{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3 - A two state system in a quantised field"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This tutorial is all about going to the next level in thinking about how two state systems interact with their environment. In the last tutorial, we actually took a semi-classical view of the effect of a perturbation - now we must be go full quantum if we are to continue on our quantum quest!\n",
"\n",
"We are covering a lot here so we've chunked it up into sections:\n",
"\n",
"1. Recap\n",
"2. What is a quantum field?\n",
"3. The Hamiltonian for a quantum field\n",
"4. Coupling to a quantum field\n",
"5. Describing coupled systems in QuTiP\n",
"6. Spontaneous emission\n",
"\n",
"You'll see that section 6 is what we promised you at the end of the last tutorial - it does take some work to get there, but we hope you'll find the experience valuable.\n"
]
},
{
"cell_type": "code",
"execution_count": 61,
"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",
"from scipy.signal import argrelextrema\n",
"import warnings\n",
"warnings.filterwarnings('ignore')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.1 - Recap"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have previously looked at a two state system whose states are allowed to couple to each other with strength $A$. This coupling resulted in a splitting of the states of constant energy. When we perturbed the energy of those states by an amount $\\pm \\delta$ we found (in [tutorial 02](https://github.com/project-ida/two-state-quantum-systems/blob/master/02-perturbing-a-two-state-system.ipynb)) that a natural way to represent the Hamiltonian is\n",
"\n",
"$$\n",
"H = \\begin{bmatrix}\n",
" A & \\delta \\\\\n",
" \\delta & -A \\\\\n",
"\\end{bmatrix} = A\\sigma_z +\\delta \\sigma_x\n",
"$$\n",
"\n",
"The base states being used to represent this system are the stationary states of the unperturbed system ($\\delta=0$) that we describe by:\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",
"where |+>, |-> correspond to the higher and lower energy states respectively. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"plus = basis(2, 0)\n",
"minus = basis(2, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the [last tutorial](https://github.com/project-ida/two-state-quantum-systems/blob/master/02-perturbing-a-two-state-system.ipynb), we made the perturbation $\\delta$ time dependent ($\\sin{\\omega t}$) and discovered a resonance effect. Even when the perturbation was small, the two level system could be made to oscillate (see [Rabi cycle](https://en.wikipedia.org/wiki/Rabi_cycle)) between the upper and lower energy state i.e. when $\\omega = 2A$ - this is the physical basis for stimulated emission."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.2 - What is a quantum field?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So far we have considered the environment to be unaffected by the two-state system. This has been a convenient approximation but naturally leaves some bits of important physics out e.g. spontaneous emission.\n",
"\n",
"To capture this missing physics we must think of the environment as a field (actually maybe many fields, but let's not over complicate things for now). For example the electric field $E$ - a continuous thing (a vector thing) that exists at all points in space and time i.e $E(r,t)$. To properly describe the interaction of our quantised two-state system with such a field, we are forced to quantise the field (in some sense) as well.\n",
"\n",
"But what does quantising a field mean? Answering this question in a completely satisfactory way will take us down the rather deep rabbit hole of [Quantum Field Theory](https://en.wikipedia.org/wiki/Quantum_field_theory) and [Lagrangian mechanics](https://en.wikipedia.org/wiki/Lagrangian_(field_theory%29) - we will not go there today! For now, we will simply summarise the most important bits (which are by no means self evident) that will help us to explore some of the physics using QuTiP. The following might still seem a bit alien but I promise we'll get to some calculations soon."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3.2.1 - Fields as harmonic oscillators\n",
"\n",
"The Lagrangian for a field (and resulting Hamiltonian that's of direct interest to us) can be represented in a way that's mathematically equivalent to a set of independent harmonic oscillators. This is actually a classical result that comes from:\n",
"- The requirements of relativity and that the field equations (like Maxwell's equations) are linear\n",
"- The field being represented as a sum of plane waves like:\n",
" \n",
"$$\n",
"\\underset{k}{\\sum} a_k(t)e^{i(k\\cdot r)}\n",
"$$\n",
"\n",
"For more information, see [Classical Mechanics](https://en.wikipedia.org/wiki/Classical_Mechanics_(Goldstein_book%29) (Section 13.6) by Goldstein and also [Student Friendly Quantum Field Theory](https://www.quantumfieldtheory.info/) (Section 3.2.3) by Kaluber"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3.2.2 - Quantising the field\n",
"\n",
"Quantisation comes from treating the classical oscillators (labeled by their mode number k) as if they are [quantum harmonic oscillators](https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator) whose energy is known to take on discrete values:\n",
"$$\n",
"E_{k,n} = \\left(n + \\frac{1}{2} \\right)\\hbar \\omega_k\n",
"$$\n",
"\n",
"where $n=0,1,2,3 ...$ and $\\omega \\propto k$. This quantisation is technically accomplished by:\n",
"- Treating the amplitudes of the field $a_k$ as operators and not simply complex numbers\n",
"- Applying a form of Heisenberg's uncertainty principle ([Canonical commutation relation](https://en.wikipedia.org/wiki/Canonical_commutation_relation))to the $a_k$'s, i.e.\n",
"$$\n",
"[a_k, a_k^{\\dagger}] \\equiv a_k a_k^{\\dagger} - a_k^{\\dagger}a_k = 1\n",
"$$\n",
"\n",
"The Hamiltonian for the quantised field then looks like\n",
"\n",
"$$\n",
"H = \\underset{k}{\\sum} \\hbar\\omega_k\\left(a_k^{\\dagger}a_k +\\frac{1}{2}\\right)\n",
"$$ \n",
"\n",
"and we can then identify the eigenvalues of the operator $a_k^{\\dagger}a_k$ as equal to $n$ (by comparing with the form of $E_{k,n}$). To understand the deeper meaning of $a_k^{\\dagger}$ and $a_k$ we must first understand how to interpret $n$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3.2.3 - The meaning of $n$\n",
"\n",
"When we first encounter the quantum harmonic oscillator, it is usually to model a particle moving in a quadratic potential well. There, we think of $n$ as simply a label for the energy state of the particle with energy $\\left(n + \\frac{1}{2} \\right)\\hbar \\omega$. \n",
"\n",
"In quantum field theory, $n$ is interpreted as a particle number. As an example, take the $k=3$ mode with $n=2$. This means the field has 2 particles with energy $\\hbar \\omega_3$. These particles are what people call bosons and they have different names depending on the field being described, e.g. photons, phonons etc.\n",
"\n",
"The particle number interpretation suggests that a natural way to describe the states of a quantum field is by the number of bosons in each mode, i.e. $|n_{k_1}, n_{k_2}, n_{k_3}, \\cdots>$ - this is called a [Fock state](https://en.wikipedia.org/wiki/Fock_state). For simplicity, consider that there is only one mode. We can represent the different states of the field as:\n",
"\n",
"$$\n",
"|0> = \\begin{bmatrix}\n",
" 1 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" \\vdots\n",
" \\end{bmatrix}, \\ \\ \\ \n",
"|1> = \\begin{bmatrix}\n",
" 0 \\\\\n",
" 1 \\\\\n",
" 0 \\\\\n",
" \\vdots\n",
"\\end{bmatrix}, \\ \\ \\\n",
"|2> = \\begin{bmatrix}\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 1 \\\\\n",
" \\vdots\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"In QuTiP, we can create Fock states using the same `basis` function that we used previously to represent our two-states system. For example, to represent a field with a single mode, with a maximum capacity of 4 bosons, that is currently occupied by only 2 bosons, we can write:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\1.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [0.]\n",
" [1.]\n",
" [0.]\n",
" [0.]]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"two = basis(5, 2)\n",
"two"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using these fock states, we can identify the operator $a_k^{\\dagger}a_k$ as having eigenvalues equal to the the number of bosons in mode k and having eigenvectors equal to the fock states, e.g.\n",
"\n",
"$$\n",
"a_k^{\\dagger}a_k |2> = 2 |2>\n",
"$$\n",
"\n",
"We therefore call $a_k^{\\dagger}a_k$ the number operator.\n",
"\n",
"But what about the individual $a_k^{\\dagger}$ and $a_k$ operators? How do we understand them? How can we construct them?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3.2.4 - The meaning of $a_k^{\\dagger}$ and $a_k$\n",
"Once we understand $a_k^{\\dagger}$ and $a_k$ we are in a position to build the Hamiltonian and start doing some simulations with QuTiP. \n",
"\n",
"Let's apply the number operator to a state that is not obviously one of its eigenstates. e.g. $a_k^{\\dagger}|2>$\n",
"\n",
"$$\n",
"a_k^{\\dagger}a_k (a_k^{\\dagger}|2>) = a_k^{\\dagger}a_k a_k^{\\dagger} |2> \\overset{[a_k, a_k^{\\dagger}]=1}{=} a_k^{\\dagger}(a_k^{\\dagger}a_k+1) |2> = a_k^{\\dagger}(2+1) |2> = 3a_k^{\\dagger}|2>\n",
"$$\n",
"\n",
"So, the number of bosons in the state $a_k^{\\dagger}|2>$ is 3. In effect, the $a_k^{\\dagger}$ operator has created a new boson so we call it a **creation** operator. We can perform a similar calculation with the $a_k$ operator to find it reduces the number of bosons and so we call it an **annihilation** or **destruction** operator.\n",
"\n",
"QuTiP allows us to construct the creation and destruction operators using the [`create` and `destroy` functions](http://qutip.org/docs/latest/apidoc/functions.html?highlight=create#qutip.operators.create)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"a = destroy(5) # We choose 5 so that we can operate on states with up to a maximum of n=4 bosons\n",
"a_dag = create(5) # we could also use a.dag()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's apply these operators to our *two* state to confirm what we just discovered in algebra."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After normalising the state we can see immediately that $|2>$ has indeed become state $|3>$ under the operation of $a_k^{\\dagger}$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\0.0\\\\1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [0.]\n",
" [0.]\n",
" [1.]\n",
" [0.]]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(a_dag*two).unit()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Similarly we can see that $|2>$ becomes $|1>$ under the $a_k$ operator"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5], [1]], shape = (5, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [1.]\n",
" [0.]\n",
" [0.]\n",
" [0.]]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(a*two).unit()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we are ready to construct the Hamiltonian."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.3 - The Hamiltonian for a quantum field"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have seen that to describe a quantum field we need to construct a Hamiltonian of the form:\n",
"\n",
"$$\n",
"H = \\underset{k}{\\sum} \\hbar\\omega_k\\left(a_k^{\\dagger}a_k +\\frac{1}{2}\\right)\n",
"$$\n",
"\n",
"where the sum is over all the possible modes of the field and $a_k^{\\dagger}$ and $a_k$ operators create and destroy bosons in the k'th mode.\n",
"\n",
"Let's continue to consider\n",
"- only a single mode\n",
"- maximum of 4 bosons in that mode\n",
"\n",
"For simplicity we'll set the energy of the mode $\\omega$ = 1 (recall $\\hbar=1$ in QuTiP)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"omega = 1\n",
"max_bosons = 4\n",
"\n",
"a = destroy(max_bosons+1)\n",
"\n",
"H = omega*(a.dag()*a+0.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's have a look at H"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 2.500 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 3.500 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 4.500\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True\n",
"Qobj data =\n",
"[[0.5 0. 0. 0. 0. ]\n",
" [0. 1.5 0. 0. 0. ]\n",
" [0. 0. 2.5 0. 0. ]\n",
" [0. 0. 0. 3.5 0. ]\n",
" [0. 0. 0. 0. 4.5]]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"H"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Because the Hamiltonian is diagonal there is no coupling between the different number states. Without doing any further calculation we can therefore say that if we start out with e.g. 3 bosons in our mode then we'll continue to have 3 bosons indefinitely. This is the same type of behaviour that we saw in the isolated two state system ([tutorial 01](https://github.com/project-ida/two-state-quantum-systems/blob/master/01-an-isolated-two-state-system.ipynb) section 1.1). - Not very exciting!\n",
"\n",
"We do however expect that bosons will get created and destroyed as a result of interaction with another system, e.g. when an electron makes a transition between different energy levels. Let's see how we can model that - this will end up giving us the spontaneous emission physics that we so far been lacking."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.4 - Coupling to a quantum field"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Firstly, a few general words on interactions. Finding the coupling between two quantum things is actually quite tricky. It requires expressing everything as its own field (even the two state system!) and imposing a certain symmetry on the Lagrangian of those combined fields. The interaction term in the Lagrangian (and resulting Hamiltonian) pops out as a consequence, how lovely! This is known as [gauge theory](https://en.wikipedia.org/wiki/Gauge_theory) and is an even deeper rabbit hole than quantum field theory. Needless to say, we shall not be going deeper into that today either. If you are curious I recommend chapter 10 of [Explorations in Mathematical Physics by Koks](https://www.bookdepository.com/Explorations-Mathematical-Physics-Don-Koks/9780387309439) for an intro.\n",
"\n",
"So, what can we say about the interaction of our two-state system with a quantised field without getting lost in rigor? *(not that rigor isn't important, but it will slow us down too much at the moment)*\n",
"\n",
"\n",
"We can make a guess at the interaction term by recalling the time dependent Hamiltonian from [Tutorial 02](https://github.com/project-ida/two-state-quantum-systems/blob/master/02-perturbing-a-two-state-system.ipynb):\n",
"\n",
"$$\n",
"H = \\begin{bmatrix}\n",
" A & \\delta\\cos{\\omega t} \\\\\n",
" \\delta\\cos{\\omega t} & -A \\\\\n",
"\\end{bmatrix} = A\\sigma_z +\\delta\\cos{\\omega t} \\sigma_x\n",
"$$\n",
"\n",
"We interpreted $\\delta$ as being related to the strength of a perturbing field and $A$ as a coupling between the two states of our system. In our now quantised field, the equivalent interaction term comes from a single mode and can be written as:\n",
"\n",
"$$\\frac{\\delta}{2}\\left( a^{\\dagger} + a \\right)\\sigma_x$$\n",
"\n",
"where $\\delta$ is the coupling constant. What we've essentially created is an interaction term that closely resembles that of an [electric](https://en.wikipedia.org/wiki/Electric_dipole_transition) and [magnetic](https://en.wikipedia.org/wiki/Magnetic_dipole_transition) dipole.\n",
"\n",
"\n",
"The overall Hamiltonian can then be written as:\n",
"\n",
"$$H = A \\sigma_z + \\hbar\\omega\\left(a^{\\dagger}a +\\frac{1}{2}\\right) + \\frac{\\delta}{2}\\left( a^{\\dagger} + a \\right)\\sigma_x$$\n",
"\n",
"The only remaining problem is figuring out how to make the QuTiP representations for the field and the two-state system compatible. Luckily QuTiP will come to our rescue."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.5 - Describing coupled systems in QuTiP\n",
"\n",
"Right now, we represent the two state system by something like\n",
"\n",
"$$\n",
"|+> = \\begin{bmatrix}\n",
" 1 \\\\\n",
" 0 \\\\\n",
" \\end{bmatrix}\n",
"$$\n",
"\n",
"and the field is represented by something like\n",
"\n",
"$$\n",
"|2> = \\begin{bmatrix}\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 1 \\\\\n",
" 0 \\\\\n",
" \\end{bmatrix}\n",
"$$\n",
"\n",
"These states clearly have different dimensions and so too do the operators in H above - we cannot simply multiply together them as our Hamiltonian would suggest. We need a new basis that is somehow a combination of the existing ones.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One way to build a new basis is to enumerate the many different configurations for the combined system, e.g.\n",
"- 2 bosons for the field and + for the two-state system, i.e. |2, ->\n",
"- 0 bosons for the field and - for the two-state system, i.e |0, +>\n",
"- etc.\n",
"\n",
"There are `(max_bosons+1) x 2` different states and we can write the probability for the system to be in those states as entries in a vector like below.\n",
"\n",
"$$ |n,\\pm> = \n",
"\\begin{bmatrix}\n",
" 0,+ \\\\\n",
" 0,- \\\\\n",
" 1,+ \\\\\n",
" 1,- \\\\\n",
" 2,+ \\\\\n",
" 2,- \\\\\n",
" 3,+ \\\\\n",
" 3,- \\\\\n",
" 4,+ \\\\\n",
" 4,- \\\\\n",
" \\vdots \n",
"\\end{bmatrix} \\ , \\ \\ \\ \\ \\ \\ \\ \\ \\ \n",
"|2, -> = \n",
"\\begin{bmatrix}\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 1 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" 0 \\\\\n",
" \\vdots \n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"\n",
"QuTiP automates the process of creating these states using [tensor products](http://qutip.org/docs/latest/guide/guide-tensor.html#using-tensor-products-and-partial-traces), which calculates, e.g.\n",
"\n",
"$$\n",
"|2,-> = |2> \\otimes |->\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5, 2], [1, 1]], shape = (10, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\1.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5, 2], [1, 1]], shape = (10, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [0.]\n",
" [0.]\n",
" [0.]\n",
" [0.]\n",
" [1.]\n",
" [0.]\n",
" [0.]\n",
" [0.]\n",
" [0.]]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"two_minus = tensor(two, minus) # The order here doesn't matter, but you need to be consistent throughout\n",
"two_minus"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> As an aside (feel free to skip this paragraph), for those who are know a bit more about the formal mathematics of the [tensor product](https://en.wikipedia.org/wiki/Tensor_product) (see also [outer product](https://en.wikipedia.org/wiki/Outer_product) ), you might be surprised that the result of `tensor(two, plus)` is a vector and not a matrix. Technically what is being done here is the [Kronecker product](https://en.wikipedia.org/wiki/Kronecker_product) and to see the explicit connection between the matrix an vector form see [here](https://en.wikipedia.org/wiki/Outer_product#Connection_with_the_Kronecker_product)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The same tensor products can be done for [operators, creating block matrices](https://en.wikipedia.org/wiki/Tensor_product#Tensor_product_of_linear_maps) e.g.\n",
"\n",
"$$\n",
"I(5) \\otimes \\sigma_z =\n",
"\\begin{bmatrix}\n",
" 1 & 0 & 0 & 0 & 0 \\\\\n",
" 0 & 1 & 0 & 0 & 0 \\\\\n",
" 0 & 0 & 1 & 0 & 0 \\\\\n",
" 0 & 0 & 0 & 1 & 0 \\\\\n",
" 0 & 0 & 0 & 0 & 1 \\\\\n",
" \\end{bmatrix} \\otimes\n",
" \\begin{bmatrix}\n",
" 1 & 0 \\\\\n",
" 0 & -1 \\\\\n",
"\\end{bmatrix} = \n",
" \\begin{bmatrix}\n",
" 1\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z \\\\\n",
" 0\\times\\sigma_z & 1\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z \\\\\n",
" 0\\times\\sigma_z & 0\\times\\sigma_z & 1\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z \\\\\n",
" 0\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z & 1\\times\\sigma_z & 0\\times\\sigma_z \\\\\n",
" 0\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z & 0\\times\\sigma_z & 1\\times\\sigma_z \\\\\n",
"\\end{bmatrix}\n",
"$$ "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5, 2], [5, 2]], shape = (10, 10), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & -1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5, 2], [5, 2]], shape = (10, 10), type = oper, isherm = True\n",
"Qobj data =\n",
"[[ 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
" [ 0. -1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. -1. 0. 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0. -1. 0. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
" [ 0. 0. 0. 0. 0. 0. 0. -1. 0. 0.]\n",
" [ 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
" [ 0. 0. 0. 0. 0. 0. 0. 0. 0. -1.]]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eye_sigmaz = tensor(qeye(5), sigmaz())\n",
"eye_sigmaz"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What's useful about this unwieldy tensorised $\\sigma_z$ operator is that it only acts on the two-state part and leaves the field part unchanged - this is because we put the identity operator first."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5, 2], [1, 1]], shape = (10, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\-1.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5, 2], [1, 1]], shape = (10, 1), type = ket\n",
"Qobj data =\n",
"[[ 0.]\n",
" [ 0.]\n",
" [ 0.]\n",
" [ 0.]\n",
" [ 0.]\n",
" [-1.]\n",
" [ 0.]\n",
" [ 0.]\n",
" [ 0.]\n",
" [ 0.]]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eye_sigmaz * two_minus"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see above that we still have the 2 bosons we started with.\n",
"\n",
"What will happen if we put the identity operator second and put the field operator $a$ first, i.e.\n",
"\n",
"$$a \\otimes I(2)$$\n",
"\n",
"and then apply it to the state |2,->?"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"a_eye = tensor(a, qeye(2))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"Quantum object: dims = [[5, 2], [1, 1]], shape = (10, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\0.0\\\\1.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
],
"text/plain": [
"Quantum object: dims = [[5, 2], [1, 1]], shape = (10, 1), type = ket\n",
"Qobj data =\n",
"[[0.]\n",
" [0.]\n",
" [0.]\n",
" [1.]\n",
" [0.]\n",
" [0.]\n",
" [0.]\n",
" [0.]\n",
" [0.]\n",
" [0.]]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(a_eye * two_minus).unit()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The boson number has gone down by one, but the two state system is still in the lower \"-\" state.\n",
"\n",
"We've finally got everything we need to explore what the title of this tutorial promised, namely explore **\"A two state system in a quantised field\"**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3.6 - Spontaneous emission"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's remind ourselves of the Hamiltonian that we're working with:\n",
"\n",
"$$H = A \\sigma_z + \\hbar\\omega\\left(a^{\\dagger}a +\\frac{1}{2}\\right) + \\frac{\\delta}{2}\\left( a^{\\dagger} + a \\right)\\sigma_x$$\n",
"\n",
"Just like in our last couple of tutorials we'll use $A=0.1$. \n",
"\n",
"We'll again only perturb the two state system by making the coupling small i.e. $\\delta/A = 0.01 \\ll 1$. \n",
"\n",
"How does the resonance that we discovered last time i.e. when $\\omega = \\omega_0 \\equiv 2A$ change now that the field is quantised."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"delta = 0.001\n",
"A = 0.1\n",
"omega = 2*A\n",
"max_bosons = 4 # The bigger this number the more accuracte your simualations will be. I tried 20 and it was almost the same as 4"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"a = tensor(destroy(max_bosons+1), qeye(2)) # tensorised boson destruction operator\n",
"sx = tensor(qeye(max_bosons+1), sigmax()) # tensorised sigma_x operator\n",
"sz = tensor(qeye(max_bosons+1),sigmaz()) # tensorised sigma_z operator\n",
"\n",
"two_state = A*sz # two state system energy\n",
"bosons = omega*(a.dag()*a+0.5) # bosons field energy\n",
"interaction = delta/2*(a.dag() + a) * sx # interaction energy\n",
"\n",
"H = two_state + bosons + interaction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Because we've got 10 possible states, the probability plots that we normally create are going to get a bit crowded. To make plots easier to understand, we'll create a function to label the simulation data according to $\\pm$ notation that we've been using up to this point to describe the two state system."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def states_to_df(states,times):\n",
" data = {}\n",
" for i in range(0,states[0].shape[0]):\n",
" which_mode = divmod(i,2)\n",
" if which_mode[1] == 0:\n",
" two_state = \"+\"\n",
" elif which_mode[1] == 1:\n",
" two_state = \"-\"\n",
" data[str(which_mode[0])+\" , \"+two_state] = np.zeros(len(times),dtype=\"complex128\")\n",
" \n",
" for i, state in enumerate(states):\n",
" for j, psi in enumerate(state):\n",
" which_mode = divmod(j,2)\n",
" if which_mode[1] == 0:\n",
" two_state = \"+\"\n",
" elif which_mode[1] == 1:\n",
" two_state = \"-\"\n",
" data[str(which_mode[0])+\" , \"+two_state][i] = psi[0][0]\n",
"\n",
" return pd.DataFrame(data=data, index=times)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The quintessential set-up for spontaneous emission is to have the field empty, i.e. no bosons $n=0$, and the two state system in it's \"excited\" (aka higher energy \"+\") state.\n",
"\n",
"Let's see what happens."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"psi0 = tensor(basis(max_bosons+1, 0), basis(2, 0)) # No bosons and two-state system is in the higher energy + state\n",
"\n",
"times = np.linspace(0.0, 15000.0, 1000) # simulation time\n",
"\n",
"result = sesolve(H, psi0, times)\n",
"df_coupled = states_to_df(result.states, times)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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