2f:T413,velocity_plot = { while(!paused) { let plot_height = 400 let plot_width = 400 const ctx = DOM.context2d(plot_height, plot_width); ctx.canvas.style.border = '1px solid black' ctx.fillStyle = "rgba(255, 255, 255, 1)"; ctx.fillRect(0, 0, canvas_width, canvas_height); axes(ctx, plot_height, plot_width, plot_width) // settings for each atom point ctx.fillStyle = "rgba(0, 0, 0, 1)"; let radius = 5 for (let i = 0; i < atoms.length; i++) { let atom = atoms[i] let p_x = atom.velocity.x * plot_width / 4 + plot_width / 2 let p_y = atom.velocity.y * plot_height / 4 + plot_height / 2 ctx.beginPath() ctx.ellipse(p_x, p_y, radius, radius, 0, 0, 2*Math.PI) ctx.closePath() // if the atom is inside at least one of the lasers, fill the ellipse if ( is_inside_at_least_one_laser(atom) && cooling_is_on) { ctx.fill() } else { ctx.stroke() } } yield visibility(ctx.canvas) } }30:Ta7b,layout = { const container = document.createElement('div'); container.classList.add("exo2"); container.style.margin = "0 auto"; container.style.maxWidth = "950px"; // LOAD SCREEN const loader = document.createElement('div'); loader.style.width = canvas_width + "px"; loader.style.height = canvas_height + "px"; loader.style.position = "absolute"; loader.style.zIndex = 99; loader.style.backgroundColor = "white"; loader.style.opacity = 0.9; loader.style.border = "1px solid gray"; loader.style.display = "flex"; loader.style.justifyContent = "center"; loader.style.alignItems = "center"; const loadTitle = document.createElement("p"); loadTitle.style.flex = "0 0 " + width + "px"; loadTitle.style.textAlign = "center"; loadTitle.appendChild(document.createTextNode("Click to Start Animation")); loader.appendChild(loadTitle); if (!loaded) { container.appendChild(loader) Object.assign(loader, {onclick: () => mutable loaded = true}) } // SIMULATION const simulation_canvas = document.createElement('canvas'); simulation_canvas.style.position = "relative"; simulation_canvas.style.width = canvas_width + 'px'; simulation_canvas.style.height = canvas_height + 'px'; simulation_canvas.width = canvas_width * 2; simulation_canvas.height = canvas_height * 2; simulation_canvas.style.border = "1px solid black"; const simulation_container = document.createElement('div'); simulation_container.style.display = 'inline-block'; simulation_container.style.verticalAlign = "top"; simulation_container.appendChild(simulation_canvas); container.appendChild(simulation_container); // CONTROLS const controls_container = document.createElement('div'); controls_container.style.display = 'inline-block'; controls_container.style.width = '400px'; if (width > 900) { controls_container.style.marginLeft = '20px'; } else { controls_container.style.marginTop = '20px'; } controls_container.style.verticalAlign = "top"; controls_container.append(controls); // GRAPH const graph_canvas = document.createElement('canvas'); graph_canvas.style.position = "relative"; graph_canvas.width = width > 400 ? 800 : width * 2; graph_canvas.height = graph_canvas.width * 0.3; graph_canvas.style.width = graph_canvas.width * 0.5 + 'px'; graph_canvas.style.height = graph_canvas.height * 0.5 + 'px'; graph_canvas.style.border = "1px solid black"; controls_container.append(graph_canvas); controls_container.appendChild(graph_description); container.appendChild(controls_container); return {container, simulation_canvas, graph_canvas} } 31:T7a0,spectrum_graph = { const ctx = layout.graph_canvas.getContext('2d'); ctx.setTransform(1, 0, 0, 1, 0, 0); ctx.scale(2,2); let w = layout.graph_canvas.width / 2 let h = layout.graph_canvas.height / 2 // const ctx = DOM.context2d(w, h); // ctx.translate(0.5, 0.5) let width_of_blend_region = 40 let blue = chroma('rgba(0, 125, 255, 0.1)') let red = chroma('rgba(255, 0, 0, 0.1)') ctx.fillStyle = "rgba(255, 255, 255, 1)"; ctx.fillRect(0, 0, w, h); // cooling region ctx.save() ctx.fillStyle = blue.css(); ctx.beginPath(); ctx.rect(0, 0, w/2 - width_of_blend_region, h) ctx.fill(); ctx.restore() // heating region ctx.save() ctx.fillStyle = red; ctx.beginPath(); ctx.rect(w/2 + width_of_blend_region, 0, w/2, h) ctx.fill(); ctx.restore() // blend between two regions var grd = ctx.createLinearGradient(w/2 - width_of_blend_region, 0, w/2 + width_of_blend_region, 0); grd.addColorStop(0, blue); grd.addColorStop(1, red); ctx.save() ctx.fillStyle = grd; ctx.fillRect(w/2 - width_of_blend_region, 0, width_of_blend_region * 2, h); ctx.restore() let points = [] for (var j=0; j< w; j++) { let x = j/(w * 5) + 0.4 let y = h - ((h-4) * cauchy_distribution(absorption_spread, x, absorption_frequency)) points.push({x:j, y:y}) } ctx.save() smoothly_plot_points(points, ctx) ctx.strokeStyle = "black"; ctx.lineWidth = 2 ctx.stroke() ctx.restore() ctx.save() ctx.beginPath(); ctx.moveTo(w * (laser_frequency_reactive - 0.4) * 5, 0); ctx.lineTo(w * (laser_frequency_reactive - 0.4) * 5, 200); ctx.strokeStyle = "rgba(0, 125, 255, 1)"; ctx.lineWidth = 2 ctx.stroke() ctx.restore() ctx.save() ctx.fillStyle = "black"; ctx.font = width > 400 ? "16px Arial" : "12px Arial"; ctx.textAlign = "center"; ctx.fillText("Cooling", w/4, 3*h/4); ctx.fillText("Heating", 3*w/4, 3*h/4); ctx.restore() yield ctx.canvas }32:T589,class Atom { constructor(position, velocity, isExcited) { this.position = position, // vector this.velocity = velocity, // vector this.absorptionFrequency = 0.5 // float this.isExcited = isExcited // boolean this.mixFactor = 0 // used for color mixing between excited and not excited, so the colors change over a number of frames this.colorChangeFrames = blink_speed // duration of color change animation in frames } move() { this.position = this.position.add(this.velocity) } isInside(area) { return area[0].x <= this.position.x && this.position.x <= area[1].x && area[0].y <= this.position.y && this.position.y <= area[1].y; } incrementMixFactor() { if (this.mixFactor < 1.0) { this.mixFactor += 1.0 / this.colorChangeFrames } } decrementMixFactor() { if (this.mixFactor > 0) { this.mixFactor -= 1.0 / this.colorChangeFrames } } draw(context) { context.save() context.beginPath() context.ellipse(this.position.x, this.position.y, atom_size * canvas_ratio, atom_size * canvas_ratio, 0, 0, 2*Math.PI) context.closePath() if(this.isExcited) { this.incrementMixFactor() } else { this.decrementMixFactor() } context.fillStyle = chroma.mix(atom_color_nonexcited, atom_color_excited, this.mixFactor).toString() context.fill() context.restore() } }33:T4fd,class Laser { constructor(direction, isOn) { this.direction = direction, // vector this.isOn = isOn // boolean this.width = beam_width this.kick = kick(this.direction, kick_amplitude) // check if laser is oriented horzontally if (this.direction.x != 0) { this.orientation = "Horizontal" this.area = [ // horizontal rectangle new Vector(0, canvas_height / 2 - this.width / 2), new Vector(canvas_width, canvas_height / 2 + this.width / 2), ] } // else, laser is oriented vertically else { this.orientation = "Vertical" this.area = [ // vertical rectangle new Vector(canvas_width / 2 - this.width / 2, 0), new Vector(canvas_width / 2 + this.width / 2, canvas_height), ] } } contains(vector) { return this.x <= vector.x && vector.x <= this.x + this.width && this.y <= vector.y && vector.y <= this.y + this.height; } draw(ctx) { ctx.save(); ctx.fillStyle = laser_fill(); ctx.beginPath(); let width = this.area[1].x - this.area[0].x let height = this.area[1].y - this.area[0].y ctx.rect(this.area[0].x, this.area[0].y, width, height); ctx.closePath(); ctx.fill(); ctx.restore(); } }34:T407,function draw_lasers(ctx) { ctx.save(); // LASERS for (const laser of lasers) { if (laser.isOn) { laser.draw(ctx) } } // ARROWS // drawn seperately so that they are layered over all the laser regions // arrow settings: ctx.fillStyle = "white" ctx.strokeStyle = "white" let offset = 100 let stroke_width = 6 let head_width = 30 let head_height = 40 let x_pos, y_pos, rot = 0 for (const laser of lasers) { if (laser.isOn) { if (laser.orientation == "Horizontal") { x_pos = canvas_width * (1 - laser.direction.x) + offset * laser.direction.x y_pos = canvas_height rot = Math.PI/2 * laser.direction.x } if (laser.orientation == "Vertical") { x_pos = canvas_width y_pos = canvas_height * (1 - laser.direction.y) + offset * laser.direction.y rot = Math.PI/2 + Math.PI/2 * laser.direction.y } arrow(ctx, x_pos, y_pos, head_width, head_height, stroke_width, offset, rot) } } ctx.restore(); }35:[] 2d:{"title":"Doppler Laser Cooling","cells":[{"id":0,"value":"md`# Doppler Laser Cooling`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"graphic = {\n const context = layout.simulation_canvas.getContext('2d');\n context.setTransform(1, 0, 0, 1, 0, 0);\n context.scale(2,2);\n \n if (!loaded) {\n clear(context)\n draw_scene(context)\n yield layout.container;\n }\n \n else {\n while(!paused) {\n await visibility();\n clear(context)\n simulation(context)\n draw_scene(context)\n yield layout.container;\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4546,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4310,"value":"draw_scene = (context) => {\n draw_lasers(context)\n for (let atom of mutable atoms) { atom.draw(context) }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4305,"value":"simulation = (context) => {\n for (let atom of mutable atoms) {\n if (atom.isInside(canvas_area)) {\n check_for_photon_absorption(atom)\n check_for_photon_emission(atom)\n atom.move()\n }\n else {\n // remove atom from the list of atoms in the simulation\n mutable atoms = mutable atoms.filter(item => item !== atom)\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4301,"value":"clear = (context) => {\n context.clearRect(0, 0, context.canvas.width, context.canvas.height);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4277,"value":"mutable loaded = false","pinned":false,"hidden":false,"mode":"ojs"},{"id":3506,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3519,"value":"md`## Visualization Controls`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3552,"value":"md`### Atoms`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3559,"value":"viewof atom_size = slider({\n min: 2, \n max: 12, \n step: 0.5, \n value: 12,\n title: \"Atom Size\", \n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":3573,"value":"viewof atom_color_excited = color({\n // value:chroma('black').hex(),\n value: \"#e63b7a\",\n title: \"Excited Color\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":3567,"value":"viewof atom_color_nonexcited = color({\n // value:chroma(blue).hex(),\n value: \"#874efe\",\n title: \"Base Color\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":3585,"value":"viewof blink_speed = slider({\n min: 1, \n max: 10, \n step: 1, \n value: 5,\n title: \"Blink Speed\", \n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":3524,"value":"md`### Lasers`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3763,"value":"viewof laser_cool_color = color({\n // value:\"#0091ff\",\n value: \"#446af3\",\n title: \"Cooling Laser Color\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":3767,"value":"viewof laser_hot_color = color({\n // value:\"#0091ff\",\n value: \"#f34481\",\n title: \"Heating Laser Color\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":3775,"value":"laser_color = () => {\n return chroma.mix(laser_cool_color, laser_hot_color, (laser_frequency.value - 0.4) * 5).toString()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":3599,"value":"md`### Simulation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3528,"value":"viewof kick_amplitude_control = slider({\n min: 0.0, \n max: 0.5, \n step: 0.01, \n value: 0.2,\n title: \"Kick Size\", \n description: \"Momentum kick from absorbing/emitting a photon.\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":3517,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1228,"value":"md`Plot of atom velocity. ${draw_inset_plot_atom(true)} represents an atom. ${draw_inset_plot_atom(false)} represents an atom that has been lost from the cooling region.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1170,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs"},{"id":3436,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2944,"value":"md`# Implementation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3445,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3440,"value":"md`### Layout and Controls`","pinned":false,"hidden":false,"mode":"ojs"},{"id":3099,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"},{"id":3847,"value":"graph_description = html`

The best cooling takes place just to the left of the peak in this graph.

`","pinned":true,"hidden":false,"mode":"ojs"},{"id":3134,"value":"controls = html`\n${viewof addAtoms}\n${viewof reset}\n

Trap Controls

\n${viewof horizontal_lasers_are_on}\n${viewof vertical_lasers_are_on}\n${viewof restoring_force_on}\n

Laser Color

\n${laser_frequency}\n

\n`;","pinned":true,"hidden":false,"mode":"ojs"},{"id":3510,"value":"breakpoint = 600","pinned":false,"hidden":false,"mode":"ojs"},{"id":3124,"value":"btn = {\n if (width < breakpoint) {\n return `\n font-family: sans-serif !important;\n padding: 10px 10px;\n font-size: 15px;\n margin-right: 10px;\n margin-bottom: 10px;\n border-radius: 5px;\n background-color: white;\n border: 1px solid black; `\n }\n else {\n return `\n font-family: sans-serif !important;\n padding: 10px 20px;\n font-size: 16px;\n margin-right: 10px;\n margin-bottom: 15px;\n border-radius: 5px;\n background-color: white;\n border: 1px solid black; `\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":255,"value":"viewof reset = html``","pinned":true,"hidden":false,"mode":"ojs"},{"id":4061,"value":"viewof addAtoms = html``","pinned":true,"hidden":false,"mode":"ojs"},{"id":480,"value":"viewof cooling_is_on = checkbox({\n description: \"\",\n options: [{ value: \"on\", label: \"Laser Cooling On\" }],\n value: \"on\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":2504,"value":"viewof horizontal_lasers_are_on = checkbox({\n description: \"\",\n options: [{ value: \"on\", label: \"Horizontal Laser\" }],\n value: \"on\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":2519,"value":"viewof vertical_lasers_are_on = checkbox({\n description: \"\",\n options: [{ value: \"on\", label: \"Vertical Laser\" }],\n value: \"on\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":466,"value":"laser_frequency = slider({\n min: 0.40, \n max: 0.60, \n step: 0.001, \n value: 0.47,\n format: v => ``,\n description: \"\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":3737,"value":"viewof restoring_force_on = checkbox({\n description: \"\",\n options: [{ value: \"on\", label: \"Restoring Force\" }],\n value: \"on\"\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":69,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":3004,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2154,"value":"md`## Atoms`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2279,"value":"md`Each **Atom** has a position (*Vector*), velocity (*Vector*), and state of excited or not excited (*Boolean*).`","pinned":false,"hidden":false,"mode":"ojs"},{"id":207,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"},{"id":2286,"value":"starting_number_of_atoms = 20","pinned":false,"hidden":false,"mode":"ojs"},{"id":156,"value":"mutable atoms = {\n reset; // recreate the initial atom array every time the reset button is pushed\n let atoms = []\n for (let i = 0; i < starting_number_of_atoms; i++) {\n atoms.push(atomFromRandomCorner())\n }\n return atoms\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":4126,"value":"number_of_new_atoms = 10","pinned":false,"hidden":false,"mode":"ojs"},{"id":4182,"value":"maximum_number_of_atoms = 100","pinned":false,"hidden":false,"mode":"ojs"},{"id":4206,"value":"atomFromRandomCorner = () => {\n let randomCorner = canvas_corners[Math.floor(Math.random() * canvas_corners.length)];\n let direction = canvas_center.subtract(randomCorner).divide(canvas_width/2)\n let random_initial_velocitiy = new Vector(direction.x * (Math.abs(random_value()) + kick_amplitude), direction.y * (Math.abs(random_value()) + kick_amplitude))\n return new Atom(randomCorner, random_initial_velocitiy, false)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4213,"value":"atomInRandomPosition = () => {\n let random_initial_position = new Vector(random_value() * beam_width + canvas_width/2, random_value() * beam_width + canvas_height/2)\n let random_initial_velocitiy = new Vector(random_value(), random_value())\n return new Atom(random_initial_position, random_initial_velocitiy, false /*is not excited */)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":4124,"value":"addMoreAtoms = {\n addAtoms;\n if (mutable atoms.length < maximum_number_of_atoms) {\n for (let i = 0; i < number_of_new_atoms; i++) {\n mutable atoms = [...mutable atoms, atomFromRandomCorner()]\n }\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2275,"value":"md`*is_inside_at_least_one_laser()*: Returns \\`\\`true\\`\\` if a particular atom is inside at least one of the lasers, \\`\\`false\\`\\` if inside no lasers:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2054,"value":"function is_inside_at_least_one_laser(atom) {\n let is_inside = false\n for (const laser of lasers) {\n if ( atom.isInside(laser.area) && laser.isOn ) {\n is_inside = true\n }\n }\n return is_inside\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2172,"value":"md`### Photon absorption and emission`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2235,"value":"md`*check_for_photon_absorption()*: If an atom absorbs a photon from one of the lasers, it becomes excited and recieves a momentum kick in the direction of the photon.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":389,"value":"function check_for_photon_absorption(atom) {\n if (atom.isExcited) {\n return; // break if atom has already absorbed a photon\n }\n let randomly_ordered_lasers = shuffle(lasers)\n for (const laser of randomly_ordered_lasers) {\n if (laser.isOn) {\n if (atom.isInside(laser.area)) {\n if (photon_is_absorbed(atom, laser)) {\n atom.velocity = atom.velocity.add(laser.kick)\n atom.isExcited = true\n }\n }\n }\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":3675,"value":"function distance_from_center(position) {\n // used for a restoring force based on distance from center\n let center = canvas_width / 2 // can be used for height as well, since canvas is square\n let distance = (center - position) / center\n return distance\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2397,"value":"function photon_is_absorbed(atom, laser) {\n let photon_is_absorbed = false\n // restoring force\n let x_probability_adjustment = 1\n let y_probability_adjustment = 1\n if (restoring_force_on) {\n x_probability_adjustment = Math.abs(laser.direction.x + distance_from_center(atom.position.x))\n y_probability_adjustment = Math.abs(laser.direction.y + distance_from_center(atom.position.y))\n }\n let combined_probability = absorption_probability(atom.velocity.x, laser.direction.x, atom.absorptionFrequency) * x_probability_adjustment + absorption_probability(atom.velocity.y, laser.direction.y, atom.absorptionFrequency) * y_probability_adjustment\n if (event_happens(combined_probability)) {\n photon_is_absorbed = true\n }\n return photon_is_absorbed\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":2265,"value":"md`Each frame of the animation, an excited photon has *probability_of_photon_emission* chance of randomly emitting a photon:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":419,"value":"probability_of_photon_emission = 0.1","pinned":false,"hidden":false,"mode":"ojs"},{"id":2245,"value":"md`*check_for_photon_emission()*: If an atom randomly emits a photon, it returns to a non-excited state and recieves a momentum kick opposite the direction of the emitted photon.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":416,"value":"function check_for_photon_emission(atom) {\n if (!atom.isExcited) {\n return; // break if atom is not excited\n }\n else {\n if (event_happens(probability_of_photon_emission)) {\n atom.isExcited = false\n let emitted_photon_direction = new Vector(random_value(), random_value()).normalize()\n atom.velocity = atom.velocity.add(kick(emitted_photon_direction, kick_amplitude))\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2175,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2157,"value":"md`## Lasers`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2290,"value":"md`Each **Laser** has a direction (*Vector*), photon kick (*Vector*), state of being on or off (*Boolean*), and area that it covers (two *Vectors* defining a rectangle) -- along with some other properties for convenience.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1575,"value":"$33","pinned":true,"hidden":false,"mode":"ojs"},{"id":1868,"value":"laser_left = new Laser(new Vector(1, 0), horizontal_lasers_are_on)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1872,"value":"laser_right = new Laser(new Vector(-1, 0), horizontal_lasers_are_on)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1874,"value":"laser_top = new Laser(new Vector(0, 1), vertical_lasers_are_on)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1876,"value":"laser_bottom = new Laser(new Vector(0, -1), vertical_lasers_are_on)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1885,"value":"lasers = [laser_left, laser_right, laser_top, laser_bottom]","pinned":false,"hidden":false,"mode":"ojs"},{"id":997,"value":"md`Because \\`\\`laser_frequency\\`\\` is not a \\`\\`viewof\\`\\` cell, the referenced value doesn't trigger reactive updates. Passing the input to a generator yields a new value whenever the input is changed, so it can be used to calculate downstream changes (like for the absorption spectrum plot above).`","pinned":false,"hidden":false,"mode":"ojs"},{"id":991,"value":"laser_frequency_reactive = Generators.input(laser_frequency)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1078,"value":"md`### Drawing laser regions`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1022,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":1609,"value":"{\n const context = DOM.context2d(canvas_width, canvas_height);\n let laser = new Laser(new Vector(1, 0), true)\n laser.draw(context)\n return context.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1016,"value":"beam_width = canvas_width * 2/5","pinned":false,"hidden":false,"mode":"ojs"},{"id":1145,"value":"laser_opacity = 0.1","pinned":false,"hidden":false,"mode":"ojs"},{"id":1125,"value":"laser_fill = () => {\n return chroma(laser_color()).alpha(laser_opacity).css()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1584,"value":"md`Arrow for showing which direction the laser is pointed:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1399,"value":"{\n const context = DOM.context2d(100, 110);\n arrow(context, 100, 10, 50, 80, 8, 100, 0)\n yield context.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1401,"value":"function arrow(ctx, x, y, width, height, strokeWidth, stemLength, rotation) {\n ctx.save();\n ctx.setTransform(2,0,0,2,x,y);\n ctx.rotate(rotation);\n \n // arrow stem\n ctx.beginPath();\n ctx.rect(-strokeWidth / 2, 0, strokeWidth, stemLength);\n ctx.fill();\n \n //arrowhead\n ctx.beginPath();\n ctx.moveTo(0, 0);\n ctx.lineTo(width/2, height/2);\n ctx.moveTo(0, 0);\n ctx.lineTo(-width/2, height/2);\n ctx.lineWidth = strokeWidth\n ctx.stroke();\n \n let capSize = strokeWidth / 2 - .3\n \n // line caps\n // top\n ctx.beginPath();\n ctx.ellipse(0, 0, capSize, capSize, 0, 0, 2 * Math.PI, true);\n ctx.fill();\n // left\n ctx.beginPath();\n ctx.ellipse(-width/2, +height/2, capSize, capSize, 0, 0, 2 * Math.PI, true);\n ctx.fill();\n // right\n ctx.beginPath();\n ctx.ellipse(+width/2, +height/2, capSize, capSize, 0, 0, 2 * Math.PI, true);\n ctx.fill();\n \n ctx.restore()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2169,"value":"md`### Momentum kick`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2300,"value":"md`Each momentum kick is a unit *Vector* multiplied by the amplitude of the kick.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":348,"value":"kick_amplitude = kick_amplitude_control * canvas_ratio","pinned":false,"hidden":false,"mode":"ojs"},{"id":315,"value":"function kick(direction, amplitude) {\n return direction.normalize().multiply(amplitude)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2178,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2185,"value":"md`## Doppler Effect and Photon Absorption`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2888,"value":"md`To begin, we'll set a \"speed of light\" for our simulation:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":504,"value":"speed_of_light = 10","pinned":false,"hidden":false,"mode":"ojs"},{"id":2315,"value":"md`We define absorption probability as ${tex`\\frac{\\gamma^2}{(f - f_0)^2 + \\gamma^2}`}, where ${tex`\\gamma`} is the **absorption spread** and ${tex`f_0`} is the **absorption frequency**.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":61,"value":"function cauchy_distribution(gamma, x, x0) {\n return (gamma**2)/((x-x0)**2 + gamma**2)\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":112,"value":"absorption_spread = 0.01","pinned":false,"hidden":false,"mode":"ojs"},{"id":111,"value":"absorption_frequency = .5","pinned":false,"hidden":false,"mode":"ojs"},{"id":2306,"value":"{\n let w = 500\n let h = 150\n const ctx = DOM.context2d(w, h);\n ctx.translate(0.5, 0.5)\n \n let points = []\n for (var j=0; j< w; j++) {\n let x = j/(w * 5) + 0.4\n let y = h - ((h-4) * cauchy_distribution(absorption_spread, x, absorption_frequency))\n points.push({x:j, y:y})\n }\n \n smoothly_plot_points(points, ctx)\n \n ctx.lineWidth = 2\n ctx.stroke()\n \n return ctx.canvas\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2464,"value":"md`Given the velocity of an atom and the direction of a laser, we can find the probability that the atom will absorb a photon by (1) calculating the frequency shift of light percieved by the atom and (2) comparing the shifted frequency to the absorption spectrum.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"function absorption_probability(atom_velocity, direction_of_laser, absorption_frequency) {\n let velocity_of_light = speed_of_light * direction_of_laser\n let percieved_frequency = shifted_frequency(atom_velocity, laser_frequency.value, velocity_of_light)\n return cauchy_distribution(absorption_spread, percieved_frequency, absorption_frequency)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2469,"value":"md`The shifted frequency is ${tex`f' = f*\\frac{v_{light} - v_{atom}}{v_{light}}`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":510,"value":"function shifted_frequency(velocity_of_atom, frequency_of_light, velocity_of_light) {\n return frequency_of_light * (velocity_of_light - velocity_of_atom) / velocity_of_light\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2198,"value":"md`### Handling probabilities/random events`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2485,"value":"md`We can decide whether or not a particular event happens by comparing the probability of the event to a random number between 0 and 1. If the number is smaller than the probability of event, the event happens (function returns \\`\\`True\\`\\`). If the number is larger, the event doesn't happen (function returns \\`\\`False\\`\\`).`","pinned":false,"hidden":false,"mode":"ojs"},{"id":374,"value":"function event_happens(probability_of_event) {\n if (Math.random() < probability_of_event) { return true }\n else { return false }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":894,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2210,"value":"md`## Utilities`","pinned":false,"hidden":false,"mode":"ojs"},{"id":28,"value":"class Vector {\n constructor(x, y) {\n this.x = x, // vector\n this.y = y // vector\n }\n\n add(vector) {\n return new Vector(this.x + vector.x, this.y + vector.y)\n }\n \n subtract(vector) {\n return new Vector(this.x - vector.x, this.y - vector.y)\n }\n \n multiply(float) {\n return new Vector(this.x * float, this.y * float)\n }\n \n divide(float) {\n return new Vector(this.x / float, this.y / float)\n }\n \n magnitude() {\n return Math.sqrt(this.x * this.x + this.y * this.y)\n }\n \n dot(vector) {\n return this.x * vector.x + this.y * vector.y\n }\n \n normalize() {\n return new Vector(this.x / this.magnitude(), this.y / this.magnitude())\n }\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":819,"value":"function trim_number(number, value = 3) {\n return Number(number.toPrecision(value))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2426,"value":"function shuffle(array) {\n let a = Array.from(array); // copy the array so we preserve the original\n // Fisher-Yates shuffle, modie from https://javascript.info/task/shuffle\n for (let i = a.length - 1; i > 0; i--) {\n let j = Math.floor(Math.random() * (i + 1)); // random index from 0 to i\n [a[i], a[j]] = [a[j], a[i]];\n }\n return a; // return the new array\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2478,"value":"md`random_value rescales Math.random() to return a random value between -1 and 1`","pinned":false,"hidden":false,"mode":"ojs"},{"id":610,"value":"function random_value() {\n return 2 * (0.5 - Math.random())\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2205,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":897,"value":"md`## Canvas settings`","pinned":false,"hidden":false,"mode":"ojs"},{"id":888,"value":"canvas_width = width > 500? 500 : width","pinned":true,"hidden":false,"mode":"ojs"},{"id":6,"value":"canvas_height = canvas_width","pinned":true,"hidden":false,"mode":"ojs"},{"id":3910,"value":"canvas_area = [\n new Vector(0, 0),\n new Vector(canvas_width, canvas_height),\n ]","pinned":true,"hidden":false,"mode":"ojs"},{"id":4136,"value":"canvas_corners = [\n new Vector(0, 0),\n new Vector(0,canvas_height),\n new Vector(canvas_width, 0),\n new Vector(canvas_width, canvas_height)\n]","pinned":true,"hidden":false,"mode":"ojs"},{"id":4160,"value":"canvas_center = new Vector(canvas_width, canvas_height).divide(2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":4115,"value":"canvas_ratio = canvas_width / 500","pinned":true,"hidden":false,"mode":"ojs"},{"id":1386,"value":"blue = \"rgba(0, 125, 255, 1)\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1225,"value":"md`### Velocity plot`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1175,"value":"function axes(ctx, x, y, l) {\n ctx.save();\n ctx.setTransform(1,0,0,1,x, y);\n \n ctx.strokeStyle = \"rgba(0, 0, 0, 0.25)\";\n \n ctx.beginPath();\n ctx.moveTo(0, l)\n ctx.lineTo(0, -l)\n ctx.lineWidth = 2;\n ctx.stroke();\n \n ctx.beginPath();\n ctx.moveTo(l, 0)\n ctx.lineTo(-l, 0)\n ctx.lineWidth = 2;\n ctx.stroke();\n \n ctx.restore();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1231,"value":"function draw_inset_plot_atom(filled) {\n const ctx = DOM.context2d(16, 16);\n ctx.fillStyle = \"rgba(0, 0, 0, 1)\";\n ctx.beginPath()\n ctx.ellipse(8, 8, 6, 6, 0, 0, 2*Math.PI)\n ctx.closePath()\n if(filled) {\n ctx.fill()\n }\n else {\n ctx.stroke()\n }\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":2149,"value":"md`### Absorption plot`","pinned":false,"hidden":false,"mode":"ojs"},{"id":678,"value":"function smoothly_plot_points(points, context) {\n // expects points to be an array of objects with x and y values, ex. {x:1,y:1}\n context.beginPath();\n context.moveTo(points[0].x, points[0].y);\n for(var i = 0; i < points.length-1; i ++)\n {\n var x_mid = (points[i].x + points[i+1].x) / 2;\n var y_mid = (points[i].y + points[i+1].y) / 2;\n var cp_x1 = (x_mid + points[i].x) / 2;\n var cp_x2 = (x_mid + points[i+1].x) / 2;\n context.quadraticCurveTo(cp_x1,points[i].y ,x_mid, y_mid);\n context.quadraticCurveTo(cp_x2,points[i+1].y ,points[i+1].x,points[i+1].y);\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":902,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":905,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs"},{"id":467,"value":"import {slider, checkbox, color, button} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":3990,"value":"import {atlasStyle} from \"@flimsyhat/quantum-atlas-component-styling\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":4241,"value":"style = {return atlasStyle;}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1126,"value":"chroma = require('chroma-js@2.1.0/chroma.js').catch(() => window[\"chroma\"])","pinned":false,"hidden":false,"mode":"ojs"},{"id":2662,"value":"gsap = require('https://bundle.run/gsap@3.5.1')","pinned":false,"hidden":false,"mode":"ojs"},{"id":910,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":913,"value":"md`## Notes & Links`","pinned":false,"hidden":false,"mode":"ojs"},{"id":916,"value":"md`https://en.wikipedia.org/wiki/Cauchy_distribution\n\nhttp://www-lpl.univ-paris13.fr/bec/bec/Teaching/lecture2_2012.pdf\n\nhttps://web.stanford.edu/~rpam/dropoff/Phys041N/lecture6-lasercooling.pdf\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2223,"value":"html`

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2215,"value":"md`### Utility controls (currently unused)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"viewof pause = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":437,"value":"viewof advance = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":308,"value":"mutable paused = true","pinned":false,"hidden":false,"mode":"ojs"},{"id":310,"value":"{\n pause;\n mutable paused = !mutable paused\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W35","stdlib":"1","titling":"auto"}