{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lifetimes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We calculate the lifetime of Rydberg states and analyze which transitions contribute to it. The calculations can be performed with a few lines of code; most of the code within this notebook is only needed for plotting." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import the libraries that we will use within the notebook." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from typing import Any\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.optimize import curve_fit\n", "\n", "import rydstate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a quick example, we show how to calculate the lifetime of the Rubidium $|60S,m=1/2\\rangle$ state via `state.get_lifetime`. At zero temperature, the lifetime is determined by the spontaneous decay. If the temperature is non-zero, black body radiation can drive transitions to neighboring Rydberg states, reducing the lifetime." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lifetime at T=0: 235.77 microsecond\n", "Lifetime at T=300K: 100.50 microsecond\n" ] } ], "source": [ "state = rydstate.RydbergStateSQDTAlkali(\"Rb\", n=60, l=0, j=0.5, m=0.5)\n", "\n", "temperature = 300 # Kelvin\n", "lifetime_0 = state.get_lifetime()\n", "lifetime = state.get_lifetime(temperature, temperature_unit=\"K\")\n", "\n", "print(f\"Lifetime at T=0: {lifetime_0.to('mus'):.2f}\")\n", "print(f\"Lifetime at T={temperature}K: {lifetime.to('mus'):.2f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Transition rates contributing to the Rydberg lifetime" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To analyze which transitions contribute to the lifetime, we can obtain the transition rates from spontaneous decay (`state.get_spontaneous_transition_rates`) and black body radiation (`state.get_black_body_transition_rates`)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of possible spontaneous decay transitions: 275\n", "Number of considered BBR transitions: 435\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Calculate the transition rates\n", "state_sp, transition_rates_sp = state.get_spontaneous_transition_rates(unit=\"1/mus\")\n", "print(f\"Number of possible spontaneous decay transitions: {len(transition_rates_sp)}\")\n", "\n", "state_bbr, transition_rates_bbr = state.get_black_body_transition_rates(temperature, \"kelvin\", unit=\"1/mus\")\n", "print(f\"Number of considered BBR transitions: {len(transition_rates_bbr)}\")\n", "\n", "# Plot the transition rates\n", "fig, ax = plt.subplots(figsize=(6, 5))\n", "\n", "n_list = np.arange(0, np.max([s.n for s in state_bbr]) + 1)\n", "rates_summed = {}\n", "for key, state, rates in [\n", " (\"BBR\", state_bbr, transition_rates_bbr),\n", " (\"SP\", state_sp, transition_rates_sp),\n", "]:\n", " rates_summed[key] = np.zeros(len(n_list))\n", " for i, s in enumerate(state):\n", " rates_summed[key][s.n] += rates[i]\n", "\n", "ax.bar(n_list, rates_summed[\"SP\"], label=\"Spontaneous Decay\", color=\"blue\", alpha=0.8)\n", "ax.bar(n_list, rates_summed[\"BBR\"], label=\"Black Body Radiation (BBR)\", color=\"red\", alpha=0.8)\n", "ax.legend()\n", "\n", "ax.set_xlabel(\"Principal Quantum Number $n$\")\n", "ax.set_ylabel(r\"Transition Rates (1 / $\\mu$s)\")\n", "ax.set_title(\"Spontaneous and BBR Transition Rates vs $n$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lifetime scaling with the principal quantum number" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a more sophisticated example, we study how the lifetime scales with the effective principal quantum number $\\nu$. Our numerics reproduce the $\\nu^3$ scaling which one expects for states with a small angular quantum number $l$. For circular states, the lifetime scales as $\\nu^5$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_list = list(range(30, 90, 5))\n", "\n", "\n", "def fit_function(x: np.ndarray, a: float, b: float) -> np.typing.NDArray[Any]:\n", " return a * x + b\n", "\n", "\n", "# Calculate lifetimes for S states\n", "kets_s = [rydstate.RydbergStateSQDTAlkali(\"Rb\", n=n, l=0, j=0.5, m=0.5) for n in n_list]\n", "nu_s = [ket.nu for ket in kets_s]\n", "lifetimes_s = [ket.get_lifetime(unit=\"mus\") for ket in kets_s]\n", "popt_s, _ = curve_fit(fit_function, np.log(nu_s), np.log(lifetimes_s))\n", "\n", "# Calculate lifetimes for circular states\n", "kets_circular = [rydstate.RydbergStateSQDTAlkali(\"Rb\", n=n, l=n - 1, j=n - 0.5, m=n - 0.5) for n in n_list]\n", "nu_circular = [ket.nu for ket in kets_circular]\n", "lifetimes_circular = [ket.get_lifetime(unit=\"mus\") for ket in kets_circular]\n", "popt_circular, _ = curve_fit(fit_function, np.log(nu_circular), np.log(lifetimes_circular))\n", "\n", "# Plot the scaling of the lifetimes\n", "fig, ax = plt.subplots(figsize=(6, 5))\n", "\n", "ax.plot(nu_s, lifetimes_s, \"o\", label=\"S states\")\n", "ax.plot(nu_circular, lifetimes_circular, \"o\", label=\"Circular states\")\n", "\n", "fit_s = np.exp(fit_function(np.log(nu_s), *popt_s))\n", "fit_circular = np.exp(fit_function(np.log(nu_circular), *popt_circular))\n", "ax.plot(nu_s, fit_s)\n", "ax.plot(nu_circular, fit_circular)\n", "\n", "ax.text(nu_s[2], fit_s[2], rf\"$\\propto \\nu^{{{popt_s[0]:.2f}}}$\", verticalalignment=\"top\")\n", "ax.text(\n", " nu_circular[2],\n", " fit_circular[2],\n", " rf\"$\\propto \\nu^{{{popt_circular[0]:.2f}}}$\",\n", " verticalalignment=\"top\",\n", ")\n", "\n", "ax.legend()\n", "ax.set_yscale(\"log\")\n", "ax.set_xscale(\"log\")\n", "ax.set_xlabel(r\"Effective Principal Quantum Number $\\nu$\")\n", "ax.set_ylabel(r\"Lifetime ($\\mu$s)\")\n", "\n", "ax.set_xticks([30, 40, 50, 60, 70, 80, 90])\n", "ax.get_xaxis().set_major_formatter(plt.ScalarFormatter())\n", "\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "rydstate", "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": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 1 }