{ "cells": [ { "cell_type": "markdown", "id": "4dda497a-9c6c-4dc9-97cc-a3986ad3c919", "metadata": {}, "source": [ "# Integrating the Bloch Hamiltonian" ] }, { "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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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mwave.integrate import bloch, 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", "sol = bloch(kvec, phi0, tfinal, delta, omega_fnc, np.array([omega]), phase_fnc, np.array([]))\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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", "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: np.abs(bloch(kvec, phi0, tfinal, delta, omega_fnc, np.array([omega]), phase_fnc, np.array([]), atol=1e-6, rtol=1e-6).y[nf_idx,-1])**2\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": null, "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 bloch, 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", "sol = bloch(kvec, phi0, tfinal, 0, omega_fnc, np.array([omega]), phase_fnc, np.array([]))\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": "raw", "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:meth:`mwave.integrate.bloch` function. This causes :py:meth:`mwave.integrate.bloch` to integrate the density matrix instead of the wavefunction." ] }, { "cell_type": "code", "execution_count": 2, "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 bloch, 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\n", "sol = bloch(kvec, phi0, tfinal, 0, omega_fnc, np.array([omega]), phase_fnc, np.array([]), Gamma_sps=Gamma_sps)\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": "3.11.0" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }