{ "cells": [ { "cell_type": "markdown", "id": "277d0f13-9158-41c2-a440-86db82dbe650", "metadata": {}, "source": [ "![](Rydiqule_Logo_Transparent_300.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "63b89db6-ae2f-4091-9776-7b302e58bc1f", "metadata": { "tags": [] }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "id": "6c04d519-de54-40fc-8d47-6bb4408733b1", "metadata": { "tags": [] }, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": 3, "id": "6d186ffc-8285-43d5-8f5b-4367c409679b", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "from scipy.spatial.transform import Rotation as R" ] }, { "cell_type": "code", "execution_count": 4, "id": "c5df7ded-adf7-429f-a158-657262afe0f3", "metadata": { "tags": [] }, "outputs": [], "source": [ "import rydiqule as rq\n", "from rydiqule.sensor_utils import get_rho_ij" ] }, { "cell_type": "markdown", "id": "ec302cf6-2c1c-4664-b48b-fe5ef5494145", "metadata": {}, "source": [ "# 3-photon Rydberg EIT #\n", "\n", "This notebook can be downloaded [here](https://github.com/QTC-UMD/rydiqule/blob/main/docs/source/examples/3-photon_example.ipynb).\n", "\n", "We demonstrate three photon coherent excitations using the system studied in Taicharoen et. al. PRA 063427 (2019). This is a rubidium vapor with a $5S_{1/2}\\rightarrow5P_{3/2}\\rightarrow5D_{5/2}\\rightarrow28F_{7/2}$ excitation pathway, with corresponding optical fields of 780 nm, 776 nm, and 1260 nm. These fields are labelled probe, dressing, and coupling, respectively.\n", "\n", "Here we demonstrate using rydiqule to solve this system under three conditions: \n", "\n", "1) Cold atoms\n", "2) Warm atoms, colinear optical beams\n", "3) Warm atoms, doppler-free angles\n", "\n", "Because there are three optical fields, the basic coherent feature observed, on resonance, is expected to the absorptive (rather than transmissive like EIT). Going to warm atoms, this feature broadens signficantly, and other coherent features can arise at non-zero detunings of the fields. Going to a Doppler-free excitation in warm atoms, we find that a transmissive feature is observed on resonance. This feature is significantly narrower than those observed in the colinear case." ] }, { "cell_type": "markdown", "id": "b4e7ad53-6cec-45ba-91f0-32adfc23e72f", "metadata": {}, "source": [ "## Doppler-free, 3 photon excitation ##\n", "\n", "With all three fields resonant, we expect to see Electromagnetically-Induced-Absorption (EIA) instead of EIT." ] }, { "cell_type": "code", "execution_count": 5, "id": "006699b7-245a-49d8-8bf9-0f24967e548a", "metadata": { "tags": [] }, "outputs": [], "source": [ "detunings = np.linspace(-20,20,41)\n", "\n", "probe = {'states':(0,1), 'rabi_frequency':2*np.pi*0.1,'detuning':2*np.pi*0}\n", "dress = {'states':(1,2), 'rabi_frequency':2*np.pi*2}\n", "couple = {'states':(2,3), 'rabi_frequency':2*np.pi*2, 'detuning':2*np.pi*detunings}\n", "\n", "basis_size = 4\n", "gam = np.zeros((basis_size,basis_size),dtype=np.float64)\n", "gam[1,0] = 6\n", "gam[2,1] = 0.66\n", "gam[3,2] = 10e-3\n", "gamma_matrix = 2*np.pi*gam\n", "\n", "sensor = rq.Sensor(basis_size)\n", "sensor.add_couplings(probe,couple)\n", "sensor.set_gamma_matrix(gamma_matrix)" ] }, { "cell_type": "code", "execution_count": 6, "id": "b11c1fa1", "metadata": { "tags": [] }, "outputs": [], "source": [ "dress['detuning'] = 2*np.pi*0\n", "sensor.add_couplings(dress)\n", "sols = rq.solve_steady_state(sensor)" ] }, { "cell_type": "code", "execution_count": 7, "id": "205f363c-476e-487a-9db5-1aab77671044", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Im($\\\\rho_{10}$)')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(detunings, get_rho_ij(sols.rho,1,0).imag)\n", "ax.set_xlabel(\"Coupling Laser Detuning (MHz)\")\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")" ] }, { "cell_type": "markdown", "id": "39cc5477-19ad-47f0-9334-e1db387251ab", "metadata": {}, "source": [ "## Colinear 3-photon Excitation with Doppler Averaging ##\n", "\n", "We can take our three fields and configure them in the (+,-,-) configuration of Taicharoen (2019). We will need to do Doppler averaging along the colinear axis to get the result. The magnitude of a field's kvector is defined such that it is the magnitude of the Doppler shift associated with the most probable speed of the Maxwell-Boltzmann distribution ($v_P\\equiv\\sqrt{2k_B T/m}$, where $k_B$ is Boltzmann's constant, $T$ is the gas temperature, and $m$ is the atomic mass). It should have units of Mrad/s like all other specifies quantities.\n", "\n", "The following reproduces Figure 2b from Taicharoen et. al. PRA 063427 (2019). Note that having all fields resonant results in an EIA feature, but it now much broader than the Doppler-free case above. If the dressing field is detuning, EIT features are observed." ] }, { "cell_type": "code", "execution_count": 8, "id": "4373bfa9-856a-4f0e-b575-664357c0dcf7", "metadata": { "tags": [] }, "outputs": [], "source": [ "detunings = np.linspace(-200,200,201)\n", "\n", "kp = 2*np.pi/780e-3*np.array([1,0,0])\n", "kd = 2*np.pi/776e-3*np.array([-1,0,0])\n", "kc = 2*np.pi/1260e-3*np.array([-1,0,0])\n", "vP = 242.387 # m/s\n", "\n", "###\n", "probe = {'states':(0,1), 'rabi_frequency':2*np.pi*10, 'kvec':kp, 'detuning': 0}\n", "dress = {'states':(1,2), 'rabi_frequency':2*np.pi*25, 'kvec':kd}\n", "couple = {'states':(2,3), 'rabi_frequency':2*np.pi*18, 'detuning':2*np.pi*detunings, 'kvec':kc}\n", "###\n", "\n", "n = 4\n", "sensor = rq.Sensor(n, vP=vP)\n", "sensor.add_decoherence((1,0), 2*np.pi*6)\n", "sensor.add_decoherence((2,1), 2*np.pi*0.66)\n", "sensor.add_decoherence((3,2), 2*np.pi*10e-3)\n", "\n", "sensor.add_couplings(probe,couple)" ] }, { "cell_type": "code", "execution_count": 9, "id": "f693eb4b-ded7-4dc2-aa78-3be2161d2644", "metadata": { "tags": [] }, "outputs": [], "source": [ "dress['detuning'] = 2*np.pi*0\n", "sensor.add_couplings(dress)\n", "sols0 = rq.solve_steady_state(sensor,doppler=True)" ] }, { "cell_type": "code", "execution_count": 10, "id": "a37080c7-c31c-4af9-9466-b4e3d25c6aca", "metadata": { "tags": [] }, "outputs": [], "source": [ "dress['detuning'] = 2*np.pi*20\n", "sensor.add_couplings(dress)\n", "solsp20 = rq.solve_steady_state(sensor,doppler=True)" ] }, { "cell_type": "code", "execution_count": 11, "id": "f8f91dc5-140b-4ec6-8c79-ee96226e37cd", "metadata": { "tags": [] }, "outputs": [], "source": [ "dress['detuning'] = -2*np.pi*20\n", "sensor.add_couplings(dress)\n", "solsm20 = rq.solve_steady_state(sensor,doppler=True)" ] }, { "cell_type": "code", "execution_count": 12, "id": "3ee8c876-741e-4fb2-abe8-1e47aa5b6bf5", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8,6))\n", "ax.plot(detunings, get_rho_ij(sols0.rho,1,0).imag, label=\"$\\\\Delta_d= 0$ MHz\")\n", "ax.plot(detunings, get_rho_ij(solsp20.rho,1,0).imag, label=\"$\\\\Delta_d= +20$ MHz\")\n", "ax.plot(detunings, get_rho_ij(solsm20.rho,1,0).imag, label=\"$\\\\Delta_d= -20$ MHz\")\n", "ax.set_xlabel(\"Coupling Laser Detuning (MHz)\")\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "e1fade4b-2b85-4c77-b543-a3f692c09fbb", "metadata": {}, "source": [ "## Doppler-Free Angles ##\n", "\n", "We can take the same co-propagating system, and instead change the angles of the three beams such that $k_p+k_d+k_c\\approx0$. \n", "\n", "We now need to do Doppler averaging in two orthogonal dimensions. Rydiqule automatically detects how many non-zero dimensions are present in the field kvectors and averages over the appropriate number of spatial dimensions." ] }, { "cell_type": "code", "execution_count": 13, "id": "3c4208cf-9c73-48b1-ac55-30b2f53b4db6", "metadata": { "tags": [] }, "outputs": [], "source": [ "detunings = np.linspace(-20,20,21)\n", "\n", "kp = 2*np.pi/780e-3*np.array([1,0,0])\n", "kd = 2*np.pi/776e-3*np.array([-1,0,0])\n", "kc = 2*np.pi/1260e-3*np.array([-1,0,0])\n", "vP = 242.387 # m/s\n", "\n", "# rotate to doppler free angles\n", "rd = R.from_euler('z',-35.964,degrees=True)\n", "rc = R.from_euler('z',72.4718,degrees=True)\n", "kdDF = rd.apply(kd)\n", "kcDF = rc.apply(kc)\n", "\n", "probe = {'states':(0,1), 'rabi_frequency':2*np.pi*10, 'kvec':kp, 'detuning':0}\n", "dress = {'states':(1,2), 'rabi_frequency':2*np.pi*25, 'kvec':kdDF}\n", "couple = {'states':(2,3), 'rabi_frequency':2*np.pi*18, 'detuning':2*np.pi*detunings, 'kvec':kcDF}\n", "\n", "n = 4\n", "sensor = rq.Sensor(n, vP=vP)\n", "sensor.add_decoherence((1,0), 2*np.pi*6)\n", "sensor.add_decoherence((2,1), 2*np.pi*0.66)\n", "sensor.add_decoherence((3,2), 2*np.pi*10e-3)\n", "\n", "sensor.add_couplings(probe,couple)" ] }, { "cell_type": "code", "execution_count": 14, "id": "19d0afc4-7257-46c1-89a1-5a21c564488d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Residual fractional kvector sum due to round-off errors\n", "[-1.41309045e-08 -4.99652620e-07 0.00000000e+00]\n" ] } ], "source": [ "print('Residual fractional kvector sum due to round-off errors')\n", "print((kp+kdDF+kcDF)/np.sqrt(kp.dot(kp)))" ] }, { "cell_type": "code", "execution_count": 15, "id": "c2b8d4f0-f6b5-48dc-a622-ead4d76ca270", "metadata": {}, "outputs": [], "source": [ "dress['detuning'] = 2*np.pi*0\n", "sensor.add_couplings(dress)\n", "sols0DF = rq.solve_steady_state(sensor,doppler=True)" ] }, { "cell_type": "code", "execution_count": 16, "id": "adaa05dc-aca8-447a-97ab-ea6ced8ccf5d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Im($\\\\rho_{10}$)')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(detunings, get_rho_ij(sols0DF.rho,1,0).imag)\n", "ax.set_xlabel(\"Coupling Laser Detuning (MHz)\")\n", "ax.set_ylabel(r\"Im($\\rho_{10}$)\")" ] }, { "cell_type": "markdown", "id": "7bea405d-1fed-4ebf-bb44-66f562efafd1", "metadata": {}, "source": [ "We observe a significantly narrower feature than in the collinear case, and it is now EIT instead of EIA." ] }, { "cell_type": "markdown", "id": "981bff6c-d3a8-447a-8eb3-fc8ee6635daa", "metadata": {}, "source": [ "The authors recognize financial support from the Defense Advanced Research Projects Agency (DARPA). Rydiqule has been approved for unlimited public release by DEVCOM Army Research Laboratory and DARPA. This software is released under the xx licence through the University of Maryland Quantum Technology Center. The views, opinions and/or findings expressed here are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government." ] }, { "cell_type": "code", "execution_count": null, "id": "7d63b11e-5350-4568-b005-49f299e2c784", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "interpreter": { "hash": "78c908cb1a9dd36d2ac072f33e7f862980c362a2c369a07a6eb11e3740dc70f2" }, "kernelspec": { "display_name": "RQ", "language": "python", "name": "rq" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.8" } }, "nbformat": 4, "nbformat_minor": 5 }