(ORDO NEWS) — Quantum Tunneling won’t help you jump through a brick wall to platform 9¾ to catch the express train to Hogwarts. But this effect, in which quantum particles can pass through seemingly insurmountable barriers, remains a paradoxical phenomenon that refutes our inner intuition. Experimental physicists in Toronto used rubidium atoms to investigate this effect, and for the first time measured how long it took for these atoms to travel through an obstacle. They published their findings in the journal Nature on July 22nd.
Scientists have proven that quantum tunneling is not instantaneous, in at least one of the concepts of this phenomenon, although recent evidence suggests otherwise. “This is a wonderful experiment,” says Igor Litvinyuk, who works in Australia at Griffith University and specializes in the problem of quantum tunneling. “It took a heroic effort to get it done.”
In order to appreciate all the oddities of quantum tunneling, take a ball that rolls on a flat surface and suddenly encounters a small rounded mound in its path. What happens next depends on the speed of the ball. He will either roll to the top and then slide down the opposite slope, or climb up a little and then slide back, because he does not have enough energy to climb.
But such rules do not apply to particles in the quantum world. Even when a particle doesn’t have enough energy to roll over the top of a hill, it sometimes gets to the opposite edge. “The particle kind of breaks through a tunnel under the hill and appears on the other side,” said study co-author Aephraim Steinberg of the University of Toronto.
Such oddities are easier to understand if you think about the wave function of a particle, which is a mathematical expression of a quantum state. The wave function develops and spreads. And its amplitude in time and space at one time or another allows us to calculate the probability of finding a particle exactly there and exactly then – if we make measurements. By definition, this probability can be different from zero in many places at the same time.
If a particle encounters an energy barrier on its way, such a collision changes the propagation of the wave function, which begins to decay exponentially inside the barrier. Nevertheless, a part of it still seeps out, and on the opposite side its amplitude does not decrease to zero. Thus, there remains a finite, albeit insignificant, probability of finding a particle behind the barrier.
Physicists have known about quantum tunneling since the late 1920s. Today, this phenomenon underlies devices such as tunnel diodes, scanning tunneling microscopes, and superconducting qubits for quantum computing.
Since the discovery of quantum tunneling, researchers have been trying to better understand what exactly happens during tunneling. So, in 1993, Steinberg, Paul Kwiat and Raymond Chiao, who were working at the University of California at Berkeley at the time, discovered photons passing through an optical barrier (a special piece of glass that reflects 99 percent of incident photons and transmits one percent). Tunneling photons, on average, appeared earlier than those that traveled the same distance, but without barriers. Tunneling photons seemed to travel faster than the speed of light.
Careful analysis has shown that, in mathematical terms, this is the peak of the wave function of tunneling photons (the most likely place to find particles), which travel at faster than light speed. But the leading edges of the wave functions of unimpeded photons and tunneling photons reach their detection devices at the same time, that is, there is no violation of Einstein’s theory of relativity. “The peak of the wavefunction can be faster than light without the superluminal movement of information or energy,” Steinberg says.
Last year, Litvinyuk and his colleagues published a study showing that when electrons in hydrogen atoms are held back by an external electric field acting as a barrier, they occasionally tunnel through it. As the intensity of the external field fluctuates, the number of tunneling electrons also changes, as theory predicts. This team found that the time lag between the moment the barrier reaches its minimum and when the maximum number of electrons tunnel through it is a maximum of 1.8 attoseconds (one billionth of a billionth of a second). Even light, which has a speed of about 300,000 kilometers per second, travels only three ten-billionth of one meter in one attosecond, that is, a distance of the size of an atom.
Some media outlets have made the highly controversial claim that an experiment conducted at Griffith University proved instantaneous tunneling. Much of this confusion is due to theoretical definitions of tunneling time. The time lag that the scientists measured was definitely close to zero, but this does not allow us to say that the electron does not spend any time in the barrier at all. Litvinyuk and colleagues did not investigate this aspect of quantum tunneling.
Steinberg, as a result of a new experiment, asserts exactly this. His team measured how long, on average, rubidium atoms spend inside a barrier before breaking through. This time is on the order of a millisecond. Therefore, tunneling cannot be called instantaneous.
To begin with, Steinberg and his colleagues cooled the rubidium atoms to about one nanokelvin, and then directed them with the help of lasers in one direction at low speed. The scientists then blocked their path with another laser, creating an optical barrier about 1.3 microns thick. The task was to measure the time spent by the particle inside the barrier during the tunneling process.
To this end, scientists have designed something like a Larmor clock, using a complex system of lasers and magnetic fields to manipulate the transitions of the atomic state. Basically, the following happens. Imagine a particle that rotates in a specific direction – like the hand of a clock. The particle hits a barrier, and inside it is a magnetic field that makes the arrow rotate. The longer the particle stays inside the barrier, the more it will interact with the magnetic field, and the more the arrow will rotate. The amount of rotation corresponds to the time spent by the particle inside the barrier.
Unfortunately, if a particle interacts with a magnetic field strong enough to correctly encode the elapsed time, it will exit the quantum state. And the tunneling process will be disrupted.
For this reason, Steinberg and his colleagues used the weak measurement method. A group of equally prepared rubidium atoms approaches the barrier. Inside the barrier, atoms fall into a weak magnetic field, with which they hardly interact. This weak interaction does not interfere with tunneling. But it forces the clock hand of each atom to travel an unpredictable distance, which can be measured when the atom exits the barrier. We take the average position of the arrows of a group of atoms and we get a number that can be represented as the correct value for one atom, although this kind of individual measurement is not possible. Taking such weak measurements, the scientists concluded that the atoms in their experiment spend about 0.61 milliseconds inside the barrier.
They also tested another bizarre thesis of quantum mechanics: the less energy, or the slower a tunneling particle moves, the less time it spends inside the barrier. This is an illogical result, because according to our understanding of the world, a slower particle should stay inside the barrier longer.
Measurements of the clock’s rotation made a great impression on Litvinyuk. “I don’t see any flaws in this,” he says. However, the scientist is in no hurry to draw conclusions. “There are many ways to interpret how this relates to tunneling time,” the physicist says.
Quantum physicist Irfan Siddiqi of the University of California at Berkeley is impressed by the technical complexity of the experiment. “What we saw is amazing because we now have the tools to test all this philosophical speculation from the last century,” he says.
Satya Sainadh Undurti, who worked for Litvinyuk team and now teaches at the Israel Institute of Technology in Haifa, agrees. “A Larmor watch is definitely the right way to find answers to tunneling time questions,” he says. “The experimental design outlined in this paper is a smart and clean way to do it.”
Steinberg admits that some quantum physicists will question his team’s findings and explanations, especially those who find weak measurements questionable. Nonetheless, he believes that this experiment points to something undeniable about tunneling time. “With the right definitions, tunneling is not instantaneous. It just goes by amazingly fast, – says the scientist. “And it seems to me that this is still a very big difference.”
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