{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Demo 4: Speed of sound in quantum matter #\n",
"\n",
"Combo hardware and simulator!! Running this entire notebook will use **8 jobs**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction ##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sound is a type of vibrational energy. In our every day lives, sound propagates through the air around us at 343 m/s (\"the speed of sound\"), where molecules bump into each other and create traveling waves (vibrations); the speed of these sound waves depends on the temperature of the medium they're traveling through. The physics of room temperature air ($\\sim$300 K) is classical... but what happens for very cold gases like the atoms in the Bose-Einstein condensate (BEC) you create with Oqtant's hardware ($\\sim$100 nK)?\n",
"\n",
"Studying sound propagation in quantum matter reveals a wealth of information about the elementary ways in which the matter can be excited. In this demo, we will show how to produce sound in a BEC, which propagates extremely slowly by everyday standards - only a few millimeters per second!\n",
"\n",
"Producing this kind of sound is straightforward using Oqtant by creating a barrier suddenly and watching the wave of density propagate symmetrically outward. The wave of density is predominantly made of excitations known as \"phonons,\" which are a low-energy excitations in the condensate in the form of sound waves. A phonon is a quantum of vibrational energy (sound) whereas the more familiar photon is a quantum of electromagnetic energy (light). The name \"phonon\" is actually derived from the same Greek root *phon* (meaning *voice* or *sound*) as words like \"telephone\" and \"symphony!\"\n",
"\n",
"In addition to exploring the speed of sound in the BEC using the Oqtant hardware, this demo notebook showcases how the Oqtant simulator can be used to observe the same behavior. The simulation predicts a very similar speed of sound, and we are able to see more details about the BEC dynamics. We encourage users to run this portion of the demo even if the hardware is currently offline.\n",
"\n",
"For further reading, see the paper [Propagation of Sound in a Bose-Einstein Condensate](https://web.archive.org/web/20010614204054id_/http://amo.mit.edu:80/~bec/publish/papers/prl/PRL00553.pdf) which used a very similar experiment to perform the same measurement of the speed of sound. If you're still interested in learning more, the paper [Sound propagation in a Bose-Einstein condensate at finite temperatures](https://browse.arxiv.org/abs/0909.3455) goes much more in-depth about how the interaction between the BEC portion of the cloud and the thermal portion of the cloud can lead to even more types of sound. \n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Imports and user authentication ##"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"from oqtant.schemas.quantum_matter import QuantumMatterFactory\n",
"\n",
"qmf = QuantumMatterFactory()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Authenticate automatically ###\n",
"\n",
"The easiest way to authenticate as an Oqtant user is to execute the following cell. This will activate a widget that will let you sign in. \n",
"If popups are blocked, or you are on a system that does not support this method, please follow the steps just below to authenticate manually instead. \n",
"Note that currently the *automatic authentication method is only compatible with classic jupyter notebooks*, and not jupyter lab, nanohub, binder, colab, etc."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"qmf.get_login()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Authenticate manually ###\n",
"\n",
"If you cannot use the automatic authentication method above, you can instead authenticate using a slightly more manual process: \n",
"\n",
"1. Copy your access token from [oqtant.infleqtion.com/oqtantAPI](https://oqtant.infleqtion.com/oqtantAPI)\n",
"2. Paste that token just below and execute the cell (the if statement keeps the code from executing if you already authenticated above)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"if qmf.login.access_token == \"\":\n",
" qmf.login.access_token = \"Paste your token here between the quotes!\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Get client ###\n",
"\n",
"At this point you should have a valid access token and be able to establish a *client* for communicating with the Oqtant REST service. Executing the cell just below should show your current job quota limits."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"qmf.get_client()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create a list of Barrier jobs with varying in-trap times ##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to visualize the propagation of sound, we will create a series of Barrier jobs to image the sound wave at different in-trap times. The barrier is turned on suddenly at time $t=0$ to create the sound wave, and is left on until the image is taken. The first job in our list of matter objects will contain no barrier, so that we have a baseline BEC distribution for data analysis. The subsequent jobs will sweep the in-trap time from 1 ms to 5 ms in steps of 1 ms. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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",
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