{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"Open            \"Open" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 - An isolated two state system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial we are going to look at a single two state system that doesn't talk to the environment around it. We'll look at two examples\n", "1. When the system is in a stationary state\n", "2. When the two states are coupled together" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from qutip import *\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.1 - Stationary state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We begin with a description of our two state system.\n", "\n", "We will call the two states **|+>** and **|->** and represent them 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", "At any time, the state of the system can be described by\n", "\n", "$$\n", "\\psi(t) = \\psi_+(t)|+> +\\,\\ \\psi_-(t)|->\n", "$$\n", "\n", "where the complex numbers $\\psi_+$ and $\\psi_-$ are [probability amplitudes](https://en.wikipedia.org/wiki/Probability_amplitude) (a.k.a quantum amplitudes or just amplitudes) whose modulus squared gives us the probability to find the system in that particular state. \n", "\n", "For this tutorial we will assume that the two states have the same energy. The hamiltonian matrix will therefore take the form\n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " E_0 & 0 \\\\\n", " 0 & E_0 \\\\\n", "\\end{bmatrix} = E_0 I\n", "$$\n", "\n", "where $I$ is the identity matrix.\n", "\n", "In this example we will set $E_0=1$.\n", "\n", "We will now use QuTiP to find out how this system evolves in time. It should be noted that $\\hbar=1$ in QuTiP so energy and frequency are interchangable." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "E0 = 1\n", "H = E0*qeye(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's initialise the 2 state system. In Qutip, this can be done in several ways (cf QuTip [intro notebook](https://github.com/jrjohansson/qutip-lectures/blob/master/Lecture-0-Introduction-to-QuTiP.ipynb) and [intro docs](http://qutip.org/docs/latest/guide/guide-basics.html))\n", "\n", "For the $|+>$ state: `Qobj([[1], [0]])` or `basis(2, 0)`\n", "\n", "For the $|->$ state: `Qobj([[0], [1]])` or `basis(2, 1)`" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "plus = basis(2, 0)\n", "minus = basis(2, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll go with $\\psi(t=0) \\equiv \\psi_0 = |+>$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "psi0 = plus" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's evolve the state $\\psi$ over time by solving the Schrödinger equation\n", "\n", "$$\n", "i \\hbar \\frac{d}{d t}\\psi(t) = \\hat H\\psi(t)\n", "$$\n", "\n", "Qutip has many [solvers](http://qutip.org/docs/latest/apidoc/functions.html#dynamics-and-time-evolution) that can do this. We will start with [sesolve](http://qutip.org/docs/latest/apidoc/functions.html#module-qutip.sesolve) as demonstrated [here](http://qutip.org/docs/latest/guide/dynamics/dynamics-master.html#unitary-evolution)." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "times = np.linspace(0.0, 10.0, 1000) # simulation time\n", "result = sesolve(H, psi0, times) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "QuTiP returns a list of the states for different times. We'll transform this into a dataframe to make things easier to visualise. We'll make a function for this so we can reuse it later." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "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": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "df_stationary = states_to_df(result.states, times)" ] }, { "cell_type": "code", "execution_count": 26, "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_stationary.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 1)\", ax=axes[0]);\n", "(df_stationary.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 2)\", ax=axes[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The probability to find the system in the $|+>$ state (i.e. $|\\psi_+|^2$) state remains constant throughout because the system is in what we call a **stationary state**, i.e. a state of constant energy.\n", "\n", "The amplitude oscillates at a frequency determined by the $E_0$ parameter which we set to equal 1 at the start and so we have a period of $2\\pi$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 Coupling between two states of the same energy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the two states are coupled, e.g. the case of the [ammonia molecule](https://www.feynmanlectures.caltech.edu/III_08.html#Ch8-S6), the hamiltonian matrix will contain off diagonal elements\n", "\n", "$$\n", "H = \\begin{bmatrix}\n", " E_0 & -A \\\\\n", " -A & E_0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "By using common two-state operators such as the [Pauli matrices](https://en.wikipedia.org/wiki/Pauli_matrices):\n", "\n", "$$\n", "\\sigma_x = \\begin{bmatrix}\n", "0 & 1 \\\\\n", " 1 & 0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "$$\n", "\\sigma_y = \\begin{bmatrix}\n", "0 & -i \\\\\n", " i & 0 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "$$\n", "\\sigma_z = \\begin{bmatrix}\n", "1 & 0 \\\\\n", " 0 & -1 \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "The hamiltonian can be re-written as:\n", "\n", "$$\n", "H = E_0 I - A \\sigma_x\n", "$$\n", "\n", "QuTiP allows us to conveniently reference the Pauli matrices using `sigmax()`, `sigmay()` and `sigmaz()`." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "psi0 = plus\n", "\n", "E0 = 1.0\n", "A = 0.1 # coupling \"strength\"\n", "\n", "H = E0*qeye(2) - A*sigmax()\n", "\n", "times = np.linspace(0.0, 70.0, 1000) # simulation time\n", "\n", "result = sesolve(H, psi0, times)\n", "df_coupled = states_to_df(result.states, times)" ] }, { "cell_type": "code", "execution_count": 28, "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_coupled.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 3)\", ax=axes[0]);\n", "(df_coupled.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 4)\", ax=axes[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the situation is more complicated.\n", "\n", "Although we again initialised the system in the $|+>$ state, the probability to find the system in that state at a later time is no longer constant - it slowly oscillates. These oscillations (often called [Rabi oscillations](https://en.wikipedia.org/wiki/Two-state_quantum_system#Rabi_formula_for_a_static_perturbation)) tell us that $|+>$ is no longer a state of constant energy (same for $|->$). What's going on?\n", "\n", "This behaviour is identical to a system of two coupled pendulums - each state in the quantum system is analagous to one of the pendulums. If you displace only one pendulum, then its maximum amplitude oscillates slowly as it transfers energy to the second pendulum and then back again (as you can see in this [video](https://youtu.be/CjJVBvDNxcE?t=56)).\n", "\n", "In the language of classical physics, this slow oscillation of the maximum amplitude results from the [beating](https://en.wikipedia.org/wiki/Beat_%28acoustics%29) of two frequencies that correspond to different [normal modes](https://www.physics.utoronto.ca/~sandra/PHY238Y/Lectures/Lect4_Coupl_osc.pdf). These modes can be distinguished when you displace both pendulums, first in phase and then out of phase (see [this video](https://youtu.be/CjJVBvDNxcE?t=14)). \n", "\n", "In the absence of coupling, there are also two frequencies in the system, but they are identical because the pendulums are identical. In effect, the coupling splits the two frequencies apart and that is also what's happening in our quantum system.\n", "\n", "Instead of our two states |+> and |-> having the same energy $E_0$, we can now expect to find that the states:\n", "\n", "$|+> + \\,\\ |->$ - in phase\n", "\n", "$|+> - \\,\\ |->$ - out of phase\n", "\n", "should be our states of constant energy - our stationary states (we will of course need to normalise these states).\n", "\n", "We can also expect to be able to describe the above Rabi oscillations in probability with something like $\\cos^2(\\Omega t/2)$, where $\\Omega = \\Delta E$ (the Rabi frequency) is given by the difference in energy (c.f. beat frequency) between the two new stationary states.\n", "\n", "Let's use QuTiP to see this." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "QuTiP allows us to easily combine states together and make sure they are normalised using the `unit()` function" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "in_phase = (plus + minus).unit()\n", "out_phase = (plus - minus).unit()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "E0 = 1.0\n", "A = 0.1\n", "\n", "H = E0*qeye(2) - A*sigmax()\n", "\n", "times = np.linspace(0.0, 10.0, 1000) \n", "\n", "# First let's get the evolution of the state when initialised as \"in phase\"\n", "result = sesolve(H, in_phase, times)\n", "df_coupled_in_phase = states_to_df(result.states, times)\n", "\n", "# Secondly let's get the evolution of the state when initialised as \"out of phase\"\n", "result = sesolve(H, out_phase, times)\n", "df_coupled_out_phase = states_to_df(result.states, times)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "## First plot the In phase solution\n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,6))\n", "df_coupled_in_phase.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 5)\", ax=axes[0]);\n", "(df_coupled_in_phase.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 6)\", ax=axes[1]);\n", "fig.suptitle('In phase', fontsize=20)\n", "\n", "## Secondly plot the Out of phase solution\n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,6))\n", "df_coupled_out_phase.plot(title=\"Real part of amplitudes Re($\\psi$) (Fig 7)\", ax=axes[0]);\n", "(df_coupled_out_phase.abs()**2).plot(title=\"Probabilities $|\\psi|^2$ (Fig 8)\", ax=axes[1]);\n", "fig.suptitle('Out of phase', fontsize=20);\n", "\n", "# Use the following to remove the y-offset from out of phase probabilities if you find there is one\n", "# axes[1].get_yaxis().get_major_formatter().set_useOffset(False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In both cases, the probabilities to find the state in either |+> or |-> is 0.5 (note any offset that can sometimes appear in the y axes of the plots). The amplitudes can also be seen to evolve with the same frequency - just like we saw in the coupled pendulum problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What about the energy of our newly found stationary states?\n", "\n", "We can use QuTiP to help us out. If we supply a list of operators to `sesolve` in the 4th argument, e.g. `sesolve(H, psi0, times,[sigmax(), sigmay()]` then instead of returning the evolution of the state we get the evolution of the expectation value of the supplied operators.\n", "\n", "Since the hamiltonian is an operator, we can supply `H` and then find how the energy of our state changes over time.\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "result_in_phase = sesolve(H, in_phase, times, [H])\n", "result_out_phase = sesolve(H, out_phase, times, [H])" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,6))\n", "plt.title(\"Expectation value of energy (Fig 9)\")\n", "plt.plot(result_in_phase.expect[0], label=\"in phase\")\n", "plt.plot(result_out_phase.expect[0], label=\"out of phase\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the energies of our new stationary states are:\n", "\n", "$E_0 - A$ for $|+> + \\,\\ |->$ - in phase\n", "\n", "$E_0 + A$ for $|+> - \\,\\ |->$ - out of phase\n", "\n", "So, there is energetic price to be paid for the states to be out of phase with each other.\n", "\n", "Returning to the Rabi oscillations, we can now calculate $\\Omega = \\Delta E =2A$ which gives an oscillation period of $2\\pi/2A \\approx 31$ - this matches very nicely with what we saw in Fig 4." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although it is fun and insightful to go through the process of solving the Schrödinger equation, there is another way to get at the stationary states and their corresponding energies - we simply need to find the eigenvectors and eigenvalues of the hamiltonian.\n", "\n", "QuTip gives us a easy way to do this using `eigenstates()`." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0.9, 1.1]),\n", " array([Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", " Qobj data =\n", " [[-0.70710678]\n", " [-0.70710678]],\n", " Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n", " Qobj data =\n", " [[-0.70710678]\n", " [ 0.70710678]]], dtype=object))" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H.eigenstates()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first part of the output gives the eigenvalues `[0.9,1.1]` - these are the energies we found above\n", "\n", "The second part gives the two normalised eigenvectors `[-0.70710678 -0.70710678]` (in phase) and `[-0.70710678 0.70710678]` (out of phase) that we also discovered earlier.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Next up...\n", "We'll introduce an external force field to our coupled two state system and in the process discover how we can use this force to create transitions between different energy states " ] } ], "metadata": { "jupytext": { "formats": "ipynb,src//md" }, "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": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 4 }