{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"Open            \"Open" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2 - Perturbing a two state system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial we are going to explore what happens when we connect a two state system to the \"outside world\". Or, put another way, what happens when we perturb a two state system? We'll look at two cases:\n", "1. Static perturbations\n", "2. Small, time-dependent perturbations\n", "\n", "A reminder that in QuTiP $\\hbar=1$ and so frequency and energy are completely interchangeable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's load the libraries and some custom code to make plotting easier later." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Libraries\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from qutip import *\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "## note, if you start getting errors when using pandas with complex numbers then update Pandas\n", "## - there was a bug that's been recently fixed https://github.com/pandas-dev/pandas/issues/27484\n", "\n", "# Function created in 01 tutorial to make plotting of states calculated from `sesolve` easier\n", "def states_to_df(states,times):\n", " psi_plus = np.zeros(len(times),dtype=\"complex128\") # To store the amplitude of the |+> state\n", " psi_minus = np.zeros(len(times),dtype=\"complex128\") # To store the amplitude of the |-> state\n", "\n", " for i, state in enumerate(states):\n", " psi_plus[i] = state[0][0][0]\n", " psi_minus[i] = state[1][0][0]\n", "\n", " return pd.DataFrame(data={\"+\":psi_plus, \"-\":psi_minus}, index=times)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1 Static perturbation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Last time we looked at an isolated two state system whose base states **|+>** and **|->** were represented as\n", "\n", "$$\n", "|+> = \\begin{bmatrix}\n", " 1 \\\\\n", " 0 \\\\\n", " \\end{bmatrix}, \n", "|-> = \\begin{bmatrix}\n", " 0 \\\\\n", " 1 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "and whose energies $E_0$ were identical. When we considered that coupling between the states could occur (with strength $A$), the hamiltonian for the system could then be represented as\n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " E_0 & -A \\\\\n", " -A & E_0 \\\\\n", "\\end{bmatrix} = E_0 I - A \\sigma_x\n", "$$\n", "\n", "\n", "where $I$ is the identity matrix and $ \\sigma_x$ one of the Pauli matrices." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial, we will introduce a perturbation in energy, $\\delta$, that differentiates between the two states. Physically, one can think of this as e.g. applying an electric field to a molecule with a permanent dipole moment. We can then represent the Hamiltonian as:\n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " E_0 + \\delta & -A \\\\\n", " -A & E_0 - \\delta \\\\\n", "\\end{bmatrix} = E_0 I - A \\sigma_x + \\delta\\sigma_z\n", "$$\n", "\n", "In effect this perturbation increase the energy of the |+> state and lowers the energy of the |-> state.\n", "\n", "Let's explore how this changes the previous case of an isolated two state system." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we represent the base states in QuTip as:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "plus = basis(2, 0)\n", "minus = basis(2, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll use the same parameters as in the previous tutorial, i.e. $E_0=1$, $A=0.1$, throughout this tutorial.\n", "\n", "We'll begin by taking the perturbation to be $\\delta = 2A$ and initialising the system in the |+> state." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "E0 = 1.0\n", "delta = 0.2\n", "A = 0.1\n", "\n", "H = E0*qeye(2) - A*sigmax() + delta*sigmaz()\n", "\n", "times = np.linspace(0.0, 70.0, 1000) \n", "\n", "result = sesolve(H, plus, times)\n", "df = states_to_df(result.states, times)\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,6))\n", "df.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 1)\", ax=axes[0]);\n", "(df.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 2)\", ax=axes[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just as in the previous tutorial (see Figs 3 & 4), we see Rabi oscillations in the probability because |+> and |-> are not stationary states. The behaviour is again like $\\cos^2(\\Omega t/2)$, but somewhat modified by the perturbation.\n", "\n", "1. The period of oscillations has gone from 31 to about 14 (recall, we have kept A the same)\n", "2. Instead of a complete oscillation from 0 to 1 of both states, we see that we are more likely to find the state as |+>. \n", "\n", "We can understand 2 by recalling that the perturbation creates an energy difference between the |+> and |->. This gives rise to a frequency difference much like what we'd have in the classical coupled pendulum problem if the lengths of the pendulums were different. In that case the coupling is much less effective and most of the energy stays in pendulums of the same length as can be seen in this [simulation video](https://www.youtube.com/watch?v=Z5rKTagEsro)\n", "\n", "To understand 1 we recall that the Rabi frequency arises as the beating between the different frequencies of the stationary states, i.e. $\\Omega = \\Delta E$. We therefore need to calculate the energy of the stationary states, i.e. we need to calculate the eigenvalues of the Hamiltonian.\n", "\n", "Let's do this for a number of different perturbation strengths:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "n_deltas = 100\n", "max_delta = 0.5\n", "deltas =np.linspace(-max_delta,max_delta,n_deltas)\n", "upper = np.zeros(n_deltas)\n", "lower = np.zeros(n_deltas)\n", "\n", "for i, d in enumerate(deltas):\n", " H_delta = E0*qeye(2) - A*sigmax() + d*sigmaz()\n", " E = H_delta.eigenenergies()\n", " upper[i] = E[1]\n", " lower[i] = E[0]\n", "energies = pd.DataFrame(data={\"upper\":upper, \"lower\":lower, \"$\\delta$/A\":deltas/A})" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "energies.plot(x=\"$\\delta$/A\", title=\"Energy (Fig 3)\", figsize=(7,6));\n", "plt.plot((deltas/A),(E0+deltas),'k--')\n", "plt.plot((deltas/A),(E0-deltas),'k--',label=\"$E_0 \\pm \\delta$\");\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see if Fig 3 makes sense. \n", "\n", "In the extreme, as $\\delta\\rightarrow \\pm \\infty$, the energy asymptotically approaches to $E_0 \\pm \\delta$ - this is consistent with the coupling becoming less and less important. At the other extreme, $\\delta \\rightarrow 0$ and we recover the result from the last tutorial, i.e. $E_0 \\pm A$.\n", "\n", "The form of the energy curve is actually a relatively simple formula $E_0 \\pm \\sqrt{A^2 + \\delta^2}$ (we won't derive this result here, but instead link you to a [lecture from Richard Feynman](https://www.feynmanlectures.caltech.edu/III_09.html#Ch9-S2)). From this we can now calculate $\\Omega = \\Delta E = 2\\sqrt{A^2 + \\delta^2} = 2\\sqrt{0.1^2 + 0.2^2} = 0.44$ giving a Rabi oscillation period of $2\\pi/\\Omega = 14$ that we saw graphically in Fig 2.\n", "\n", "For more of a deep dive into the dependence of energy on the various parts the Hamiltonian, consult the intimately connected topic of [avoided crossings](https://en.wikipedia.org/wiki/Avoided_crossing).\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the energy has changed a lot due to the perturbation, what about the stationary states themselves?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0.7763932, 1.2236068]),\n", " array([Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", " Qobj data =\n", " [[-0.22975292]\n", " [-0.97324899]],\n", " Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", " Qobj data =\n", " [[-0.97324899]\n", " [ 0.22975292]]], dtype=object))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H.eigenstates()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare these to the stationary states we found in the previous tutorial - let's rewrite them here for convenience:\n", "\n", "$\\frac{|+> + \\,\\ |->}{\\sqrt{2}}$ - in phase (a.k.a symmetric) - lower energy state\n", "\n", "$\\frac{|+> - \\,\\ |->}{\\sqrt{2}}$ - out of phase (a.k.a anti-symmetric) - higher energy state" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "in_phase = (plus + minus).unit()\n", "out_phase = (plus - minus).unit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the lower energy state is symmetric as in the previous tutorial (i.e both parts of the state have the same sign) and we have less of the energetically expensive |+> state and more of the |->.\n", "\n", "Other than the symmetry, there isn't much similarity with the stationary states from the last tutorial. This makes sense when we recall that $\\delta=2A$ - it's a strong perturbation so it changes the system a lot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is some really interesting physics that happens when we don't perturb the system too much, i.e $\\delta/A \\ll 1$, so we are going to explore this regime next in the context of time dependent perturbation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2 Time dependent perturbation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now going to consider a time dependent perturbation of the form $\\delta\\sigma_z\\cos(\\omega t)$ with $\\delta/A = 0.01 \\ll 1$. \n", "\n", "With QuTiP, we can add [time dependence in several ways](http://qutip.org/docs/latest/guide/dynamics/dynamics-time.html). We will use the [string based method](http://qutip.org/docs/latest/guide/dynamics/dynamics-time.html#string-format-method) because the code compiles into C and so it's faster (this means you need to have Cython installed on your computer).\n", "\n", "It works by specifying the Hamiltonian as $H=H_0 + H_1C(t)$, where $C$ should be a function (or combinations) from the list below\n", "\n", "```\n", "'abs', 'acos', 'acosh', 'arg', 'asin', 'asinh', 'atan', 'atanh', 'conj',\n", " 'cos', 'cosh','exp', 'erf', 'zerf', 'imag', 'log', 'log10', 'norm', 'pi',\n", " 'proj', 'real', 'sin', 'sinh', 'sqrt', 'tan', 'tanh'\n", "```\n", "\n", "In QuTip, we put this together as the list `H = [H0, [H1,C]]` and feed it into `sesolve` just like we did before.\n", "\n", "The question now is, what should we choose the frequency $\\omega$ to be?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Resonance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because we are only perturbing the system slightly, we can expect that the energy difference between the two unperturbed stationary states (i.e. $2A$) should still be something of interest. It is natural therefore to begin by setting $\\omega = \\omega_0 \\equiv 2A$. \n", "\n", "Intuitively we do expect some kind of resonance phenomenon because we are matching the driving frequency to the \"natural\" frequency of the two state system - but how will this resonance manifest?\n", "\n", "Let's start things off in a stationary state of the unperturbed system, specifically the higher energy state |+> - |->. Does the system stay close to this state as we might expect, given the smallness of the perturbation.\n", "\n", "Let's see." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "E0 = 1.0\n", "delta = 0.001\n", "A = 0.1\n", "\n", "H0 = E0*qeye(2) - A*sigmax() \n", "\n", "H1 = delta*sigmaz()\n", "\n", "H = [H0,[H1,'cos(w*t)']]\n", "\n", "times = np.linspace(0.0, 15000.0, 1000) \n", "\n", "result = sesolve(H, out_phase, times, args={'w':2*A})\n", "df_res = states_to_df(result.states, times)\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,6))\n", "df_res.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 4)\", ax=axes[0]);\n", "(df_res.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 5)\", ax=axes[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clearly see something interesting is happening. The probabilities are undergoing full oscillation from 1 to 0 and we can see a much longer oscillation timescale than before.\n", "\n", "It is however, quite difficult to be more specific from this plot. That's because we are still using the |+> and |-> basis to describe the system. The best basis to work with is one in which the base states are exactly, or at least close to, the stationary states. In this case, that's $\\frac{|+> + \\,\\ |->}{\\sqrt{2}}$ and $\\frac{|+> - \\,\\ |->}{\\sqrt{2}}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Changing the basis of a state is actually very easy in QuTiP, we just take any state `s` and apply the [transform](http://qutip.org/docs/latest/apidoc/classes.html?highlight=transform#qutip.Qobj.transform) method to it `s.transform(new_base_states)`.\n", "\n", "Each state vector needs to be transformed separately, so let's create a function to do this for the many states that comes from solving the Schrödinger equation." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def change_basis_to_df(states, times, new_basis, new_basis_labels):\n", " psi_new_basis_0 = np.zeros(len(times),dtype=\"complex128\") # To store the amplitude of the new_basis_0 state\n", " psi_new_basis_1 = np.zeros(len(times),dtype=\"complex128\") # To store the amplitude of the new_basis_1 state\n", "\n", " for i, state in enumerate(states):\n", " transformed_state = state.transform(new_basis)\n", " psi_new_basis_0[i] = transformed_state[0][0][0]\n", " psi_new_basis_1[i] = transformed_state[1][0][0]\n", "\n", " return pd.DataFrame(data={new_basis_labels[0]:psi_new_basis_0, new_basis_labels[1]:psi_new_basis_1}, index=times)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "df_res_basis = change_basis_to_df(result.states, times, [out_phase,in_phase], [\"|x> - |->\", \"|x> + |->\"])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,6))\n", "df_res_basis.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 6)\", ax=axes[0]);\n", "(df_res_basis.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 7)\", ax=axes[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can see better.\n", "\n", "Even though we only perturb the system slightly, i.e $\\delta/A = 0.01$ is small, when we \"resonantly\" perturb the system we cause a significant change, i.e. we cause the the system to transition between higher an lower energy states - this is the essence of stimulated emission/absorption in atomic systems.\n", "\n", "The oscillation of the probability is again referred to as Rabi oscillations (or sometimes called the [Rabi cycle](https://en.wikipedia.org/wiki/Rabi_cycle)). This time, however, the Rabi frequency is not determined by the beat frequency between the unperturbed stationary states but instead by the perturbation strength alone. \n", "\n", "Specifically, $\\Omega = \\delta$, giving a period of $2\\pi/\\Omega = 2\\pi/0.001 \\approx 6300$.\n", "\n", "This result is not immediately intuitive (see [derivation](https://en.wikipedia.org/wiki/Rabi_problem#Semiclassical_approach)), so we will return to this at a later point and derive it using perturbation theory.\n", "\n", "For now we will continue exploring. Now that we've seen the effect of resonance, it is natural to wonder how sensitive it is to changes in frequency." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Off resonance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start by changing the frequency so that $(\\omega-\\omega_0)/\\omega_0 = 1\\%$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "E0 = 1.0\n", "delta = 0.001\n", "A = 0.1\n", "\n", "H0 = E0*qeye(2) - A*sigmax()\n", "\n", "H1 = delta*sigmaz()\n", "\n", "H = [H0,[H1,'cos(w*t)']]\n", "\n", "times = np.linspace(0.0, 15000.0, 1000) \n", "\n", "result = sesolve(H, out_phase, times, args={'w':(2*A)*1.01})\n", "df_off_res = states_to_df(result.states, times)\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "df_off_res_basis = change_basis_to_df(result.states, times, [out_phase,in_phase], [\"|x> - |->\", \"|x> + |->\"])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "lines_to_next_cell": 0 }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,6))\n", "df_off_res_basis.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 8)\", ax=axes[0]);\n", "(df_off_res_basis.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 9)\", ax=axes[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the resonance is exquisitely sensitive. When the frequency is just 1% off resonance, the amplitude of probability oscillation is reduced to 20% of it's previous value. The Rabi frequency has also changed. The modified value is often called the [generalised Rabi frequency](https://en.wikipedia.org/wiki/Rabi_frequency#Generalized_Rabi_frequency) and has the form $\\bar\\Omega = \\sqrt{\\Omega^2 + (\\omega-\\omega_0)^2} = \\sqrt{\\delta^2 + (\\omega-\\omega_0)^2} = \\sqrt{0.001^2 + 0.002^2} = 0.002$, giving the period $2\\pi/\\bar\\Omega = 2\\pi/0.002 \\approx 3100$ that we can see in Fig 9." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Transition probability" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can be more quantitative with our assessment of the resonance effect by considering the time average probabilities like those seen in Fig 9.\n", "\n", "More specifically, in Fig 9, we begin our simulation in state |+> - |-> and we see that the probability to remain in that state (blue line) oscillates around about 0.9. If we imagine that we randomly observe our system at some point in time (and repeat this observation many times), then on average there is a probability of 0.9 that the system will still be in the state |+> - |->. Put another way, there is a probability of 0.1 that the system will have **transitioned** to another state - in this case there is only one other, namely |+> + |-> .\n", "\n", "We can therefore calculate a transition probability from our simulations as $T = 1-\\text{mean}(P_{\\psi_0})$, where $P_{\\psi_0}$ is the probability for the system to be in the state that we stated with." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're going to calculate $T$ for many values of the perturbation frequency $\\omega$ and so it's necessary that we make some optimisations so that the code doesn't take too long to run. We'll also introduce some simplifications that you'll often see in the literature.\n", "\n", "**Transform the Hamiltonian**\n", "\n", "We have already discovered that the natural basis to represent the perturbed system is using |+> + |-> and |+> - |->. To avoid transforming the results of our simulation many times over, we will instead change the basis of our Hamiltonian (we'll only need to do this once). Let's compare the H's before and after transformation (ignore time dependence of the perturbation for a moment so we can get a feeling for things):" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & -0.100\\\\-0.100 & 0.999\\\\\\end{array}\\right)\\end{equation*}" ], "text/plain": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", "Qobj data =\n", "[[ 1.001 -0.1 ]\n", " [-0.1 0.999]]" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Before\n", "H0+H1" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.100 & 0.001\\\\0.001 & 0.900\\\\\\end{array}\\right)\\end{equation*}" ], "text/plain": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", "Qobj data =\n", "[[1.1e+00 1.0e-03]\n", " [1.0e-03 9.0e-01]]" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# After\n", "(H0+H1).transform([out_phase,in_phase])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that H has changed from from \n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " E_0 + \\delta & -A \\\\\n", " -A & E_0 - \\delta \\\\\n", "\\end{bmatrix} = E_0 I - A \\sigma_x + \\delta\\sigma_z\n", "$$\n", "\n", "\n", "to \n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " E_0 + A & \\delta \\\\\n", " \\delta & E_0 - A \\\\\n", "\\end{bmatrix} = E_0 I + A\\sigma_z +\\delta \\sigma_x\n", "$$\n", "\n", "In this basis, we can see directly (from the difference in the diagonal elements) that the effect of the coupling ($A$) splits the energy of the unperturbed ($\\delta=0$) stationary states by an amount $2A$. We can also see directly that the perturbation couples the two energy states, as we have seen in our last two simulations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Shift all the energies**\n", "\n", "Because we can only measure differences in energy, we are free to set the \"zero\" value of energy to be wherever we like. In particular, we can set $E_0 = 0$. The Hamiltonian is then:\n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " A & \\delta \\\\\n", " \\delta & -A \\\\\n", "\\end{bmatrix} = A\\sigma_z +\\delta \\sigma_x\n", "$$\n", "\n", "When written in this form, it resembles the [Hamiltonian for spin 1/2 particle in a magnetic field](https://www.feynmanlectures.caltech.edu/III_10.html#Ch10-S6) with $B_z \\propto A$ and $B_x\\propto \\delta$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Calculate the transition probabilities**\n", "\n", "We note 2 things:\n", "\n", "1. In our new basis, the |+> and |-> states now represent the higher (|+> - |->) and lower (|+> + |->) energy states from our previous basis\n", "\n", "2. We previously calculated $\\psi$ and then computed the probabilities from it. We can make the computation faster by computing the probabilities directly. This is done by calculating the expectation value of |+><+| to get $P_{|+>}$ and |-><-| to get $P_{|->}$. In QuTiP we can make these operators using the [`ket`](http://qutip.org/docs/latest/apidoc/functions.html?highlight=ket#qutip.states.ket) and [`bra`](http://qutip.org/docs/latest/apidoc/functions.html?highlight=bra#qutip.states.bra) functions (alternatively using [`projection`](http://qutip.org/docs/latest/apidoc/functions.html?highlight=projection#qutip.states.projection))" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [], "source": [ "P_plus = ket([0])*bra([0]) # Or use projection(2,0,0)\n", "P_minus = ket([1])*bra([1]) # Or use projection(2,1,1)" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}" ], "text/plain": [ "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n", "Qobj data =\n", "[[1. 0.]\n", " [0. 0.]]" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_plus" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's calculate the transition probability for the simulation shown in Fig 9 as a sense check." ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.09702508180589431" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = 0.001\n", "A = 0.1\n", "\n", "H0 = A*sigmaz()\n", "\n", "H1 = delta*sigmax()\n", "\n", "H = [H0,[H1,'cos(w*t)']]\n", "\n", "times = np.linspace(0.0, 15000.0, 1000) \n", "\n", "# Passing the P_plus operator to sesolve gives us the expectation value directly.\n", "result = sesolve(H, plus, times,[P_plus], args={'w':(2*A)*1.01})\n", "T = 1 - result.expect[0].mean()\n", "T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$T$ is very close to 0.1, great!\n", "\n", "Now let's repeat this for many different values of $\\omega$. We'll scan over the resonance region, i.e. near $\\omega/\\omega_0 = 1$" ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [], "source": [ "omega = np.arange(0.9,1.1,0.005)" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [], "source": [ "Ts = np.zeros(omega.size)" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [], "source": [ "delta = 0.001\n", "A = 0.1\n", "\n", "H0 = A*sigmaz()\n", "\n", "H1 = delta*sigmax()\n", "\n", "H = [H0,[H1,'cos(w*t)']]\n", "\n", "times = np.linspace(0.0, 15000.0, 1000)\n", "\n", "for i,w in enumerate(omega):\n", " \n", " result = sesolve(H, plus, times,[P_plus], args={'w':(2*A)*w}) # recall 2*A = omega_0\n", " Ts[i] = 1 - result.expect[0].mean()\n" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,6))\n", "plt.plot((omega-1),Ts)\n", "plt.xlabel(\"$(\\omega-\\omega_0)/\\omega_0$\")\n", "plt.ylabel(\"Probability\")\n", "plt.title(\"Transition Probability (Fig 10)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now quantify the sensitivity of the resonance by calculating the [full width half max (FWHM)](https://en.wikipedia.org/wiki/Full_width_at_half_maximum) from the data." ] }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.010000000000000231" ] }, "execution_count": 196, "metadata": {}, "output_type": "execute_result" } ], "source": [ "index_of_half_max = np.argmin(abs(Ts-max(Ts)/2))\n", "(omega[index_of_half_max]-1)*2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Next up...\n", "So far, we've developed an intuition for a simple two state system and how it behaves in a presence of an external perturbation. We've uncovered the physical basis for stimulated emission and absorption in atomic systems. You might be wondering, what about spontaneous emission? We cannot describe it using this model 😞. We must go a level deeper and consider not only how the perturbation acts on the two state system, but how the two state system acts on the perturbation. Put another way, we need to consider the perturbation as a field that can itself be quantised 🤯." ] } ], "metadata": { "jupytext": { "formats": "ipynb,src//md" }, "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": "3.7.1" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }