{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# QuTiP Lecture: Photon Scattering in Quantum Optical Systems\n", "\n", "\n", "Author: Ben Bartlett, Stanford University: [benbartlett@stanford.edu](mailto:benbartlett@stanford.edu) | [stanford.edu/people/benbartlett](https://stanford.edu/people/benbartlett) | [github:bencbartlett](https://github.com/bencbartlett/)\n", "\n", "This Jupyter notebook demonstrates functionality for numerically computing photon scattering in arbitrary driven systems coupled to some configuration of output waveguides using [QuTiP: The Quantum Toolbox in Python](http://qutip.org/). This notebook closely follows the treatment of the problem given in K.A. Fischer, et.al. (2017), \"Scattering of Coherent Pulses from Quantum-Optical Systems\" (arXiv: [1710.02875](https://arxiv.org/abs/1710.02875))." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from qutip import * \n", "from multiprocessing import Pool, cpu_count\n", "from IPython.display import display, Math, Latex\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'\n", "\n", "worker_count = max(cpu_count() - 1, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "$$\n", "\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}\n", "\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}\n", "$$\n", "In this section, we briefly review the generalized problem of photon scattering in quantum optical systems discussed in Fischer, et.al. (2017); see the publication for a more complete treatment of the problem. \n", "\n", "### Problem definition\n", "Consider an arbitrary system with a Hamiltonian $H_S(t)$ coupled to a bath of waveguide modes:\n", "\n", "![system_waveguide_coupling](./images/system_waveguide_coupling.png \"Schematic showing system waveguide coupling\")\n", "\n", "The problem we address in this notebook is this: if we drive the system with some excitation field, such as a laser pulse, how do photons scatter from the system into the waveguide?\n", "\n", "The system Hamiltonians we will consider take the form\n", "\\begin{equation}\n", "H_\\textrm{S}(t) =\n", "\\begin{cases}\n", "H_\\textrm{0S}+ H_\\textrm{1S}(t) & \\text{if } 0=H_\\textrm{I}(t)\\left|\\Psi_\\textrm{I}(t)\\right>.\n", "\\end{equation}\n", "\n", "### Coarse-grained dynamics and the scattering operator\n", "However, practically integrating this equation is not feasible, so we instead \"coarse-grain\" the temporal dynamics to $\\Delta t$ and take a continuous limit as $\\Delta t \\rightarrow 0$. If we define an \"effective Hamiltonian\" $H_\\text{eff}(t)=H_S(t)-i\\frac{\\gamma}{2}a^\\dagger a$, we can generate an effective propagator mapping the system from the $k^\\text{th}$ to the $k+1^\\text{th}$ time bin which is correct up to $\\mathscr{O}(\\Delta t)$:\n", "\n", "\\begin{equation}\n", "U_\\text{eff}[k+1,k] \\equiv \\bra{0_k} U[k+1,k] \\ket{0_k} \\approx \\exp\\left[-i\\int_{k\\Delta t}^{(k+1)\\Delta t} dt H_\\text{eff}(t)\\right].\n", "\\end{equation}\n", "\n", "From this, we can derive the scattering operator for the system into the system of waveguides (see the paper for more detail). For scattering of $N$ photons into single waveguide, this operator $\\left < \\hat{\\Omega}^\\dagger_- \\right > _{\\vec{\\tau}^{(m)}} $ takes the form:\n", "\n", "$$ \\left < \\hat{\\Omega}^\\dagger_- \\right > _{\\vec{\\tau}^{(m)}} = \\left<0_S\\right| U_\\text{eff}(\\tau_\\text{max},\\tau_m) \\prod_{q=N}^1 \\sqrt\\gamma a U_\\text{eff}(\\tau_q, \\tau_{q-1}) \\left| \\psi_S(0) \\right>,$$\n", "\n", "with $\\tau_0 = 0$, $\\tau_\\text{max} = \\max (T_p, \\tau_m )$. The multi-waveguide case will be discussed later in the notebook.\n", "\n", "### The temporal basis\n", "For a system coupled to $W$ waveguides emitting $N$ photons approximated by coarse-grained dynamics with $T$ time bins, the temporal basis described in Fischer, et al. (Eq. 138 and 153, with slight notation changes) can be thought of as a system of $T$ qubits for each of the $W$ waveguides with a total of $N$ creation operators applied to $\\ket{0}$:\n", "\n", "\\begin{equation}\n", "\\ket{\\vec{\\tau}_{(W)}^{(N)}} = \\ket{\\vec{\\tau}_1^{(w_1)}, \\vec{\\tau}_2^{(w_2)}, \\cdots ,\\vec{\\tau}_W^{(w_W)}} = \\prod_{i=1}^N b_{w_i,\\tau_{1}}^\\dagger b_{w_i,\\tau_{2}}^\\dagger \\cdots b_{i,\\tau_{n_i}}^\\dagger \\ket{0},\n", "\\end{equation}\n", "\n", "where $w_k$ denotes scattering into the $k$th waveguide and $n_i$ denotes the maximum number of photons scattered into some waveguide. Although this basis is exact, it has an intractable space complexity of $\\mathscr{O}(2^{T\\cdot M})$, making it insuitable for simulation work. \n", "\n", "The temporal basis we use in the `qutip.scattering` module is more closely modeled after ladder operators and explicitly restricts the basis to $N$ emissions. To generate the basis, we make $M$ copies of the $T$ time bins. Emission of a photon at the $i$th time bin into the $w$th waveguide is represented by an entry in the $(w T + i)$th index of a $(W T)$-dimensional vector, so the overall temporal basis is given by:\n", "\n", "\\begin{equation}\n", "\\ket{\\vec{\\tau}_{(W)}^{(N)}} = \\ket{\\vec{\\tau}_1^{(w_1)}, \\vec{\\tau}_2^{(w_2)}, \\cdots ,\\vec{\\tau}_W^{(w_W)}} = \\bigotimes_{n=1}^N \\ket{\\tau_{n, w_n}} = \\bigotimes_{n=1}^N \\mathscr{\\vec T}[w_n T + \\tau_n],\n", "\\end{equation}\n", "\n", "where $\\tau_{n, w_n}$ denotes emission into the $w_n$th waveguide of the $n$th photon and $\\mathscr{\\vec T}[w_n T + \\tau_n]$ denotes the basis vector corresponding to $\\tau_{n, w_n}$, namely the $(w_n T+\\tau_n)$-th index. The creation operators in the original temporal basis are mapped to $(w_i T + \\tau_n)$ applications of the \"temporal ladder operator\": \n", "\n", "\\begin{equation}\n", "b_{w_i,\\tau_n}^\\dagger = \\frac{(a^\\dagger)^{w_i T + \\tau_n}}{\\sqrt{(w_i T + \\tau_n)!}}\n", "\\end{equation}\n", "\n", "This gives this basis a space complexity of $\\mathscr{O}\\left((W T)^N\\right)$, which is more managable given that for most applicaitons $T\\gg W,N$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single waveguide: driven quantum two-level system\n", "\n", "To demonstrate the `qutip.scattering` module, we'll start with the simplest case of a two-level quantum system coupled to a single output waveguide. The system has initial state $\\left |{\\psi_0} \\right> = \\left|e\\right>_\\text{sys} \\otimes \\left|vac\\right>_\\text{wg}$ with a bare Hamiltonian of $H_{0S} = \\omega_0 \\sigma^\\dagger \\sigma $. Adding an effective non-Hermitian term to govern the evolution of the system under spontaneous emission, $H_\\text{eff} = H_{0S} - i \\frac{\\gamma}{2}\\sigma^\\dagger \\sigma$. When the system is driven by a coherent pulse, it undergoes Rabi oscillations. Picking a square pulse to give a simple Hamiltonian, the overall effective Hamiltonian is $H_\\text{eff}(t) = H_{0S} - H_{1S}(t)- i \\frac{\\gamma}{2}\\sigma^\\dagger \\sigma$, where\n", "\n", "$$H_{1S}(t) = \\begin{cases} \n", "\\Omega\\left( i e^{-i \\omega_0 t} \\sigma^\\dagger - i e^{i\\omega_0 t} \\sigma \\right) & \\text{ if } 0 = |0>\n", "\n", "def Htls(gamma, pulseLength, pulseArea):\n", " RabiFreq = pulseArea / (2*pulseLength)\n", " \n", " # Bare Hamiltonian for a TLS\n", " H0S = w0 * create(2) * destroy(2) \n", "\n", " # Define H_1S(t)\n", " H1S1 = lambda t, args: RabiFreq * 1j*np.exp(-1j*w0*t) * (t < pulseLength) \n", " H1S2 = lambda t, args: RabiFreq * -1j*np.exp(1j*w0*t) * (t < pulseLength)\n", "\n", " # Put the Hamiltonian in QuTiP list-callback form\n", " return [H0S - 1j/2 * sm.dag() * sm, \n", " [sm.dag(), H1S1], \n", " [sm, H1S2]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing photon scattering amplitudes\n", "\n", "Let's begin by computing the scattering amplitude of a single-photon emission as a function of time. For this, we can use the `temporal_scattered_state()` function in the `scattering` module, which computes:\n", "\n", "$$ \n", "\\begin{align}\n", "\\left| \\phi_n \\right> & = \\int_0^\\infty d\\tau_1 \\int_{\\tau_1}^\\infty d\\tau_2 \\cdots \\int_{\\tau_{n-1}}^\\infty d\\tau_n \\left<0_S, \\{ \\tau_1,\\tau_2,\\cdots,\\tau_n \\} \\mid \\psi(t\\rightarrow \\infty) \\right> \\left|\\tau_1,\\tau_2,\\cdots,\\tau_n\\right> \\\\\n", "& = \\int_{\\vec\\tau_n} d\\vec\\tau_n \\left<0_S, \\{\\vec\\tau_n \\} \\mid \\psi(t\\rightarrow \\infty) \\right> \\left|\\vec\\tau_n\\right> \\\\\n", "& = \\int_{\\vec\\tau_n} d\\vec\\tau_n \\left < \\hat{\\Omega}^\\dagger_- \\right > _{\\vec{\\tau}_n} \\left|\\vec\\tau_n\\right> \\\\\n", "& = \\hat{\\Omega}^\\dagger_- \\ket{\\psi_0}.\n", "\\end{align}\n", "$$\n", "\n", "This function takes as arguments the Hamiltonian or the effective Hamiltonian, the initial system state, the number of emissions, a list of collapse operators (one for each waveguide - see the following section for more detail), and a list of times. The list of times must exceed the duration of the pulse for the function to yield sensible results (or, if the pulse does not have a well-defined end, the times list must contain most of the temporal region of interest). \n", "\n", "By passing the keyword argument `construct_effective_hamiltonian`, you can tell the function whether the Hamiltonian you provided is $H$ or $H_\\text{eff}$; by default, the value is `True`, so an effective Hamiltonian will be constructed from the provided list of collapse operators as $H_\\text{eff} = H - \\frac{i}{2} \\sum_n \\tt{\\text{c_ops}}[n]$. The function iteratively calls `photon_scattering_operator()` and returns the temporal scattered state as a `Qobj`, so to extract the amplitudes $a_t$, we will need to project it onto the temporal basis:\n", "\n", "$$a_t = \\left< t \\mid \\phi_n \\right> = \\bra{t}\\hat{\\Omega}^\\dagger_- \\ket{\\psi_0} = \\bra{t}\\int_{\\vec\\tau_n}d\\vec\\tau_n \\left < \\hat{\\Omega}^\\dagger_- \\right > _{\\vec{\\tau}_n} \\left|\\vec\\tau_n\\right>,$$\n", "\n", "which we can do usng the `temporal_basis_vector()` function. This function takes a nested list of temporal emission indices for each waveguide and the total number of time bins. For the single-waveguide case, the nested list of time indices simply reduces to `[[indexOf(t)]]`.\n", "\n", "Computing the scattering amplitudes using the same parameters as the ones used in the analytical results of Figure 5(b) in Fischer, et al., we obtain visually identical results:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 267, "width": 406 } }, "output_type": "display_data" } ], "source": [ "T = 200\n", "tlist = np.linspace(0,1.5/gamma,T)\n", "pulse_length = 0.2 / gamma\n", "pulse_areas = [np.pi, 2*np.pi, 3*np.pi]\n", "\n", "for pulse_area in pulse_areas:\n", " # Use construct_effective_hamiltonian=False since we are providing H_eff in this case\n", " scattered_state = temporal_scattered_state(Htls(gamma, pulse_length, pulse_area), psi0, 1, [sm], tlist, \n", " construct_effective_hamiltonian = False)\n", " amplitudes = []\n", " for i in range(T):\n", " amplitudes.append((temporal_basis_vector([[i]], T).dag() * scattered_state).full().item())\n", " # Adjust amplitudes for time evolution\n", " amplitudes = np.real(np.array(amplitudes) * np.exp(1j * w0 * tlist))\n", " plt.plot(tlist, amplitudes, label = \"$A_R = {}\\pi$\".format(round(pulse_area / np.pi)))\n", " \n", "plt.ylim(-1,1)\n", "plt.xlim(tlist[0],tlist[-1])\n", "plt.xlabel('Time index, $\\\\tau_1$ [$1/\\gamma$]')\n", "plt.ylabel('$\\phi_1 ( \\\\tau_1) e^{-i \\omega_0 \\\\tau_1} [\\gamma^{1/2}]$')\n", "plt.legend(loc = 'upper right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Total photon scattering probability\n", "\n", "To calculate the total probability of emitting a certain number of photons, $P_n = \\left<\\phi_n \\mid \\phi_n\\right>$, we can expand in terms a complete set of temporal projection operators $\\int_{\\vec\\tau_n} \\left| \\tau_n \\right>\\left<\\tau_n \\right| d \\tau_n$:\n", "\n", "$$\\begin{align}\n", "P_n & = \\left<\\phi_n \\mid \\phi_n\\right> \\\\\n", "& = \\int_{\\vec\\tau_n} d\\vec\\tau_n \\left<\\phi_n \\mid \\vec\\tau_n \\right>\\left<\\vec\\tau_n \\mid \\phi_n \\right> \\\\\n", "& = \\int_0^\\infty d\\tau_1 \\int_{\\tau_1}^\\infty d\\tau_2 \\cdots \\int_{\\tau_{n-1}}^\\infty d\\tau_n \\left<\\phi_n \\mid \\tau_1, \\tau_2, \\cdots \\tau_n \\right>\\left<\\tau_1, \\tau_2, \\cdots \\tau_n \\mid \\phi_n \\right> \\\\\n", "\\end{align}$$\n", "\n", "More simply, however, you can use the `scattering_probability()` function, which recursively integrates the results of `temporal_scattered_state()` to return the total probability of $N$ photons being scattered from the system over the specified list of times. Notably, the time list does not need to be linear - the integration routines will account for unevenly spaced time bins. This allows you to do things like provide logarithmically spaced times, which better captures regions closer to $t=0$ where more interesting dynamics occur.\n", "\n", "To make things faster, we'll remove the time dependence of $H_\\text{eff}$ with a rotating frame transformation. We'll also drop the $-\\frac{i}{2} \\sigma^\\dagger \\sigma$ term and the `construct_effective_hamiltonian = False` argument to allow `temporal_scattered_state()` to construct the effective Hamiltonian on its own. \n", "\n", "Since `scattering_probability()` returns a pickleable result (a number), it is also very easily multiprocessed, so we'll take this opportunity to show how this can be done. (Note that this does make debugging untested code a more opaque process.) Computing the total scattering probabilities for $N=0,1,2$ photons as a function of pulse area yields a similar result to Figure 5(a) in Fischer, et al:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def Htls_rft(gamma, pulseLength, pulseArea):\n", " RabiFreq = pulseArea / (2*pulseLength)\n", " return [[sm.dag() + sm, lambda t, args: RabiFreq * (t < pulseLength)]]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 267, "width": 380 } }, "output_type": "display_data" } ], "source": [ "pulse_length = 0.2 / gamma\n", "pulse_areas = np.linspace(0,4*np.pi,100)\n", "tlist = np.geomspace(gamma, 7*gamma, 40) - gamma\n", "emission_nums = [0,1,2]\n", "\n", "def scattering_probability_multiprocess(pulse_area, n):\n", " # Helper function to allow pool.map parallelism\n", " return scattering_probability(Htls_rft(gamma, pulse_length, pulse_area), psi0, n, [sm], tlist)\n", "\n", "pool = Pool(worker_count)\n", "for n in emission_nums:\n", " args = [(pulse_area, n) for pulse_area in pulse_areas]\n", " scatter_probs = pool.starmap(scattering_probability_multiprocess, args)\n", " plt.plot(pulse_areas / np.pi, scatter_probs, label = \"$P_{}$\".format(n))\n", "pool.close()\n", "\n", "plt.ylim(0,1)\n", "plt.xlim(pulse_areas[0]/np.pi, pulse_areas[-1]/np.pi)\n", "plt.xlabel(\"Pulse area, $A_R [\\\\pi]$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing second-order coherence in the scattered state\n", "\n", "In experiments, the two-photon wavefunction is often characterized from the second-order coherence:\n", "\n", "\\begin{equation}\n", "G^{(2)}(t_1,t_2) \\approx \\bra{\\phi_2} b_0^\\dagger(t_1) b_0^\\dagger(t_2) b_0(t_2) b_0(t_1) \\ket{\\phi_2}.\n", "\\end{equation}\n", "\n", "Since the creation operators $b_0^\\dagger$ do not translate exactly into the temporal basis used in `qutip.scattering`, this is not directly computable in this form, but we can still calculate $G^{(2)}$ with creative application of `temporal_basis_vector()`. The second-order coherence measures the correlations for photons to be emitted at times $t_1$ and $t_2$ with corresponding time-bin indices `i` and `j`. To compute the coherence, we first compute the temporal scattered state, then project it onto `temporal_basis_vector([[i,j]], T)`, which gives the basis vector corresponding to photons emitted at time indices `i` and `j` (into the same - first - waveguide) out of `T` total time bins. This projection onto a (approximately) complete set of temporal basis vectors gives the second-order coherence, which is Figure 5(c) in Fischer, et al.:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 267, "width": 320 } }, "output_type": "display_data" } ], "source": [ "T = 200\n", "tlist = np.linspace(0,1.5/gamma,T)\n", "pulse_area = 6*np.pi\n", "pulse_length = 0.2 / gamma\n", "correlations = np.zeros((T, T))\n", "\n", "H = Htls_rft(gamma, pulse_length, pulse_area)\n", "scattered_state = temporal_scattered_state(H, psi0, 2, [sm], tlist)\n", "\n", "for i in range(T):\n", " for j in range(T):\n", " # temporal_scattered_state() computes only using ordered emission times, so to \n", " # get the full set of correlations, we need to use ordered temporal basis vector\n", " [a,b] = sorted([i,j])\n", " basis_vec = temporal_basis_vector([[a,b]], T)\n", " correlations[i,j] = np.abs((basis_vec.dag() * scattered_state).full().item())**2\n", "\n", "fig, ax1 = plt.subplots(1,1)\n", "cax = ax1.imshow(correlations, interpolation='nearest', origin='lower')\n", "ax1.set_xticks(np.linspace(0,T-1,4))\n", "ax1.set_xticklabels([0.0, 0.5, 1.0, 1.5])\n", "ax1.set_xlabel(\"Time, $t_1$ [$1/\\gamma$]\")\n", "ax1.set_yticks(np.linspace(0,T-1,4))\n", "ax1.set_yticklabels([0.0, 0.5, 1.0, 1.5])\n", "ax1.set_ylabel(\"Time, $t_2$ [$1/\\gamma$]\")\n", "fig.colorbar(cax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pulse-wise second-order coherence\n", "\n", "Experimentally accessing the temporal correlations given by $G^{(2)}$ or photocount distributions $P_m$ can be quite challenging, so typically a quantity called the pulse-wise second-order coherence is used, defined as:\n", "\n", "\\begin{equation}\n", "g^{(2)}[0] = \\frac{\\sum_m m(m-1) P_m}{\\left( \\sum_m m P_m \\right)^2} \\approx \\frac{2 P_2}{(P_1+2P_2)^2}.\n", "\\end{equation}\n", "\n", "We can easily compute this with `scattering_probability`, obtaining similar results to Figure 5(d) in Fischer, et al.:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 267, "width": 388 } }, "output_type": "display_data" } ], "source": [ "pulse_length = 0.2/gamma\n", "pulse_areas = np.linspace(0.01,4*np.pi,150)\n", "emission_nums = [1,2]\n", "# you can use non-linearly space time bins with scattering_probability()\n", "tlist = np.geomspace(gamma, 21*gamma, 40) - gamma \n", "\n", "def scatter_prob(pulse_area, n):\n", " # Helper function to allow pool.map parallelism\n", " return scattering_probability(Htls_rft(gamma, pulse_length, pulse_area), psi0, n, [sm], tlist)\n", "\n", "pool = Pool(worker_count)\n", "Pm = dict.fromkeys(emission_nums)\n", "for n in emission_nums:\n", " args = [(pulse_area, n) for pulse_area in pulse_areas]\n", " Pm[n] = np.array(pool.starmap(scatter_prob, args))\n", "pool.close()\n", "\n", "# Calculate pulse-wise coherence\n", "pulseWiseCoherence = np.sum([m * (m-1) * Pm[m] for m in Pm], axis=0) / \\\n", " np.square(np.sum([m * Pm[m] for m in Pm], axis=0))\n", "\n", "plt.plot(pulse_areas/np.pi, pulseWiseCoherence)\n", "plt.ylim(0,6)\n", "plt.xlim(pulse_areas[0]/np.pi, pulse_areas[-1]/np.pi)\n", "plt.xlabel(\"Pulse area, $A_R$ $[\\pi]$\")\n", "plt.ylabel(\"$g^{(2)}[0]$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiple waveguides: spontaneous parametric downconversion\n", "\n", "We'll now extend the problem to multiple waveguides by simulating the scattering dynamics of spontaneous parametric downconversion. The scattering amplitude discussed above extended to a system with $W$ waveguides is:\n", "\n", "\n", "\\begin{equation}\n", "\\left<\\hat{\\Omega}_{-}^\\dagger\\right>_{\\tilde{\\tau}^{(N)}}\\equiv\\left<\\hat{\\Omega}_{-}^\\dagger\\right>_{\\vec{\\boldsymbol{\\tau}}_1^{(m_1)},\\vec{\\boldsymbol{\\tau}}_2^{(m_2)},\\dots, \\vec{\\boldsymbol{\\tau}}_M^{(m_M)}} =\\bra{\\textbf{0}_\\text{S}} U_\\text{eff}(\\tau_\\text{max}, \\tilde{\\tau}_N) \\prod_{q=N}^1 \\sqrt{\\gamma_{Q[q]}}a_{Q[q]} U_\\text{eff}(\\tilde{\\tau}_q,\\tilde{\\tau}_{q-1}) \\ket{\\psi_\\text{S}(0)}\n", "\\end{equation}\n", "\n", "as a projection onto $|\\vec{\\boldsymbol{\\tau}}_1^{(m_1)},\\vec{\\boldsymbol{\\tau}}_2^{(m_2)},\\dots, \\vec{\\boldsymbol{\\tau}}_W^{(m_W)}\\rangle$, where $N = m_1+m_2+ \\cdots+ m_W$ is the total number of photons scattered, $\\tilde{\\tau}^{(N)}$ is a chronologically sorted set of all time indices from the $\\vec{\\boldsymbol{\\tau}}_i^{(m_i)}$'s, and $Q[q]$ is the index of the waveguide corresponding to the photon scattered at $\\tilde{\\tau}_q$. We present this equation without derivation; see Fischer, et al. for more details.\n", "\n", "Consider a SPDC cavity with a Hamiltonian given by a sum of time-independent and -dependent parts $H=H_{0S}+H_{1S}$, with:\n", "\n", "$$H_{0S} = \\omega_1 a_1^\\dagger a_1 + \\omega_2 a_2^\\dagger a_2,$$ \n", "\n", "and \n", "\n", "$$H_{1S} = g(t) \\left(e^{i\\omega_p t} a_1 a_2 + e^{-i\\omega_p t} a_1^\\dagger a_2^\\dagger \\right),$$\n", "\n", "where $a_1$ and $a_2$ annihilate photons at frequencies $\\omega_1$ and $\\omega_2$, respectively, $\\omega_p = \\omega_1 + \\omega_2$, and $g(t)$ is a function depending on the amplitude of the pump beam and the nonlinear susceptibility of the cavity. As a specific example, let's consider driving the system with a Gaussian pulse, such that $g(t) = g_0 \\exp \\left( -\\frac{(t-t_0)^2}{2\\tau^2} \\right)$. Truncating the cavity excitation capacity to $n=6$, we define the Hamiltonian for the system, again using a rotating frame transformation as before:\n", "\n", "$$H_\\text{SPDC} = \\left(a_1^\\dagger a_2^\\dagger + a_1 a_2\\right) g(t) + H_\\text{eff}\\text{ terms},$$ \n", "\n", "where we allow the scattering functions to construct the effective Hamiltonian by adding the $-\\frac{i}{2} \\sum_n \\tt{\\text{c_ops}}[n]$ terms." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "Ncav = 6 # truncated cavity excitation capacity\n", "a1 = tensor(destroy(Ncav), qeye(Ncav)) # left cavity annihilator\n", "a2 = tensor(qeye(Ncav), destroy(Ncav)) # right cavity annihilator\n", "cavity_vac = tensor(basis(Ncav, 0), basis(Ncav, 0)) # vacuum state, 0 excitations in either cavity\n", "w1 = w2 = 1/gamma # cavity frequencies\n", "wp = w1 + w2 # pump frequency\n", "spdc_c_ops = [np.sqrt(gamma)*a1, np.sqrt(gamma)*a2] # cavity collapse operators\n", "\n", "# Gaussian laser pulse\n", "def g(t, t0, g0, tau):\n", " return g0 * np.exp(-1 * (t-t0)**2 / (2 * tau**2))\n", "\n", "# SPDC Hamiltonian with rotating frame transformation applied\n", "def Hspdc(t0, g0, tau): \n", " return [[a1.dag() * a2.dag() + a1 * a2, lambda t, args: g(t, t0, g0, tau)]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Two-photon scattering amplitudes\n", "\n", "Here we compute the amplitude for the two-photon part of the output state projected onto the temporal basis. We plot only the case where one photon is scattered into the first waveguide and the other into the second: this is of course symmetric under reversal, and the cases of two photons scattered into only one waveguide are forbidden and have amplitude 0, since the difference in the number of photons in the two cavities is conserved in the presence of the pump beam. \n", "\n", "Using similar parameters as Fig 6(a) in Fischer, et al., we obtain a similar result:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 266, "width": 324 } }, "output_type": "display_data" } ], "source": [ "tau = 0.05 / gamma # width of gaussian pulse\n", "t0 = 3.5 * tau # center of gaussian pulse\n", "g0 = gamma # amplitude of gaussian pulse\n", "T = 100 # number of time bins\n", "W = 2 # number of waveguides\n", "\n", "tlist = np.linspace(0, 3/gamma, T)\n", "phi = temporal_scattered_state(Hspdc(t0, g0, tau), cavity_vac, 2, spdc_c_ops, tlist)\n", "amplitudes = np.zeros((W, W, T, T,))\n", "\n", "for i, tau1 in enumerate(tlist):\n", " for j, tau2 in enumerate(tlist):\n", " [a,b] = sorted([i,j]) # sort the indices to comply with time-ordering\n", " for wg1 in [0,1]:\n", " for wg2 in [0,1]:\n", " indices = [[] for _ in range(W)]\n", " indices[wg1].append(a)\n", " indices[wg2].append(b) \n", " basisVec = temporal_basis_vector(indices, T)\n", " amplitudes[wg1,wg2,i,j] = np.abs((basisVec.dag() * phi).full().item())**2\n", " \n", "# Plot the correlation for emission times emitted into different waveguides; note\n", "# that amplitudes[0][0] = amplitudes[1][1] = 0 and amplitudes[0][1] = amplitudes[1][0].\n", "fig, ax1 = plt.subplots(1,1)\n", "cax = ax1.imshow(amplitudes[0][1], interpolation='nearest', origin='lower')\n", "ax1.set_xticks(np.linspace(0,T-1,4))\n", "ax1.set_xticklabels([0, 1, 2, 3])\n", "ax1.set_xlabel(\"Time, $t_1$ [$1/\\gamma$]\")\n", "ax1.set_yticks(np.linspace(0,T-1,4))\n", "ax1.set_yticklabels([0, 1, 2, 3])\n", "ax1.set_ylabel(\"Time, $t_2$ [$1/\\gamma$]\")\n", "fig.colorbar(cax)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multi-waveguide photon emission probability\n", "\n", "Finally, we can compute the variation in probability of single-and two-photon emission as a function of the pulse length. This simulation exhibits a slight variation from the expected behavior in Figure 5(c) of Fischer, et al., more apparent at larger times, due to the interaction timescale of interest increasing relative to the total timescale as a function of pulse length. However, the results do closely resemble the expected analytical results:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "image/png": { "height": 267, "width": 373 } }, "output_type": "display_data" } ], "source": [ "emission_nums = [0, 2]\n", "pulse_lengths = np.linspace(0.05/gamma, 1.1 / gamma, 50)\n", "tlist = np.geomspace(1/gamma, 21/gamma, 50) - 1/gamma\n", "\n", "def scattering_probability_multiprocess(pulse_length, n):\n", " tau = pulse_length\n", " t0 = 3.5 * tau\n", " H = Hspdc(t0, gamma, tau)\n", " return scattering_probability(H, cavity_vac, n, spdc_c_ops, tlist)\n", "\n", "pool = Pool(worker_count)\n", "probs = {}\n", "for n in emission_nums:\n", " args = [(pulse_length, n) for pulse_length in pulse_lengths]\n", " probs[n] = np.array(pool.starmap(scattering_probability_multiprocess, args))\n", "pool.close()\n", "\n", "# Compute the purity of the output state\n", "purity = [probs[2][p] / (1-probs[0][p]) for p in range(len(pulse_lengths))]\n", "\n", "# Plot it\n", "for n in probs:\n", " plt.plot(pulse_lengths / gamma, probs[n], label = \"$P_{}$\".format(n))\n", "plt.plot(pulse_lengths / gamma, purity, '--', label = \"Purity\")\n", "plt.ylim(0,1)\n", "plt.xlim(pulse_lengths[0]/gamma, pulse_lengths[-1]/gamma)\n", "plt.xlabel(\"Pulse length, $\\\\tau$ $[1/\\gamma]$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Software version:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
SoftwareVersion
QuTiP4.3.0.dev0+7a7236e1
Numpy1.13.3
SciPy0.19.1
matplotlib2.1.0
Cython0.26.1
Number of CPUs4
BLAS InfoINTEL MKL
IPython6.2.1
Python3.6.3 |Anaconda custom (64-bit)| (default, Oct 6 2017, 12:04:38) \n", "[GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]
OSposix [darwin]
Sun Apr 08 17:43:59 2018 PDT
" ], "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qutip.ipynbtools import version_table\n", "version_table()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }