Just when the basic equations of quantum mechanics were discovered, physicists discovered one of the strangest phenomena allowed by theory: quantum tunneling. This phenomenon shows how far-reaching the difference between microscopic particles such as electrons and larger objects can be. When we throw the ball on the wall, it will bounce back; When the ball hits the bottom, it stays there. However, particles occasionally cross or pass through "walls" (barriers). As two physicists wrote in the journal Nature in 1928, particles may "slide over mountains and escape from the bottom", which is one of the earliest descriptions of the tunneling effect.
Physicists soon discovered that the ability of particles to cross obstacles can solve many mysteries. It explains various chemical bonds and radioactive decay, and how hydrogen nuclei in the sun overcome their repulsion and merge to produce sunlight. But physicists are beginning to wonder. This curiosity was mild at first, but then it became a little morbid. They want to know, how long does it take a particle to cross the barrier?
The problem is that none of the answers to this question are meaningful.
Scientists tentatively calculated the tunneling time for the first time in 1932. Even earlier, there may have been a private attempt, but as affret Steinberg, a physicist at the University of Toronto, said, "When you get an answer that you can't understand, you won't publish it."
Until 1962, Thomas, a semiconductor engineer at Texas Instruments, USA? Thomas Hartman has just published a paper, which clearly expounds the amazing significance of this mathematical theory.
Hartman found that the barrier seemed to be a shortcut. When particles tunnel, when there is a potential barrier, it takes less time. Even more surprising, he calculated that the increase of the barrier hardly increased the time required for particles to cross obstacles. This means that if the barrier is thick enough, particles can jump from one side to the other faster than light can travel the same distance in a vacuum.
In short, quantum tunneling seems to allow faster travel than light, but it is physically impossible. "After Hartman explained this effect, people began to worry," Steinberg said.
This discussion has lasted for decades, partly because the question of tunnel time seems to touch some of the most mysterious parts of quantum mechanics. Eli Pollak, a theoretical physicist at Weizmann Academy of Sciences in Israel, said: "This involves many general questions, including what is time? How do we measure time in quantum mechanics? What is its significance? " Physicists finally derived at least 10 mathematical expressions about the tunneling time, each of which reflected a different perspective of the tunneling process. Of course, none of these mathematical expressions can solve this problem.
Now, the problem of quantum tunneling time is back, and a series of ingenious experiments in the laboratory to accurately measure tunneling time have promoted this progress.
In July this year, Nature reported the most acclaimed quantum tunneling experiment to date, in which Steinberg's research team in Toronto used a method called "larmor Clock" to measure how long it takes rubidium atoms to pass through the repulsive laser field.
Igor Park Jung Su Vinyuk, a physicist at Griffith University in Australia, said: "larmor clock is the best and most intuitive method to measure the tunneling time. This experiment is the first time to measure it very accurately." In 20 19, Park Jung Su Vinyak reported another method to measure the tunneling time in nature.
Luiz Manzoni, a theoretical physicist at Concordia College in Minnesota, USA, also thinks that the measurement results of larmor clock method are convincing. "They did measure the tunneling time," he said.
The recent experiment brought people's attention back to an unsolved problem. In the 60 years since Hartman published his paper, no matter how carefully physicists redefine the tunneling time or how accurately they measure it in the laboratory, they find that quantum tunneling always shows Hartman effect. Quantum tunneling is almost absolutely superluminal.
"How can a tunnel particle travel faster than the speed of light?" Park Jungsu Vignac said, "Before the measurement, this was purely theoretical speculation."
What time?
It is difficult to accurately measure the tunneling time, because the reality itself is like this. On the macro scale, the time required for an object to travel from point A to point B is equal to the distance divided by the speed of the object. But quantum theory tells us that it is impossible to know the distance and speed accurately at the same time.
In quantum theory, a particle has a series of possible positions and velocities. Some properties can be exported from these options only when measuring. How this process happened is one of the most profound problems in physics.
So, before the particle hits the detector, it is everywhere, everywhere. This makes it difficult to judge how long a particle has stayed in a certain place (for example, in a potential barrier). Park Jung Su Vinyak said, "You can't tell how long it has been there, because it can be in two places at the same time."
In order to understand this problem in the context of quantum tunneling, we can draw a bell curve to indicate the possible position of a particle. This bell-shaped curve is called wave packet, and its center position is A. Now imagine the wave packet moving towards the obstacle like a tsunami. Quantum mechanical equations describe how wave packets split into two when they encounter potential barriers. Most of the particles reflect back and move towards A, but there is a small probability that the peak will slide over the barrier and continue to move towards B, so this particle has a chance to be recorded by the detector there.
However, when a particle reaches point B, can we measure its journey or its time in the barrier? Before this particle suddenly appeared, it was a two-part probability wave-both reflected and transmitted. It entered the barrier, but it didn't. The meaning of "tunneling time" becomes vague here.
However, any particle from point A to point B will undeniably interact with the potential barrier between them, and this interaction, as Eli Pollack said, "is a matter of time." The question is, how much time is there?
In the 1990s, when Steinberg was a graduate student, he had a "superficial obsession" with quantum tunneling time. He explained that the root of this problem lies in the particularity of time. Objects have certain properties, such as mass or position; But they don't have an internal "time" that we can directly measure. "I can ask you,' Where is the baseball?' But ask,' When is baseball?' "It doesn't make sense," Steinberg said. Time is not an attribute of any particle. "On the contrary, we track other changes in the world, such as the ticking of the clock (essentially the change of position), and call its increment time.
But in the case of quantum tunneling, there is no clock inside the particle itself. So what changes should be tracked when measuring? Physicists have discovered countless possible methods for measuring tunnel time.
Tunnel time
1932 Hartman and Leroy archibald McColl, who tried before him, adopted the simplest method to measure the time required for quantum tunneling. Hartman calculated the most possible time difference between particles in free space and particles that must pass through the barrier from point A to point B. He made this calculation possible by considering how the barrier position changes the position of the peak value of the transmitted wave packet.
However, this method has another problem except that the potential barrier can accelerate particles. It is impossible to simply compare the initial peak and the final peak of a particle wave packet. Calculating the difference between the most likely departure time (when the peak of the bell curve is at point A) and the most likely arrival time (when the peak reaches point B) can't tell you the flight time of any single particle, because the particles detected at point B don't necessarily start from point A ... In the initial probability distribution, they may be anywhere, including the front end of the bell curve, closer to the potential barrier. This gives it a chance to get to point B quickly.
Because the exact trajectory of particles is unknown, researchers began to seek a more probabilistic method. They take into account the fact that when a wave packet touches an obstacle, at any moment, particles have some probability in the obstacle (and some probability is not). Then, physicists add up the probabilities at each moment to get the average tunneling time.
As for how to measure probability, physicists have conceived various thinking experiments since the late 1960s. In these experiments, the "clock" can be attached to the particle itself. If the clock of each particle ticks only in the barrier, and you can read the clocks of many transmitted particles, then they will show different time ranges and get the tunneling time after averaging.
Of course, all this is easier said than done. Ramon Ramos, the first author of the paper published in Nature in July, said: "They just came up with some crazy ideas to measure this time and thought it would never happen. Now that science has advanced, we are very happy to turn this experiment into reality. "
Embedded clock
Although physicists began to measure the tunneling time in 1980s, the ultra-accurate measurement in recent years began at 20 14, which was first realized by Ursula Keller Laboratory of Federal Institute of Technology in Zurich. Her team uses a technique called "attoclock" to measure the tunneling time. In Keller's attosecond, electrons from helium atoms hit the barrier, which turned in place like the hands of a clock. Electron tunneling most often occurs when the electron barrier is in a certain direction, which we call "noon" of attosecond. Then, when electrons emerge from the barrier, they will be kicked in one direction, which depends on the arrangement of the barrier at this time. To measure the tunneling time, Keller's team measured the angle difference between "noon" (corresponding to the time when most tunneling events started) and the angle at which most electrons were emitted. The difference they measured was 50 attosecond (1 attosecond is one billionth of a billionth of a second, that is, 1 10- 18 seconds).
In a paper published on 20 19, Park Jung Su Vinyak's team improved Keller's attosecond experiment by replacing helium atoms with simpler hydrogen atoms. Their measurement time is even shorter, up to 2 attosecond, which indicates that the tunneling effect is almost instantaneous.
However, some experts later concluded that the length of time measured in attosecond does not represent the tunneling time well. Manzoni published an analysis paper on the measurement results on 20 19. He thinks that this method has the same defect as Hartmann's definition of tunneling time: from the point of view of post-operation, electron tunneling through the barrier can be said to be one step ahead.
At the same time, Steinberg, Ramos and their colleagues at the University of Toronto, David Spierings and Isabelle Racicot, conducted a more convincing experiment.
This alternative method takes advantage of the spin characteristics of many particles. In quantum mechanics, spin is the inherent property of particles, from which magnetic fields can be generated. When measuring, the spin is like an arrow, which can only point up or down. But before the measurement, the spin can point in any direction. As the Irish physicist Joseph Larmor discovered in 1897, when a particle is in a magnetic field, the spin angle will rotate, or "precession". The research team at the University of Toronto used this precession as a pointer to the so-called "larmor clock".
The researchers used the laser as a barrier and turned on the magnetic field. Then, they prepared rubidium atoms with spins arranged in a specific direction and let them drift towards the barrier. Next, they measured the spins of the atoms coming out from the other side of the barrier. Measuring the spin of any single atom always returns an "up" or "down" fuzzy answer. But through repeated measurements, the collected measurements will reveal the average precession angle of atoms inside the barrier-and the time they usually stay there.
Researchers report that the average time of rubidium atoms in the barrier is 0.6 1 millisecond, which is consistent with the larmor clock time predicted theoretically in 1980s. This is shorter than the time for atoms to move in free space. Therefore, these calculations show that if the barrier is thick enough, the acceleration will make the atomic tunneling speed exceed the speed of light.
Confusion rather than contradiction
Albert Einstein realized in 1907 that his theory of relativity made communication beyond the speed of light impossible. Imagine two people, Alice and Bob, separating at a very high speed. Because of relativity, their clocks show different times. Therefore, if Alice sends a signal faster than light to Bob, and Bob immediately sends a reply faster than light to Alice, then Bob's reply can reach Alice before Alice sends the initial message. "The achieved result precedes the cause," Einstein wrote.
Experts generally believe that quantum tunneling has not really broken the causal relationship, but the exact reason has not been found yet. "I don't think our views on this issue are completely unified," Steinberg said. "This is a mystery, not a paradox."
Some good guesses proved to be wrong. Manzoni and a colleague recalculated the problem of superluminal tunnel in the early 20th century. They believe that if the relativistic effect is considered (for fast-moving particles, time will slow down), the tunneling effect will drop to sub-light speed. "To our surprise, ftl tunnels are also possible," manzoni said. "In fact, this problem is more extreme in relativistic quantum mechanics."
The researchers stressed that as long as superluminal signals are not allowed, superluminal tunnels are not a problem. This is similar to Einstein's confused "ghostly action at a distance". The action of distance means that particles that are far apart have the ability to "entangle" each other, so the measurement of one particle can determine the properties of two particles at the same time. This instantaneous connection between distant particles will not cause contradiction, because it cannot be used to transmit signals from one particle to another.
Surprisingly, however, compared with the despair of physicists about the action at a distance, the study of superluminal tunnels is rarely too surprising. "For quantum tunneling, you are not dealing with two independent systems, and their states are not connected in a creepy way," said Grace Field, who studies tunnel time at Cambridge University. "You are dealing with a single system running in space. To some extent, this seems to be more strange than entanglement. "
In a paper published in the Journal of New Physics in September, Eli Pollack and two colleagues believe that the reason why superluminal signals are not allowed to be sent in superluminal tunnels is due to statistical reasons: although the speed of tunneling in extremely thick barriers is very fast, the probability of such an event is extremely low. Signal senders always tend to send signals through free space.
However, why not explode a large number of particles on the ultra-thick barrier, hoping that one of them can pass at superluminal speed? Isn't just one particle enough to transmit information and break the laws of physics? Steinberg agrees with the statistical view of this situation, but thinks that a single tunneling particle cannot transmit information. Signals need detail and structure. When trying to send any detailed signal, it is always faster to send it through the air than through an unreliable barrier.
Pollack said that these problems will be the theme of future research. "I believe Steinberg's experiment will promote more theories. I don't know where the future research will go. "
These ideas will lead to more experiments, some of which are already on Steinberg's plan list. He said that by determining the location of the magnetic field in different areas of the magnetic barrier, his team plans to detect "not only how long the particles stayed in the barrier, but also the location where the particles stayed in the barrier". Theoretical calculation predicts that rubidium atoms spend most of their time near the entrance and exit of the barrier, and little time in the middle of the barrier. "It's a little surprising, not intuitive at all," Ramon Ramos said.
By exploring the average experience of a large number of tunneling particles, the researchers have drawn a picture of the inside of the barrier, which is more vivid than the pioneers of quantum mechanics expected a century ago. In Steinberg's view, although quantum mechanics gives people an incredible impression, these advances have made people understand one thing: "When you see the end of a particle, you will know what it was doing before." (Ren Tian)