{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# $F=0 \\rightarrow F'=1$ MOT forces\n", "\n", "This example covers calculating the textbook example of forces in a one-dimensional MOT with an $F=0\\rightarrow F'=1$ atom. We will focus on two governing equations: the `heuristic` equation and the `rateeq`. In this example, we'll calculate the forces using both and compare. We will also calculate the trapping frequencies and damping coefficients as well." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp\n", "from pylcp.atom import atom\n", "import scipy.constants as cts" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Choose the units\n", "\n", "Whatever units we use, let's run numbers that are realistic for a common atom, Rb.:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "80528.75481555492 2.62348e-08 6066558.277246076\n" ] } ], "source": [ "rb87 = atom('87Rb')\n", "\n", "klab = 2*np.pi*rb87.transition[1].k # Lab wavevector (without 2pi) in cm^{-1}\n", "taulab = rb87.state[2].tau # Lifetime of 6P_{3/2} state (in seconds)\n", "gammalab = 1/taulab \n", "Blab = 15 # About 15 G/cm is a typical gradient for Rb\n", "\n", "print(klab, taulab, gammalab/2/np.pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As with any problem in `pylcp`, the units that one chooses are arbitrary. We will denote all explicit units with a subscript and all quantities where we have removed the units with an overbar, e.g. $\\bar{x} = x/x_0$. Our choice in this script will be different from the default choices of $x_0=1/k$ and $t_0 =1/\\Gamma$. Let's try a system where lengths are measured in terms of $x_0 = \\hbar\\Gamma/\\mu_B B'$ and $t_0 = k x_0/\\Gamma$. This unit system has the advantage that it measures lengths in terms of Zeeman detuning in the trap. Moreover, velocities are measured in $\\Gamma/k$. Namely,\n", "\n", "$$\n", "v = \\bar{v} \\frac{x_0}{t_0} = \\bar{v} \\frac{\\Gamma}{k}\n", "$$\n", "\n", "From the documentation, the consistent mass scale is\n", "\n", "$$\n", "\\bar{m} = m\\frac{x_0^2}{\\hbar t_0}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```\n", "# Now, here are our `natural' length and time scales:\n", "x0 = cts.hbar*gammalab/(cts.value('Bohr magneton')*1e-4*15) # cm\n", "t0 = klab*x0*taulab # s\n", "mass = 87*cts.value('atomic mass constant')*(x0*1e-2)**2/cts.hbar/t0\n", "\n", "# And now our wavevector, decay rate, and magnetic field gradient in these units:\n", "k = klab*x0\n", "gamma = gammalab*t0\n", "alpha = 1.0*gamma # The magnetic field gradient parameter\n", "\n", "print(x0, t0, mass, k, gamma, alpha)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we can just use the default unit system:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.2417924532552691e-05 2.62348e-08 805.2161255642717 1.0 1.0 4.297436175809039e-05\n" ] } ], "source": [ "# Now, here are our `natural' length and time scales:\n", "x0 = 1/klab # cm\n", "t0 = taulab # s\n", "\n", "mass = 87*cts.value('atomic mass constant')*(x0*1e-2)**2/cts.hbar/t0\n", "\n", "# And now our wavevector, decay rate, and magnetic field gradient in these units:\n", "k = klab*x0\n", "gamma = gammalab*t0\n", "alpha = cts.value('Bohr magneton')*1e-4*15*x0*t0/cts.hbar\n", "\n", "print(x0, t0, mass, k, gamma, alpha)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It turns out there is another choice of units, useful in the next example, \n", "that works extremely well if the radiative force is the *only* force." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the problem\n", "\n", "One has to define the Hamiltonian, laser beams, and magnetic field." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Define the atomic Hamiltonian:\n", "Hg, mugq = pylcp.hamiltonians.singleF(F=0, muB=1)\n", "He, mueq = pylcp.hamiltonians.singleF(F=1, muB=1)\n", "\n", "dijq = pylcp.hamiltonians.dqij_two_bare_hyperfine(0, 1)\n", "\n", "ham = pylcp.hamiltonian(Hg, He, mugq, mueq, dijq, mass=mass, gamma=gamma, k=k)\n", "\n", "det = -4.\n", "s = 1.5\n", "\n", "# Define the laser beams:\n", "laserBeams = pylcp.laserBeams(\n", " [{'kvec':k*np.array([1., 0., 0.]), 's':s, 'pol':-1, 'delta':det*gamma},\n", " {'kvec':k*np.array([-1., 0., 0.]), 's':s, 'pol':-1, 'delta':det*gamma}],\n", " beam_type=pylcp.infinitePlaneWaveBeam\n", ")\n", "\n", "# Define the magnetic field:\n", "linGrad = pylcp.magField(lambda R: -alpha*R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define both governing equations\n", "\n", "We'll add in the OBEs in a later example." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "rateeq = pylcp.rateeq(laserBeams, linGrad, ham, include_mag_forces=True)\n", "heuristiceq = pylcp.heuristiceq(laserBeams, linGrad, gamma=gamma, k=k, mass=mass)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculate equilibrium forces\n", "Let's define both positions and velocities and calculate the forces in the resulting 2D phase space" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Completed in 16.61 s. \n", "Completed in 4.26 s. \n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.arange(-30, 30, 0.4)/(alpha/gamma)\n", "v = np.arange(-30, 30, 0.4)\n", "\n", "X, V = np.meshgrid(x, v)\n", "\n", "Rvec = np.array([X, np.zeros(X.shape), np.zeros(X.shape)])\n", "Vvec = np.array([V, np.zeros(V.shape), np.zeros(V.shape)])\n", "\n", "rateeq.generate_force_profile(Rvec, Vvec, name='Fx', progress_bar=True)\n", "heuristiceq.generate_force_profile(Rvec, Vvec, name='Fx', progress_bar=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot it up, and compare to the heuristic force equation for this geometry, which is given by\n", "\n", "$$\n", "f = \\frac{\\hbar k\\Gamma}{2}\\left(\\frac{s}{1+2s +4(\\Delta - k v - \\mu_B B' x/\\hbar)^2/\\Gamma^2} - \\frac{s}{1+2s +4(\\Delta + k v + \\mu_B B' x/\\hbar)^2/\\Gamma^2}\\right).\n", "$$\n", "\n", "where $s = I/I_{\\rm sat}$. Note that the quadrupole field parameter defined above $\\alpha = \\mu_B B'/\\hbar$\n", "\n", "No matter what unit system we use above, we want to measure lengths in terms of the magnetic field. Dividing by the field gradient is enough to accomplish that:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$v/(\\\\Gamma/k)$')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "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(nrows=1, ncols=2, num=\"Expression\", figsize=(6.5, 2.75))\n", "\n", "ax[0].plot(x*(alpha/gamma), rateeq.profile['Fx'].F[0, int(np.ceil(x.shape[0]/2)), :]/gamma/k)\n", "ax[0].plot(x*(alpha/gamma), heuristiceq.profile['Fx'].F[0, int(np.ceil(x.shape[0]/2)), :]/gamma/k)\n", "ax[0].plot(x*(alpha/gamma), (s/(1+2*s + 4*(det-alpha*x/gamma)**2) - s/(1+2*s + 4*(det+alpha*x/gamma)**2))/2, 'k-', linewidth=0.5)\n", "ax[0].set_ylabel('$f/(\\hbar k \\Gamma)$')\n", "ax[0].set_xlabel('$x/(\\hbar \\Gamma/\\mu_B B\\')$')\n", "ax[0].set_xlim((-10, 10))\n", "\n", "im1 = ax[1].contourf(X*(alpha/gamma), V, rateeq.profile['Fx'].F[0]/gamma/k, 25)\n", "fig.subplots_adjust(left=0.08, wspace=0.2)\n", "cb1 = plt.colorbar(im1)\n", "cb1.set_label('$f/(\\hbar k \\Gamma)$')\n", "ax[1].set_xlabel('$x/(\\hbar \\Gamma/\\mu_B B\\')$')\n", "ax[1].set_ylabel('$v/(\\Gamma/k)$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that heuristic equation produces less force at resonance in $x$, because it is over-estimating the total saturation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute the trap frequencies and damping rates\n", "\n", "And we can compare to simple 1D theory. Let's take the force equation above and expand it about $x=0$ and $v=0$. We get\n", "\n", "$$\n", "f \\approx \\frac{\\hbar k}{2\\Gamma}\\left(\\frac{s \\Delta}{1+2s + 4\\Delta^2/\\Gamma^2}\\right)\\left( \\frac{\\mu_B B'}{\\hbar} x + k v\\right)\n", "$$\n", "\n", "The damping coefficient $\\beta$, most easily expressed in units of $\\hbar k^2$, and is given by\n", "\n", "$$\n", "\\frac{\\beta}{\\hbar k^2} = \\frac{8 s \\delta}{1 + 2s + 4\\delta^2}\n", "$$\n", "\n", "where $\\delta = \\Delta/\\Gamma$. Note that the trapping frequency is defined through \n", "\n", "$$\n", "\\ddot{x} - \\frac{\\beta}{m} \\dot{x} + \\omega^2 x = 0\n", "$$\n", "\n", "and therefore, its square is most easily measured in units of $k \\mu_B B'/m$,\n", "\n", "$$\n", "\\frac{\\omega^2}{k \\mu_B B'/m} = \\frac{8 s \\delta}{1 + 2s + 4\\delta^2}\n", "$$\n", "\n", "Note as well that we defined $\\alpha$, the quadrupole field parameter above to be $\\alpha = \\hbar \\mu_B B'$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dets = np.arange(-5, 0.05, 0.05)\n", "intensities = np.array([0.1, 1, 10])\n", "\n", "omega = np.zeros(intensities.shape + dets.shape)\n", "dampingcoeff = np.zeros(intensities.shape + dets.shape)\n", "\n", "omega_heuristic = np.zeros(intensities.shape + dets.shape)\n", "dampingcoeff_heuristic = np.zeros(intensities.shape + dets.shape)\n", "\n", "for ii, det in enumerate(dets):\n", " for jj, intensity in enumerate(intensities):\n", " # Define the laser beams:\n", " laserBeams = [None]*2\n", " laserBeams[0] = pylcp.laserBeam(kvec=k*np.array([1., 0., 0.]), s=intensity,\n", " pol=-1, delta=gamma*det)\n", " laserBeams[1] = pylcp.laserBeam(kvec=k*np.array([-1., 0., 0.]), s=intensity,\n", " pol=-1, delta=gamma*det)\n", "\n", " rateeq = pylcp.rateeq(laserBeams, linGrad, ham, include_mag_forces=False)\n", " heuristiceq = pylcp.heuristiceq(laserBeams, linGrad, gamma=gamma, mass=mass)\n", " \n", " omega[jj, ii] = rateeq.trapping_frequencies(axes=[0], eps=0.0002)\n", " dampingcoeff[jj, ii] = rateeq.damping_coeff(axes=[0], eps=0.0002)\n", " \n", " omega_heuristic[jj, ii] = heuristiceq.trapping_frequencies(axes=[0], eps=0.0002)\n", " dampingcoeff_heuristic[jj, ii] = heuristiceq.damping_coeff(axes=[0], eps=0.0002)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.75))\n", "for ii, intensity in enumerate(intensities):\n", " ax[0].plot(dets, omega[ii]/np.sqrt(k*alpha/mass), '-', color='C{0:d}'.format(ii),\n", " label='$s_0 = %.1f$'%intensity)\n", " ax[0].plot(dets, omega_heuristic[ii]/np.sqrt(k*alpha/mass), '--', color='C{0:d}'.format(ii))\n", " ax[0].plot(dets, np.sqrt(-8*dets*intensity/(1 + 2*intensity + 4*dets**2)**2), 'k-', linewidth=0.5)\n", " ax[1].plot(dets, dampingcoeff[ii]/k**2, '-', color='C{0:d}'.format(ii))\n", " ax[1].plot(dets, dampingcoeff_heuristic[ii]/k**2, '--', color='C{0:d}'.format(ii))\n", " ax[1].plot(dets, -8*dets*intensity/(1 + 2*intensity + 4*dets**2)**2, 'k-', linewidth=0.5)\n", "\n", "ax[0].legend(fontsize=7, loc='upper left')\n", "ax[1].set_ylabel('$\\\\beta/\\hbar k^2$')\n", "ax[0].set_ylabel('$\\\\omega/\\sqrt{k \\mu_B B\\'/m}$')\n", "ax[0].set_xlabel('$\\Delta/\\Gamma$')\n", "ax[1].set_xlabel('$\\Delta/\\Gamma$')\n", "\n", "fig.subplots_adjust(left=0.08, wspace=0.25)" ] } ], "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 }