{ "cells": [ { "cell_type": "markdown", "id": "d432d126-c329-4f02-b1f9-71e27268f775", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Simultaneous Conjugate Interferometer with realistic beamsplitters\n", "\n", "Numerical phase calculations can be integrated into the phase calculation in a relatively straightforward way. These calculations might be somewhat limited and less efficient compared to what code designed for a particular interferometer geometry could achieve--if you want to study a specific interferometer configuration in depth, you probably want to write a dedicated function from scratch. However this approach is good for exploring the performance of different interferometers.\n", "\n", "In this example we will replicate Fig. 3b from the paper [High-Resolution Atom Interferometers with Suppressed Diffraction Phases](http://dx.doi.org/10.1103/PhysRevLett.115.083002)." ] }, { "cell_type": "raw", "id": "5613716c-0ee5-49a3-ab5c-da35587d3440", "metadata": { "raw_mimetype": "text/restructuredtext", "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "First we will define the code that links the numerical calculation code to the :py:mod:`mwave.symbolic` module." ] }, { "cell_type": "code", "execution_count": 1, "id": "0157f7d5-e3df-456b-80ce-f94ecc585233", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "from mwave.symbolic import Interferometer, InterferometerNode, Beamsplitter, FreeEv, set_constants, eval_sympy_var\n", "from mwave.integrate import gbragg, make_kvec, make_phi\n", "import sympy as sp\n", "\n", "# Define a numeric unitary operator for single frequency Bragg\n", "class SingleFreqBragg(Beamsplitter):\n", " \n", " def gen_numeric(self, node, subs={}):\n", " delta = eval_sympy_var(self.delta, subs)\n", " n_init = eval_sympy_var(node.parent.n, subs)\n", " n_final = eval_sympy_var(node.n, subs)\n", " kvec, n0_idx, nf_idx = make_kvec(n_init, n_final)\n", " def fnc(omega, sigma, v, ratio):\n", " sol = gbragg(kvec, make_phi(kvec, n_init), 2*2.716*sigma, delta + 2*v, -2*np.pi*omega, sigma)\n", " return sol.y[nf_idx,-1]\n", " return fnc\n", "\n", "# Define a numeric unitary operator for multi frequency Bragg\n", "class MultiFreqBragg(Beamsplitter):\n", "\n", " def __init__(self, n1, n2, delta, k, omega_m):\n", " super().__init__(n1, n2, delta + omega_m, k)\n", " self.delta_numeric = delta\n", " self.omega_m = omega_m\n", " \n", " def gen_numeric(self, node, subs={}):\n", " delta = float(eval_sympy_var(self.delta_numeric, subs))\n", " omega_m = float(eval_sympy_var(self.omega_m, subs))\n", " n_init = eval_sympy_var(node.parent.n, subs)\n", " n_final = eval_sympy_var(node.n, subs)\n", " kvec, n0_idx, nf_idx = make_kvec(n_init, n_final)\n", " def fnc(omega, sigma, v, ratio):\n", " sol = gbragg(kvec, make_phi(kvec, n_init), 2*2.716*sigma, delta + 2*v, -2*np.pi*omega*ratio/4, sigma, omega_mod=omega_m)\n", " return sol.y[nf_idx,-1]\n", " return fnc" ] }, { "cell_type": "raw", "id": "d56b3e00-ba72-496e-8de1-587d3feee4e0", "metadata": { "editable": true, "raw_mimetype": "text/restructuredtext", "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Here we have defined two classes, each of which inherit from the :py:class:`mwave.symbolic.Beamsplitter` class. The first, :code:`SingleFreqBragg`, will act exactly as the :py:class:`mwave.symbolic.Beamsplitter` class does, although it implements the function :code:`gen_numeric`, which we need to override to implement numerical phase calculations.\n", "\n", "The second, :code:`MultiFreqBragg`, modifies the behavior of the :py:class:`mwave.symbolic.Beamsplitter` class slightly as it sets the value of :code:`delta` passed to the super :code:`__init__` function to :code:`delta+omega_m`. This ensures that the analytically calculated phase uses the correct detuning. It then saves the :code:`delta` passed into its own :code:`__init__` function as :code:`delta_numeric`, which is used inside the :code:`gen_numeric` function.\n", "\n", "Both :code:`SingleFreqBragg` and :code:`MultiFreqBragg` return a function titled :code:`fnc`. When called :code:`fnc` computes the wavefunction obtained after applying a Bragg pulse. To do this it uses the :py:meth:`mwave.integrate.gbragg` function. The function calls in :code:`SingleFreqBragg` and :code:`MultiFreqBragg` are very similar--the main difference is that the multifrequency one modifies the intensity by `ratio` and passes in :code:`omega_mod` to compute a multifrequency pulse.\n", "\n", "Next we set up our interferometer as usual by defining our constants, our unitary operators, and writing down the sequence of unitary operators needed to generate the SCI. Finally we determine which nodes are interfering." ] }, { "cell_type": "code", "execution_count": 2, "id": "36bc23b7-9a29-466e-9759-9d26541a3873", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "# Set up symbols for symbolic computation\n", "k, c, hbar, m, n, T, Tp, delta, omega_m, omega_r, t_traj, g, v0, Toffset = sp.symbols('k c hbar m n T T_p delta omega_m omega_r t_traj g v_0 T_offset', real=True)\n", "k_eff = 2*k\n", "set_constants(m=m,hbar=hbar,c=c,t_traj=t_traj)\n", "\n", "# Define the operators needed for an SCI\n", "bs1 = SingleFreqBragg(n, 0, delta, k_eff)\n", "bs2 = MultiFreqBragg(0, -n, delta, k_eff, -omega_m)\n", "bs2u = MultiFreqBragg(n, 2*n, delta, k_eff, +omega_m)\n", "fe1 = FreeEv(T)\n", "fe2 = FreeEv(Tp)\n", "\n", "# Define the interferometer\n", "ii = Interferometer(init_node=InterferometerNode(n=n, v=2*hbar*k*n/m))\n", "ii.apply(bs1)\n", "ii.apply(fe1)\n", "ii.apply(bs1)\n", "ii.apply(fe2)\n", "ii.apply(bs2)\n", "ii.apply(bs2u)\n", "ii.apply(fe1)\n", "ii.apply(bs2)\n", "ii.apply(bs2u)\n", "\n", "# Determine the intefering nodes\n", "inodes = ii.interfere()" ] }, { "cell_type": "markdown", "id": "c6840382-2407-48e3-b66f-97492379cbef", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Lets check that we get the expected SCI phase." ] }, { "cell_type": "code", "execution_count": 3, "id": "0671c492-6bcb-468d-83b3-960a60e51a51", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "16*T*n**2*omega_r - 2*T*n*omega_m - 2*pi\n" ] } ], "source": [ "phi_A, phi_B, phi_C, phi_D = ii.phases()\n", "print(sp.expand(sp.simplify(phi_A - phi_C).subs(k, sp.sqrt(2*m*omega_r/hbar))))" ] }, { "cell_type": "markdown", "id": "d0695989-9ef9-49ea-b9ba-df2bc3ed663d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "That is expected! Next lets plot the trajectories so we can determine which node corresponds to $\\left|\\phi\\right\\rangle_\\text{uuu}$, $\\left|\\phi\\right\\rangle_\\text{uud}$, $\\left|\\phi\\right\\rangle_\\text{udu}$, etc." ] }, { "cell_type": "code", "execution_count": 4, "id": "1dd00544-bee6-4aad-8036-8b9de962fe2b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "# Define our substitutions for the analytic calculation\n", "subs = {hbar:1, k:1, m: 1, n: 5, delta: 4*n, omega_m: 8*n, T:5, Tp: 2}\n", "\n", "tfinal = float(inodes[0][0].t.evalf(subs=subs))\n", "t = np.linspace(0, tfinal, 1000)\n", "\n", "plt.figure()\n", "\n", "def plot_pair(i):\n", " f0 = inodes[i][0].get_trajectory(subs=subs)\n", " plt.plot(t, f0(t), label=f'inodes[{i}][0], $n={sp.latex(inodes[i][0].n)}$')\n", " f1 = inodes[i][1].get_trajectory(subs=subs)\n", " plt.plot(t, f1(t), label=f'inodes[{i}][1], $n={sp.latex(inodes[i][1].n)}$')\n", " \n", "plot_pair(0)\n", "plot_pair(2)\n", "\n", "plt.legend()\n", "plt.ylabel('position')\n", "plt.xlabel('time')\n", "plt.show()\n", "\n", "plt.figure()\n", "plot_pair(1)\n", "plot_pair(3)\n", "plt.legend()\n", "plt.ylabel('position')\n", "plt.xlabel('time')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fe3987c0-4f27-4075-960c-5b027d5b4e67", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Now that we have identified which nodes correspond to which outputs we are ready to perform the numerical calculation. Lets generate functions that can be used to compute the wavefunction at each output.\n", "\n", "Note that we will have these calculations ignore some of the unitary operations: the upper interferometer third and fourth pulses should not be subjected to the unitary operator that describes the multifrequency beamsplitter operation happening on the lower interferometer third and fourth pulses. To do this we define a filter function which only returns true if the node momentum state is equal to one of the states that the beamsplitter is resonant with.\n", "\n", "(Note that you could define the `MultiFreqBragg` operator in a different way where it determines all of the states it is resonant with automatically instead of just those specified by `n1` and `n2`--then we wouldn't need to use the filter function.)" ] }, { "cell_type": "code", "execution_count": 5, "id": "5f129474-f42e-4146-868a-ef2eb5f6b03e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "# Write a filter function that ensures we don't double-count the effect of the multifrequency beamsplitters\n", "def filterfnc(node, unitary):\n", " return node.n == unitary.n1 or node.n == unitary.n2\n", "\n", "# Get the numeric phase calculation for each output\n", "uuu = inodes[1][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "udu = inodes[1][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "uud = inodes[0][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "udd = inodes[0][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "duu = inodes[3][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "ddu = inodes[3][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "dud = inodes[2][0].gen_numeric_wf_func(subs, filter=filterfnc)\n", "ddd = inodes[2][1].gen_numeric_wf_func(subs, filter=filterfnc)\n", "\n", "# Create a function to compute the differential phase\n", "def calc_diff_phase(omega, sigma, v, ratio):\n", " ph = -(np.angle(-uuu(omega, sigma, v, ratio)/udu(omega, sigma, v, ratio)) - np.angle(-duu(omega, sigma, v, ratio)/ddu(omega, sigma, v, ratio)))\n", " phh = -(np.angle(uud(omega, sigma, v, ratio)/udd(omega, sigma, v, ratio)) - np.angle(dud(omega, sigma, v, ratio)/ddd(omega, sigma, v, ratio)))\n", " return (ph+phh)/2" ] }, { "cell_type": "markdown", "id": "cd3563a2-1f06-4468-9223-8068c6502a31", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Now we can determine how the phase changes as a function of the input state velocity." ] }, { "cell_type": "code", "execution_count": 6, "id": "693c9db8-5943-4ab6-bb33-6a3eb4b8521b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 200/200 [00:46<00:00, 4.32it/s]\n" ] } ], "source": [ "from tqdm import tqdm\n", "from scipy.interpolate import interp1d\n", "\n", "# Compute phase value at several velocities\n", "velocities = np.linspace(-3,3,200)\n", "phase_values = np.full_like(velocities, np.nan)\n", "for i in tqdm(range(len(velocities))):\n", " phase_values[i] = calc_diff_phase(5.05, 0.2, velocities[i]/2, 4.1)\n", "\n", "# Interpolate\n", "phase_v_fnc = interp1d(velocities, phase_values)" ] }, { "cell_type": "markdown", "id": "b6c25ee0-0afe-46aa-adf5-633b00abc692", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "We can now plot this against the raw data from Fig. 3b." ] }, { "cell_type": "code", "execution_count": 7, "id": "bf307dd7-6cc3-4b0e-b596-a0a751367582", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set raw data\n", "raw_data_x = np.array([-0.77444,-0.38722,0,0.38722,0.7744,1.16167])\n", "raw_data_y = np.array([0.1785, 0.139,0.108,0.106,0.127,0.1705])\n", "raw_data_err = np.array([0.0054,0.0058,0.00285,0.00155,0.002575,0.0036])\n", "\n", "# Plot\n", "vv = np.linspace(-1.5,1.5)\n", "plt.plot(vv,1000*phase_v_fnc(vv-0.225)/16/25/2/np.pi)\n", "plt.errorbar(raw_data_x, raw_data_y, raw_data_err, marker='.', linestyle='none')\n", "plt.xlim([-1,1.5])\n", "plt.ylim([0,0.2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d3d9fb7a-ee0c-4c74-8db0-c79872478311", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "It doesn't agree because the model in Fig 3b assumes that there is a distribution of velocities entering the interferometer. Lets come up with a form for the velocity distribution based on what we expect after a Raman velocity pulse." ] }, { "cell_type": "code", "execution_count": 8, "id": "95443b00-05fe-462e-8bf9-b97af9e42e3b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import nquad\n", "\n", "# We do double velocity selection, so Brian Estey's equation on p.99 of his thesis is relevant\n", "def vel_dist(w, v):\n", " OmR = np.pi/w\n", " return (OmR**2/(v**2 + OmR**2)*np.sin((v**2 + OmR**2)**0.5*w/2)**2)**2\n", "\n", "# Normalize the velocity distribution\n", "norm_factor = nquad(lambda x: vel_dist(400/77, x), ((-np.inf, np.inf),), opts={'limit':1000})[0]\n", "def vel_dist_norm(v):\n", " return vel_dist(400/77,v)/norm_factor\n", "\n", "# Plot\n", "vv = np.linspace(-2,2,200)\n", "plt.plot(vv, vel_dist_norm(vv))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5bee7ebe-9313-4c95-88d6-a473c4d0f91c", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "\n", "\n", "Now that we have a form for the velocity distribution we can average the phase over it.\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "ebc1e83e-0e78-438c-85ac-b51fa92b9b17", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jack/miniconda3/envs/lab/lib/python3.11/site-packages/scipy/integrate/_quadpack_py.py:1260: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.\n", " If increasing the limit yields no improvement it is advised to analyze \n", " the integrand in order to determine the difficulties. If the position of a \n", " local difficulty can be determined (singularity, discontinuity) one will \n", " probably gain from splitting up the interval and calling the integrator \n", " on the subranges. Perhaps a special-purpose integrator should be used.\n", " quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n", "/Users/jack/miniconda3/envs/lab/lib/python3.11/site-packages/scipy/integrate/_quadpack_py.py:1260: IntegrationWarning: The occurrence of roundoff error is detected, which prevents \n", " the requested tolerance from being achieved. The error may be \n", " underestimated.\n", " quad_r = quad(f, low, high, args=args, full_output=self.full_output,\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define function which computes the phase averaged over the velocity distribution\n", "def weighted_phase_function(v):\n", " return nquad(lambda x: vel_dist_norm(x)*phase_v_fnc(v+x), ((-1, 1),))[0]\n", "\n", "# Compute the phase for a range of different incoming velocities\n", "incoming_velocities = np.linspace(-1.5,1.5)\n", "phases_averaged_over_vdist = np.array([weighted_phase_function(x-0.225) for x in incoming_velocities])\n", "\n", "# Plot\n", "plt.plot(incoming_velocities,1000*phases_averaged_over_vdist/16/25/2/np.pi, label='with velocity distribution')\n", "plt.plot(incoming_velocities,1000*phase_v_fnc(incoming_velocities-0.225)/16/25/2/np.pi, '--', label='without velocity distribution')\n", "plt.errorbar(raw_data_x, raw_data_y, raw_data_err, marker='.', linestyle='none', label='raw data')\n", "plt.legend()\n", "plt.xlim([-1,1.5])\n", "plt.ylim([0,0.2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "f6ea5862-5d96-4a35-8193-f619d5ef6178", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "This is the same as Fig. 3b." ] } ], "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 }