{ "cells": [ { "cell_type": "markdown", "id": "7cfb587e-bcac-48d5-93d2-2dbdadada238", "metadata": {}, "source": [ "# Interferometer Geometries" ] }, { "cell_type": "markdown", "id": "3e0f89f2-1011-49b4-9c44-3a1a2346eded", "metadata": {}, "source": [ "## Mach-Zender Interferometer" ] }, { "cell_type": "markdown", "id": "78f062c1-d28e-4684-ba0f-e69bd7f0a64f", "metadata": {}, "source": [ "Define the needed constants, initialize the required unitary operators, and define the interferometer." ] }, { "cell_type": "code", "execution_count": 1, "id": "30e582e2-884e-4543-a08b-d7eb392e7524", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from mwave import symbolic as msym\n", "import numpy as np\n", "import sympy as sp\n", "from matplotlib import pyplot as plt\n", "\n", "# Set up symbols for symbolic computation\n", "m, c, hbar, k, g, gamma, delta, n, T, t_traj = sp.symbols('m c hbar k g gamma delta n T t_traj', real=True)\n", "k_eff = 2*k\n", "\n", "# Register constants\n", "msym.set_constants(m=m, c=c, hbar=hbar, t_traj=t_traj)\n", "\n", "# Define unitary operators needed for an MZ interferometer\n", "bs = msym.Beamsplitter(0, n, delta, k_eff)\n", "mirror = msym.Mirror(0, n, delta, k_eff)\n", "free = msym.FreeEv(T, gravity=g, gravity_grad=gamma)\n", "\n", "# Create interferometer object, perform MZ sequence\n", "ifr = msym.Interferometer()\n", "(bs @ (free @ (mirror @ (free @ (bs @ ifr)))))" ] }, { "cell_type": "markdown", "id": "6cd3e7f2-0285-4d3d-ba1a-ce7cc44b73a7", "metadata": {}, "source": [ "Generate and optionally vizualize the directed tree structure representing the interferometer object." ] }, { "cell_type": "code", "execution_count": 2, "id": "72799857-6871-4f62-9cb9-5df456fb0c32", "metadata": {}, "outputs": [], "source": [ "# Create a graphviz object of the tree\n", "d_test = ifr.generate_graph()\n", "\n", "# Uncomment to display the graph\n", "# d_test.view()" ] }, { "cell_type": "markdown", "id": "d5ed1206-0746-45db-9d86-333c92077d4f", "metadata": {}, "source": [ "Check for interferance, set the gravity gradient to zero as otherwise the interferometer won’t perfectly close and no interferance will be detected." ] }, { "cell_type": "code", "execution_count": 3, "id": "12d3789c-239c-49a7-b5f1-55808cdb9145", "metadata": {}, "outputs": [], "source": [ "inodes = ifr.interfere(subs={gamma: 0})" ] }, { "cell_type": "markdown", "id": "2bdb787d-e2e5-4bd6-a954-d632b0befc38", "metadata": {}, "source": [ "Determine which port each output is in" ] }, { "cell_type": "code", "execution_count": 4, "id": "6c1c6f69-9269-4e42-af50-4a98378fb15f", "metadata": {}, "outputs": [], "source": [ "iports, jports, noport = ifr.get_ports({n:'upper', 0: 'lower'})" ] }, { "cell_type": "markdown", "id": "0c73d40d-16b6-4c77-8a1f-916100c366e8", "metadata": {}, "source": [ "Check that we don’t have any unexpected ports" ] }, { "cell_type": "code", "execution_count": 5, "id": "07d9ce81-3f2d-47d4-964e-ecad4027c73a", "metadata": {}, "outputs": [], "source": [ "if len(jports) != 0 or len(noport) != 0:\n", " print('Unexpected output')" ] }, { "cell_type": "markdown", "id": "565bb9b9-29fb-413c-a567-752ddcb30c36", "metadata": {}, "source": [ "Set interferometer parameters for plotting" ] }, { "cell_type": "code", "execution_count": 6, "id": "be5c0321-466a-42bc-a5b4-69db30cb4231", "metadata": {}, "outputs": [], "source": [ "subs = {m: 1, c: 1, hbar: 1, k: 1, g: 0.3, gamma: 0.001, delta: 4*3, n: 3, T: 5}" ] }, { "cell_type": "markdown", "id": "6f92b369-330f-4644-b347-f974d8df9469", "metadata": {}, "source": [ "Determine the final interferometer time by evaluating the value of t at the end of the interferometer. We can pick a random interferometer port to do this." ] }, { "cell_type": "code", "execution_count": 7, "id": "ad90912a-0d64-415e-a631-13b6f152ab6e", "metadata": {}, "outputs": [], "source": [ "tfinal = float(iports['upper'][0].t.evalf(subs=subs))" ] }, { "cell_type": "markdown", "id": "1713e928-1ed2-43a9-a6c9-224dac97481a", "metadata": {}, "source": [ "Plot the trajectory of the interferometer paths" ] }, { "cell_type": "code", "execution_count": 8, "id": "d8bcc1da-af65-4c77-8940-ac7491e079a2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, tfinal, 1000)\n", "plt.figure()\n", "for node_pair, ls in zip([iports['upper'], iports['lower']], ['-', '--']):\n", " fnc_traj = node_pair[0].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", " fnc_traj = node_pair[1].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", "plt.xlabel('time')\n", "plt.ylabel('position')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5af1af94-c134-4fd7-9506-e063682014ff", "metadata": {}, "source": [ "Compute the phase of the interferometer" ] }, { "cell_type": "code", "execution_count": 9, "id": "7b2b3b15-f3ec-4d3e-b2f6-4a74a6bcb000", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "phase_1=(-3*T**10*g*gamma**4*k*m*n + 10*T**9*gamma**4*hbar*k**2*n**2 - 34*T**8*g*gamma**3*k*m*n + 56*T**7*gamma**3*hbar*k**2*n**2 - 53*T**6*g*gamma**2*k*m*n + 60*T**5*gamma**2*hbar*k**2*n**2 + 84*T**4*g*gamma*k*m*n - 144*T**3*gamma*hbar*k**2*n**2 + 144*T**2*g*k*m*n - 72*pi*m)/(72*m)\n", "phase_2=T**2*k*n*(-3*T**8*g*gamma**4*m + 10*T**7*gamma**4*hbar*k*n - 34*T**6*g*gamma**3*m + 56*T**5*gamma**3*hbar*k*n - 53*T**4*g*gamma**2*m + 60*T**3*gamma**2*hbar*k*n + 84*T**2*g*gamma*m - 144*T*gamma*hbar*k*n + 144*g*m)/(72*m)\n", "total population sum=1\n" ] } ], "source": [ "# Compute the differential phase\n", "phi1, phi2 = ifr.phases()\n", "print(f'phase_1={sp.simplify(phi1)}')\n", "print(f'phase_2={sp.simplify(phi2)}')\n", "\n", "# Print out the total population, check it is equal to 1\n", "pop = 0\n", "for node in ifr.get_nodes():\n", " pop += (node.get_amp())**2\n", "print(f'total population sum={sp.simplify(pop)}')" ] }, { "cell_type": "markdown", "id": "386c82e5-7776-4547-b16b-f76c30b3c615", "metadata": {}, "source": [ "## Simultaneous Conjugate Interferometer" ] }, { "cell_type": "markdown", "id": "7e251736-0146-4aca-99ae-52bf32762aa2", "metadata": {}, "source": [ "Define the needed constants, initialize the required unitary operators, and define the interferometer." ] }, { "cell_type": "code", "execution_count": 1, "id": "daf88caa-9e0a-4e1d-b1fc-eb73656328b3", "metadata": {}, "outputs": [], "source": [ "from mwave import symbolic as msym\n", "import numpy as np\n", "import sympy as sp\n", "from matplotlib import pyplot as plt\n", "\n", "# Set up symbols for symbolic computation\n", "m, c, hbar, k, omega_r, delta, n, omega_m, T, Tp, t_traj = sp.symbols('m c hbar k omega_r delta n omega_m T Tp t_traj', real=True)\n", "k_eff = 2*k\n", "\n", "# Register constants\n", "msym.set_constants(m=m, c=c, hbar=hbar, t_traj=t_traj)\n", "\n", "# Define unitary operators needed for an SCI interferometer\n", "bs1 = msym.Beamsplitter(n, 0, delta, k_eff)\n", "bs2 = msym.Beamsplitter(0, -n, delta - omega_m, k_eff)\n", "bs2u = msym.Beamsplitter(n, 2*n, delta + omega_m, k_eff)\n", "fe1 = msym.FreeEv(T)\n", "fe2 = msym.FreeEv(Tp)\n", "\n", "# Create interferometer object, perform MZ sequence\n", "ifr = msym.Interferometer()\n", "ifr.apply(bs1)\n", "ifr.apply(fe1)\n", "ifr.apply(bs1)\n", "ifr.apply(fe2)\n", "ifr.apply(bs2)\n", "ifr.apply(bs2u)\n", "ifr.apply(fe1)\n", "ifr.apply(bs2)\n", "ifr.apply(bs2u)" ] }, { "cell_type": "markdown", "id": "54cfd9fe-9821-4bf0-bfcc-87e8e2270f94", "metadata": {}, "source": [ "Generate and optionally vizualize the directed tree structure representing the interferometer object." ] }, { "cell_type": "code", "execution_count": 2, "id": "27190677-68f6-47ea-9887-47f914b38fa1", "metadata": {}, "outputs": [], "source": [ "# Create a graphviz object of the tree\n", "d_test = ifr.generate_graph()\n", "\n", "# Uncomment to display the graph\n", "# d_test.view()" ] }, { "cell_type": "markdown", "id": "27d75a26-7ec9-44b5-9b00-3a6853f81ded", "metadata": {}, "source": [ "Check for interferance, set the gravity gradient to zero as otherwise the interferometer won't perfectly close and no interferance will be detected." ] }, { "cell_type": "code", "execution_count": 3, "id": "4a6191fd-476a-4652-ba6d-4191d702e105", "metadata": {}, "outputs": [], "source": [ "inodes = ifr.interfere()" ] }, { "cell_type": "markdown", "id": "7b944eb1-c5a4-406a-8dfb-62f9c9701636", "metadata": {}, "source": [ "Determine which port each output is in" ] }, { "cell_type": "code", "execution_count": 4, "id": "5cfce863-32e1-4cbb-9d09-7c404494fb95", "metadata": {}, "outputs": [], "source": [ "iports, jports, noport = ifr.get_ports({2*n:'A', n:'B', 0:'C', -n:'D'})" ] }, { "cell_type": "markdown", "id": "0fa5843e-773e-49dc-ac72-f5d3086f4e75", "metadata": {}, "source": [ "Check that we don't have any unexpected ports" ] }, { "cell_type": "code", "execution_count": 5, "id": "b09c0b4b-73d5-447d-b41f-ac9047c5a455", "metadata": {}, "outputs": [], "source": [ "if len(jports) != 4 or len(noport) != 0:\n", " print('Unexpected output')" ] }, { "cell_type": "markdown", "id": "c117b755-0a15-452d-880e-6028c6ffedf9", "metadata": {}, "source": [ "Set interferometer parameters for plotting" ] }, { "cell_type": "code", "execution_count": 6, "id": "032d8eff-04b8-47a4-93e2-bbc0dea12a53", "metadata": {}, "outputs": [], "source": [ "subs = {m: 1, c: 1, hbar: 1, k: 1, delta: 4*3, n: 3, T: 5, Tp: 1}" ] }, { "cell_type": "markdown", "id": "ab52f977-cf93-473b-be05-90c1456f6364", "metadata": {}, "source": [ "Determine the final interferometer time by evaluating the value of t at the end of the interferometer. We can pick a random interferometer port to do this." ] }, { "cell_type": "code", "execution_count": 7, "id": "e11007ae-cd82-4281-92d9-3b7c564b866b", "metadata": {}, "outputs": [], "source": [ "tfinal = float(iports['A'][0].t.evalf(subs=subs))" ] }, { "cell_type": "markdown", "id": "6eda08df-4137-4616-b8a8-c108042cde6e", "metadata": {}, "source": [ "Plot the trajectory of the interferometer paths" ] }, { "cell_type": "code", "execution_count": 8, "id": "c1347b56-1d8f-49db-a58e-740ea2d7107f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, tfinal, 1000)\n", "plt.figure()\n", "for port, ls in zip(['A', 'B', 'C', 'D'], ['-', '--', '-.', ':']):\n", " fnc_traj = iports[port][0].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", " fnc_traj = iports[port][1].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", "plt.xlabel('time')\n", "plt.ylabel('position')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4929e29b-94f1-4d5d-ac81-6d08e41f3be6", "metadata": {}, "source": [ "Compute the phase of the interferometer" ] }, { "cell_type": "code", "execution_count": 9, "id": "3e4f2efb-3f48-40f8-a4cc-41a5be932bfb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "differential phase=16*T*n**2*omega_r - 2*T*n*omega_m - 2*pi\n", "total population sum=1\n" ] } ], "source": [ "# Compute the differential phase\n", "phiA, phiB, phiC, phiD = ifr.phases()\n", "print(f'differential phase={sp.simplify(phiA - phiC).subs(k, sp.sqrt(2*m*omega_r/hbar))}')\n", "\n", "# Print out the total population, check it is equal to 1\n", "pop = 0\n", "for node in ifr.get_nodes():\n", " pop += (node.get_amp())**2\n", "print(f'total population sum={sp.simplify(pop)}')" ] }, { "cell_type": "markdown", "id": "afe272e8-7804-4875-9b32-e726a5361f95", "metadata": {}, "source": [ "## Simulatenous Conjugate Interferometer with single Bragg pulses" ] }, { "cell_type": "code", "execution_count": 1, "id": "d29d2f87-c8bd-4948-b7df-1831fb28516a", "metadata": {}, "outputs": [], "source": [ "from mwave import symbolic as msym\n", "import numpy as np\n", "import sympy as sp\n", "from matplotlib import pyplot as plt\n", "\n", "# Set up symbols for symbolic computation\n", "k, c, hbar, m, g, T_spacing, T, Tp, delta, t_traj, omega_r, omega_0 = sp.symbols('k c hbar m g T_spacing T Tp delta t_traj omega_r omega_0', real=True)\n", "k_eff = 2*k\n", "\n", "# Register constants\n", "msym.set_constants(m=m, c=c, hbar=hbar, t_traj=t_traj)" ] }, { "cell_type": "markdown", "id": "ce61505f-bc4d-44b9-bf13-c7ea05eb2f91", "metadata": {}, "source": [ "For an n=2 SCI with single Bragg pulses we must run the following pulse sequences for beam splitters\n", "```\n", "Pulse sequence 1: Split initial state into two, mirror one of the outputs to bragg order n\n", "1 2 ... n\n", "pi/2 -> pi -> ... -> pi\n", "\n", "Pulse sequence 2: Mirror state at momentum n down to 1, then pi/2 to bring to correct state and diffract initially undiffracted arm to 1, then mirror initially undiffracted arm up to n\n", "1 n-1 n n+1 n+n-1\n", "pi -> ... -> pi -> pi/2 -> pi -> ... -> pi\n", "\n", "Pulse sequence 3: pi/2 lower interferometer upper arm down (pi/2 necessary to avoid diffracting away the lower arm), pi pulse to -n. Simulaneously do the same for the upper interferometer lower arm\n", "1 2 n\n", "pi/2 -> pi -> ... -> pi\n", "\n", "Pulse sequence 4: pi lower interferometer upper arm up to 0, pi/2 pulse to interfere 0 and -1 states. Simulaneously do the same for the upper interferometer lower arm\n", "1 2 n\n", "pi -> ... -> pi -> pi/2\n", "```\n", "We will next implement the unitary operators needed to perform these sequences" ] }, { "cell_type": "code", "execution_count": 2, "id": "03c4b423-1683-4801-9131-561d493a5130", "metadata": {}, "outputs": [], "source": [ "nbragg = 2\n", "\n", "bsdict = {}\n", "mdict = {}\n", "\n", "# Make function to get/construct a beamsplitter between the two specified states\n", "def get_bs(n0, nf):\n", " tid = (min(n0,nf), max(n0,nf))\n", " if tid in bsdict:\n", " return bsdict[tid]\n", " else:\n", " bsdict[tid] = msym.Beamsplitter(min(n0,nf), max(n0,nf), 4*(n0+nf)*omega_0, k_eff)\n", " return bsdict[tid]\n", "\n", "# Make function to get/construct a mirror between the two specified states\n", "def get_m(n0, nf):\n", " tid = (min(n0,nf), max(n0,nf))\n", " if tid in mdict:\n", " return mdict[tid]\n", " else:\n", " mdict[tid] = msym.Mirror(min(n0,nf), max(n0,nf), 4*(n0+nf)*omega_0, k_eff)\n", " return mdict[tid]\n", "\n", "# Free evolutions\n", "feTs = msym.FreeEv(T_spacing)\n", "feT = msym.FreeEv(T)\n", "feTp = msym.FreeEv(Tp)\n", "\n", "# Beamsplitter sequences\n", "def pulse1(ifr):\n", " ifr.apply(get_bs(0, 1))\n", " for n in range(1, nbragg):\n", " ifr.apply(feTs)\n", " ifr.apply(get_m(n, n+1))\n", "\n", "def pulse2(ifr):\n", " for n in range(nbragg, 1, -1):\n", " ifr.apply(get_m(n, n-1))\n", " ifr.apply(feTs)\n", " ifr.apply(get_bs(1, 0))\n", " for n in range(1, nbragg):\n", " ifr.apply(feTs)\n", " ifr.apply(get_m(n, n+1))\n", " \n", "def pulse3(ifr):\n", " ifr.apply(get_bs(0, -1))\n", " ifr.apply(get_bs(nbragg, nbragg+1))\n", " for n in range(1, nbragg):\n", " ifr.apply(feTs)\n", " ifr.apply(get_m(-n, -n-1))\n", " ifr.apply(get_m(nbragg+n, nbragg+n+1))\n", " \n", "def pulse4(ifr):\n", " for n in range(nbragg, 1, -1):\n", " ifr.apply(get_m(-n, -n+1))\n", " ifr.apply(get_m(nbragg+n, nbragg+n-1))\n", " ifr.apply(feTs)\n", " ifr.apply(get_bs(0, -1))\n", " ifr.apply(get_bs(nbragg, nbragg+1))" ] }, { "cell_type": "markdown", "id": "f783f9e9-3f25-4afe-94e0-1a239e216579", "metadata": {}, "source": [ "Create the interferometer object and apply our sequence of unitary operators" ] }, { "cell_type": "code", "execution_count": 3, "id": "f3e4d22c-4884-4d16-aab9-55933e79ed6d", "metadata": {}, "outputs": [], "source": [ "ifr = msym.Interferometer()\n", "pulse1(ifr)\n", "ifr.apply(feT)\n", "pulse2(ifr)\n", "ifr.apply(feTp)\n", "pulse3(ifr)\n", "ifr.apply(feT)\n", "pulse4(ifr)" ] }, { "cell_type": "markdown", "id": "a784ae21-4a35-48d7-978d-b297f710a336", "metadata": {}, "source": [ "Generate and optionally vizualize the directed tree structure representing the interferometer object." ] }, { "cell_type": "code", "execution_count": 4, "id": "3a436640-ed6a-4ed5-ae96-929f34a02a62", "metadata": {}, "outputs": [], "source": [ "# Create a graphviz object of the tree\n", "d_test = ifr.generate_graph()\n", "\n", "# Uncomment to display the graph\n", "# d_test.view()" ] }, { "cell_type": "markdown", "id": "a5a9c352-262b-4637-9202-d9fc29f67b41", "metadata": {}, "source": [ "Check for interferance, set the gravity gradient to zero as otherwise the interferometer won't perfectly close and no interferance will be detected." ] }, { "cell_type": "code", "execution_count": 5, "id": "9d6e3b5c-3195-40c4-a4f5-1a26f8a51f56", "metadata": {}, "outputs": [], "source": [ "inodes = ifr.interfere()" ] }, { "cell_type": "markdown", "id": "6aaddfa5-1c0c-4cad-a8e6-af13ba15896b", "metadata": {}, "source": [ "Determine which port each output is in" ] }, { "cell_type": "code", "execution_count": 6, "id": "952d59f2-32d3-45d4-86de-cf6566234dd7", "metadata": {}, "outputs": [], "source": [ "iports, jports, noport = ifr.get_ports({nbragg+1:'A', nbragg:'B', 0:'C', -1:'D'})" ] }, { "cell_type": "markdown", "id": "b63de540-a912-43bf-879c-780548ec8634", "metadata": {}, "source": [ "Check that we don't have any unexpected ports" ] }, { "cell_type": "code", "execution_count": 7, "id": "5eef4093-f6a7-47b3-9ef3-a1ad09dbdbb8", "metadata": {}, "outputs": [], "source": [ "if len(jports) != 4 or len(noport) != 0:\n", " print('Unexpected output')" ] }, { "cell_type": "markdown", "id": "83169aa7-381e-4e27-9908-9da7e656779e", "metadata": {}, "source": [ "Set interferometer parameters for plotting" ] }, { "cell_type": "code", "execution_count": 8, "id": "0fb41365-c280-408a-b9af-9c003d9f4377", "metadata": {}, "outputs": [], "source": [ "subs = {k: 2, c: 1, hbar: 1, m: 1, T_spacing: 1, delta: 4*omega_r, omega_r: 1, T:5, Tp: 3, g: 1}" ] }, { "cell_type": "markdown", "id": "078d9cf9-8335-4241-bf30-ad626d7ed742", "metadata": {}, "source": [ "Determine the final interferometer time by evaluating the value of t at the end of the interferometer. We can pick a random interferometer port to do this." ] }, { "cell_type": "code", "execution_count": 9, "id": "b6f7b937-560b-4ec5-ac0e-21fb6827375c", "metadata": {}, "outputs": [], "source": [ "tfinal = float(inodes[0][0].t.evalf(subs=subs))" ] }, { "cell_type": "markdown", "id": "61c52882-40e9-422b-b69d-8d1e53092f80", "metadata": {}, "source": [ "Plot the trajectory of the interferometer paths" ] }, { "cell_type": "code", "execution_count": 10, "id": "69352ff1-59c2-4cdb-9fbd-8ed980611ddf", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, tfinal, 1000)\n", "plt.figure()\n", "for port, ls in zip(['A', 'B', 'C', 'D'], ['-', '--', '-.', ':']):\n", " fnc_traj = iports[port][0].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", " fnc_traj = iports[port][1].get_trajectory(subs=subs)\n", " plt.plot(t, fnc_traj(t), linestyle=ls)\n", "plt.xlabel('time')\n", "plt.ylabel('position')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2993b56d-fb03-46ac-b372-789f10fdd5ff", "metadata": {}, "source": [ "Compute the phase of the interferometer" ] }, { "cell_type": "code", "execution_count": 11, "id": "857b5077-4a1f-4d93-a920-80f7d4515190", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "differential phase=-64*T*omega_0 + 64*T*omega_r - 48*T_spacing*omega_0 + 48*T_spacing*omega_r - 2*pi\n", "total population sum=1\n" ] } ], "source": [ "# Compute the differential phase\n", "phiA, phiB, phiC, phiD = ifr.phases()\n", "print(f'differential phase={sp.simplify(phiA - phiC).subs(k, sp.sqrt(2*m*omega_r/hbar))}')\n", "\n", "# Print out the total population, check it is equal to 1\n", "pop = 0\n", "for node in ifr.get_nodes():\n", " pop += (node.get_amp())**2\n", "print(f'total population sum={sp.simplify(pop)}')" ] } ], "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": "3.11.10" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }