In fact, as early as the beginning of the 20th century, physicists noticed that light exerts radiation pressure on atoms. However, due to limitations in instruments and equipment, the laser cooling technology for atoms did not see substantial development until the invention of laser cooling devices in recent decades.
In his Stanford University laboratory in 1985, Steven Chu used a three-dimensional laser beam to form a magneto-optical trap to trap atoms in a small area of space and cool them, thus obtaining an optical adhesive with a lower temperature.
After more than a decade of dedicated research, Mr. Zhu and his research partners made even greater progress, using this technology to achieve extremely low temperatures below the photon recoil limit. For this achievement, Mr. Zhu, Cohen-Danoki, and Phillips were jointly awarded the Nobel Prize in Physics in 1997.
A decade or two later, as the 21st century dawned, in the laboratory of Nangang Second High School, Teacher Mu, based on Nobel Prize in Physics, posed a question, "In the laser cooling experiment of atoms, considering the recoil effect, what is the minimum temperature at which this occurs?"
The students in the audience scratched their heads, saying, "Teacher Mu, we're just high school students! With this kind of wild imagination, wouldn't we be winning the Nobel Prize?"
Only Shen Qi remained silent. He understood the meaning behind Teacher Mu's question; she didn't expect any high school student to be at the level of Nobel Prize.
This question involves laser emitters and atomic trapping, which seems incredibly advanced at first glance. Ultimately, the laser cooling experiment of atoms is a verification of the theoretical assumptions of Doppler, De Broglie, and others, and a further development and refinement of those assumptions.
In High School Physics textbooks, students learn about concepts such as the Doppler effect, De Broglie Wave, wave-particle duality of light, the Bohr level model, alpha particle bombardment, and the fundamental theory of atomic electrons. Of course, these are among the most difficult parts of High School Physics to understand.
Shen Qi had already learned about physics on his own, so the obstacles to his understanding were relatively small.
In terms of problem-solving alone, if you are not proficient in the necessary mathematical tools (formulas, corollaries, theorems, etc.), you will be helpless to solve the corresponding math problems. Physics problems are more about progressive understanding, supplemented by a small amount of calculation.
"This doesn't require Nobel Prize -level ingenuity; all you need is a physics competition-level imagination," Teacher Mu smiled and asked, "Do you think this question is difficult?"
"Disaster!"
"This is roughly the level of difficulty in the IPhO medium-difficulty exam, or the theoretical questions in the CPhO National Final," Teacher Mu said, scanning the audience. "You should know that during the competition, no one will show you instructional videos. You won't see 3D demonstrations or animations; the only clue is the planar diagram on the exam paper. See, it's similar to this planar diagram on the screen. That's why I showed you the animation twice and explained it simultaneously. You shouldn't be looking at me with those bewildered expressions. Future physicists, show me your true abilities, and don't let me down."
The audience fell completely silent.
The members of the Physics Competition Team are naturally quite skilled, and Shen Qi is not the only one who has self-studied elective courses or some basic physics knowledge.
All members of the Physics Competition Team picked up their pens and buried themselves in their notebooks, writing and drawing, deriving calculations.
Shen Qi arrived empty-handed, without pen or paper, staring intently at the two-dimensional diagram of the atomic reference frame on the screen, deep in thought.
"Dude, you can't possibly calculate the minimum temperature in your head, can you?" Lin Xingyu asked as he wrote, noticing that Shen Qi was sitting firmly with his arms crossed next to him.
"Mental arithmetic? That doesn't exist." Shen Qi shook his head and spread out his palm. "Give me a pen."
Lin Xingyu's pencil case contained a bunch of pens. He took out the most expensive ballpoint pen and handed it to Shen Qi.
"Give me the paper." Shen Qi spread his hands again.
Sizzle.
Lin Xingyu tore a page from his notebook and handed it to Shen Qi.
Thinking that one page of draft paper wouldn't be enough, Lin Xingyu tore off several sheets in quick succession.
"One sheet of draft paper is enough." Shen Qi waved his hand and began to deduce on the draft paper with his pen.
In this laser cooling experiment of the atom, the minimum temperature value needs to be calculated. The amount of calculation is not large, but the derivation steps are quite complicated. Shen Qi has to make drafts. Even when showing off, he has to control the scale appropriately according to the actual situation.
Swish, swish, swish.
Shen Qi wrote with lightning speed, quickly filling both sides of the draft paper.
"Phew... I see." Shen Qi tilted his head back and breathed a sigh of relief, then twisted his neck. Done.
Teacher Mu noticed Shen Qi: "It seems that Shen Qi has already made a decision?"
Smack
Shen Qi snapped his fingers, "Got it."
Slap slap
Teacher Mu snapped her fingers with both hands, "Then, Shen Qi, please show us your results."
After erasing the submarine question from the blackboard, Teacher Mu invited Shen Qi to come up to the stage to answer it.
Shen Qi went up to the stage, picked up a piece of chalk, and started writing on the blackboard.
The first step in solving this problem is to obtain the frequency of the laser. According to the classical Doppler effect, we can obtain:
ω(1+vx/c)
In fact, Doppler himself could not have realized that the theoretical effects he had proposed in his flash of inspiration would be widely applied in various countries and fields around the world a century or two later.
The color Doppler ultrasound used in hospitals today is based on Doppler effect, which is also widely used in the military and at the atomic level.
Shen Qi ordered Doppler to open an exit for the vanguard officer. Based on the question's setting, Doppler, the vanguard officer, would storm into the enemy camp and launch a surprise attack.
If electrons bombard us at a positive velocity v, we will get a backward motion, and the lateral dimension of the entire figure will shrink in proportion to cv and c.
After taking the second derivative, Shen Qi can calculate an electric field. When high-energy electrons pass through, they emit radiation along the direction of their movement. This is bremsstrahlung. The output of the Doppler vanguard ends here. He has completed the task assigned by Shen Qi.
Next, it was General De Broglie's turn to take the field.
The De Broglie Wave actually touches on the basics of Quantum Mechanics. High School Physics textbooks don't just talk about it superficially; they cover the essence, but with more conclusive descriptions and fewer specific explanations.
Shen Qi ordered General De Broglie's camp. He wrote on the blackboard the momentum of an atom absorbing a photon as follows:
ω0/c
Assuming the temperature is T, the corresponding De Broglie Wave is:
λ=/√mkT
Wave number is the rate of change of phase with respect to distance, frequency is the rate of change of phase with respect to time, and ω and k are similar to time and space in a spatial direction.
Mr. Steven Chu used a three-dimensional laser beam to form a magneto-optical trap to imprison atoms in a small area of space and cool them down. The 3D animation that Teacher Mu just played simply simulated this experimental process, showing the propagation of light in three-dimensional space and the interaction between atoms, the number of atoms after absorbing photons, and the momentum generated by each absorption and radiation of the atoms to float to the surface... Shen Qi filled the left blackboard with his writing, and the solution process was nearly half completed.
Teacher Mu remained silent and observed, while Lin Xingyu, sitting in the audience, had the draft that Shen Qi had just made in front of him.
Lin Xingyu looked down at Shen Qi's draft, then looked up at the solution process on the blackboard. Something was wrong; Shen Qi's draft was different from what he had written on the blackboard.
Lin Xingyu could understand most of what was written on the blackboard, but he couldn't understand Shen Qi's draft paper at all.
Because Shen Qi wrote relatively independent core steps on the draft paper, his thinking was too jumpy, and few people besides himself could understand what he wanted to express.
Using the core steps as a framework, Shen Qi unfolded a detailed solution on the blackboard. Soon, the answer will be revealed.