", "lost\n", "lost\n", "lost\n", "lost\n", "lost\n", "lost\n" ] } ], "source": [ "for sol in sols:\n", " if len(sol.t_events[0]) == 1:\n", " print('captured')\n", " elif len(sol.t_events[1]) == 1:\n", " print('lost')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve for the capture velocity $v_c$\n", "\n", "Let's define a function that figures out if we were captured or not, then use that to find the capture velocity:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def iscaptured(v0, z0, eqn, captured_condition, lost_condition, tmax=1000, max_step=0.1, **kwargs):\n", " eqn.set_initial_position_and_velocity(np.array([0., 0., z0]),\n", " np.array([0., 0., v0]))\n", " eqn.evolve_motion([0., tmax], events=[captured_condition, lost_condition],\n", " max_step=max_step)\n", " \n", " if len(eqn.sol.t_events[0]) == 1:\n", " return +1.\n", " else:\n", " return -1.\n", " \n", "iscaptured(1.3, z[0], eqn, captured_condition, lost_condition)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use `scipy.optimize.bisect` to see where the `iscaptured` function changes from `-1` (false) to `1` (true):" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6.20770263671875,\n", " converged: True\n", " flag: 'converged'\n", " function_calls: 17\n", " iterations: 15\n", " root: 6.20770263671875)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bisect(iscaptured, 1.0, 15.,\n", " args=(z[0], eqn, captured_condition, lost_condition),\n", " xtol=1e-4, rtol=1e-4, full_output=True\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dependence of $v_c$ on detuning and intensity\n", "\n", "We will figure out how the capture velocity depends on and compare to this equation from the paper in the introduction:\n", "\n", "$$\n", "v_c = \\left(\\frac{a_0^2s^2\\kappa}{(1+s)^{3/2}}\\right)^{1/3}\\left(\\frac{8\\pi\\delta^2}{1+s+4\\delta^2}\\right)^{1/3}\\zeta^{-2/3}\n", "$$\n", "\n", "where $a_0 = \\hbar k \\Gamma/(2 m)$, $\\zeta = \\mu_B B'/(\\hbar\\Gamma)$, and $\\kappa = 2\\pi/(\\lambda \\Gamma)=k/\\Gamma$ . To compare, we need to express it in a way which connects with our formulae above. The first thing to note is that $\\zeta = 1/x_0$. We also need to multiple both sides by $k/\\Gamma$, so that we have $v_c/(\\Gamma/k)$ on the left side, which is our observable. Then, we realize that\n", "\n", "$$\n", "\\frac{\\hbar k\\Gamma}{2m} = \\frac{1}{2\\bar{m}}\\frac{x_0}{t_0^2}~~~~~\\text{and}~~~~~\\frac{k}{\\Gamma} = \\frac{t_0}{x_0} \n", "$$\n", "\n", "Putting it all together:\n", "\n", "$$\n", "\\frac{v_c}{\\Gamma/k} = \\frac{t_0}{x_0}\\left(\\frac{1}{2\\bar{m}}\\right)^{2/3} \\frac{x_0^{2/3}}{t_0^{4/3}}\\frac{t_0^{1/3}}{x_0^{1/3}} x_0^{2/3}\\left(\\frac{s^2}{(1+s)^{3/2}}\\right)^{1/3}\\left(\\frac{8\\pi\\delta^2}{1+s+4\\delta^2}\\right)^{1/3} = \\left(\\frac{1}{2\\bar{m}}\\right)^{2/3}\\left(\\frac{s^2}{(1+s)^{3/2}}\\right)^{1/3}\\left(\\frac{8\\pi\\delta^2}{1+s+4\\delta^2}\\right)^{1/3}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 15:07. \n" ] } ], "source": [ "dets = -np.logspace(-1, np.log10(5), 30)[::-1]\n", "intensities = np.array([0.3, 1., 3.])\n", "\n", "DETS, INTENSITIES = np.meshgrid(dets, intensities)\n", "\n", "it = np.nditer([DETS, INTENSITIES, None, None],\n", " op_dtypes=['float64', 'float64', 'float64', np.object])\n", "\n", "progress = progressBar()\n", "for (det, s, vc, full_results) in it:\n", " laserBeams = pylcp.laserBeams([\n", " {'kvec':np.array([0., 0., 1.]), 'pol':np.array([0., 0., 1.]), 's':s, 'delta':det},\n", " {'kvec':np.array([0., 0., -1.]), 'pol':np.array([1., 0., 0.]), 's':s, 'delta':det}],\n", " beam_type=pylcp.infinitePlaneWaveBeam\n", " )\n", "\n", " # Heuristic equation or rate equation?\n", " eqn = pylcp.heuristiceq(laserBeams, magField, gamma=1, mass=mass)\n", " #eqn = pylcp.rateeq(laserBeams, magField, hamiltonian, include_mag_forces=False)\n", " \n", " if isinstance(eqn, pylcp.rateeq):\n", " eqn.set_initial_pop(np.array([1., 0., 0., 0.]))\n", " \n", " vc[...], full_results[...] = bisect(\n", " iscaptured, 0.5, 15.0,\n", " args=(z[0], eqn, captured_condition, lost_condition),\n", " rtol=1e-4, xtol=1e-4, full_output=True\n", " )\n", "\n", " progress.update((it.iterindex+1)/it.itersize)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def vc_from_paper(delta, s, mbar):\n", " return 1/(2*mbar)**(2./3.)*(s**2/(1+s)**(3./2.))**(1./3.)*(8*np.pi*delta**2/(1+s+4*delta**2))**(1./3.)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dets_thr = -np.logspace(-1, np.log10(5), 51)[::-1]\n", "fig, ax = plt.subplots(1, 1, figsize=(3.25, 2))\n", "for ii, (s, vc_vs_det) in enumerate(zip(intensities, it.operands[2])):\n", " ax.plot(dets, vc_vs_det, label='$s=%.1f$' % s,\n", " color='C%d'%ii, linewidth=0.75)\n", " ax.plot(dets_thr, vc_from_paper(dets_thr, s, mass), '--',\n", " color='C%d'%ii, linewidth=0.5)\n", "\n", "#ax.legend(fontsize=8)\n", "ax.set_xlabel('$\\Delta/\\Gamma$')\n", "ax.set_ylabel('$v_c/(\\Gamma/k)$')\n", "\n", "fig.subplots_adjust(left=0.13, bottom=0.2)" ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }