/How Long Does Quantum Tunneling Take? (via Qpute.com)
How Long Does Quantum Tunneling Take?

How Long Does Quantum Tunneling Take? (via Qpute.com)


Cartoon of quantum tunneling process.

Cartoon of the tunneling process, where a particle with wave properties is shot at a barrier. The classical probability of finding such a particle (black line) drops suddenly to zero at the barrier edge, but the quantum version (blue line) extends

Chad Orzel

It’s very important to note that this phenomenon is absolutely and unquestionably real, demonstrated in countless ways. The most dramatic of these is sunlight— the Sun wouldn’t be able to fuse hydrogen into helium without quantum tunneling— but it’s also got more down-to-earth technological applications. Tunneling serves as the basis for Scanning Tunneling Microscopy, which uses the tunneling of electrons across a tiny gap between a sharp tip and a surface to produce maps of that surface that can readily resolve single atoms. It’s also essential for the Josephson effect, which is the basis of superconducting detectors of magnetic fields and some of the superconducting systems proposed for quantum computing.

So, there is absolutely no debate among physicists about whether quantum tunneling is a thing that happens. Physicists get a bit twitchy without something to argue over, though, and you don’t have to dig into tunneling (heh) very far to find a disputed question, namely “How long does quantum tunneling take?”

This is an active area of research, and one I’ve written about before. The tricky part is that the distances involved in quantum tunneling are necessarily very small, making the times involved extremely short. It’s also very difficult to ensure that you know where and when the process starts, because, again, the whole business needs to be quantum, with all the measurement and uncertainty issues that brings in.

In the old post linked above, I talked about a couple of experiments involving intense and ultra-fast laser pulses, which rip an electron out of an atom, and then deflect its path in a direction that varies in time. This is a really clever trick, and the experiments are impressive technical achievements; unfortunately, they don’t entirely agree, with some experiments suggesting a short but definitely not zero tunneling time, and others finding a time so short it might as well be zero. So the question isn’t completely settled…

The latest contribution to the ongoing argument showed up on the arxiv just last night, in the form of a new tunneling-time paper from Aephraim Steinberg’s group at the University of Toronto. This one uses the internal states of atoms tunneling through a barrier to make a kind of clock that only “ticks” while the atoms are inside the barrier region.

As with so many things involving atomic physics these days, the key enabling technology here is Bose-Einstein Condensation. They’re able to measure the tunneling of rubidium atoms (which many thousands of times bigger and heavier than the electrons in the pulsed-laser experiments) across a barrier a bit more than a micron thick (several thousand times the distance in the pulsed-laser experiments) because the atoms are incredibly cold and slow-moving. The temperature of their atom cloud is just a few billionths of a degree above absolute zero, and they push them into the barrier at speeds of just a few millimeters per second.

The big advantage this offers is that unlike electrons, which are point particles, atoms have complicated internal structure and can be put in a bunch of different states. This lets them make an energy barrier out of a thin sheet of laser light that increases the energy of the atom in the light. They can control the energy shift by adjusting the laser parameters to get any height they want— they can even “turn off” the barrier without turning off the laser, by making a small shift in the laser frequency, which is crucial for establishing the timing.

The laser also changes the internal state of the atoms in a way that varies in time, letting them use the atoms as a kind of clock. They prepare a sample that’s exclusively in one particular state, and set the laser up in such a way that it drives a slow evolution into a different internal state. They separate the two different states on the far side of the barrier, and measure the probability of changing states. Once they have that, it’s relatively easy to convert that into a measurement of how much time the atoms spent interacting with the laser.

They end up with a number that’s definitely not zero— between 0.55ms and 0.69ms— that agrees well with one of the quantum methods for predicting tunneling time, and disagrees with a “semiclassical” model very badly. It’s always nice to get this kind of discrimination between models; their method also gives them a nice way to separate out the perturbation that comes from making the measurement from the “clock” they’re using, which is a nice bonus.

As a fellow cold-atom guy, I find this experiment very impressive and convincing, and there’s potential to extend this to other cool tunneling-related measurements, maybe even tracking the atoms as they move through the barrier. Physicists being physicists, though, I expect the argument over what, exactly, this all means will continue— I’d be a little surprised if zero-tunneling-time partisans gave up without finding some feature of this system to claim as a loophole.

Arcane disputes aside, though, it’s worth taking a step back to note how absolutely incredible it is that we can even have a sensible conversation about something as arcane as the amount of time a tunneling atom spends in places where classical physics says it can’t possibly be. The technology we’ve developed for probing the weirdest of quantum phenomena over the last few decades is mind-boggling, and continues to get better all the time.

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The phenomenon known as “tunneling” is one of the best-known predictions of quantum physics, because it so dramatically confounds our classical intuition for how objects ought to behave. If you create a narrow region of space that a particle would have to have a relatively high energy to enter, classical reasoning tells us that low-energy particles heading toward that region should reflect off the boundary with 100% probability. Instead, there is a tiny chance of finding those particles on the far side of the region, with no loss of energy. It’s as if they simply evaded the “barrier” region by making a “tunnel” through it.

It’s very important to note that this phenomenon is absolutely and unquestionably real, demonstrated in countless ways. The most dramatic of these is sunlight— the Sun wouldn’t be able to fuse hydrogen into helium without quantum tunneling— but it’s also got more down-to-earth technological applications. Tunneling serves as the basis for Scanning Tunneling Microscopy, which uses the tunneling of electrons across a tiny gap between a sharp tip and a surface to produce maps of that surface that can readily resolve single atoms. It’s also essential for the Josephson effect, which is the basis of superconducting detectors of magnetic fields and some of the superconducting systems proposed for quantum computing.

So, there is absolutely no debate among physicists about whether quantum tunneling is a thing that happens. Physicists get a bit twitchy without something to argue over, though, and you don’t have to dig into tunneling (heh) very far to find a disputed question, namely “How long does quantum tunneling take?”

This is an active area of research, and one I’ve written about before. The tricky part is that the distances involved in quantum tunneling are necessarily very small, making the times involved extremely short. It’s also very difficult to ensure that you know where and when the process starts, because, again, the whole business needs to be quantum, with all the measurement and uncertainty issues that brings in.

In the old post linked above, I talked about a couple of experiments involving intense and ultra-fast laser pulses, which rip an electron out of an atom, and then deflect its path in a direction that varies in time. This is a really clever trick, and the experiments are impressive technical achievements; unfortunately, they don’t entirely agree, with some experiments suggesting a short but definitely not zero tunneling time, and others finding a time so short it might as well be zero. So the question isn’t completely settled…

The latest contribution to the ongoing argument showed up on the arxiv just last night, in the form of a new tunneling-time paper from Aephraim Steinberg’s group at the University of Toronto. This one uses the internal states of atoms tunneling through a barrier to make a kind of clock that only “ticks” while the atoms are inside the barrier region.

As with so many things involving atomic physics these days, the key enabling technology here is Bose-Einstein Condensation. They’re able to measure the tunneling of rubidium atoms (which many thousands of times bigger and heavier than the electrons in the pulsed-laser experiments) across a barrier a bit more than a micron thick (several thousand times the distance in the pulsed-laser experiments) because the atoms are incredibly cold and slow-moving. The temperature of their atom cloud is just a few billionths of a degree above absolute zero, and they push them into the barrier at speeds of just a few millimeters per second.

The big advantage this offers is that unlike electrons, which are point particles, atoms have complicated internal structure and can be put in a bunch of different states. This lets them make an energy barrier out of a thin sheet of laser light that increases the energy of the atom in the light. They can control the energy shift by adjusting the laser parameters to get any height they want— they can even “turn off” the barrier without turning off the laser, by making a small shift in the laser frequency, which is crucial for establishing the timing.

The laser also changes the internal state of the atoms in a way that varies in time, letting them use the atoms as a kind of clock. They prepare a sample that’s exclusively in one particular state, and set the laser up in such a way that it drives a slow evolution into a different internal state. They separate the two different states on the far side of the barrier, and measure the probability of changing states. Once they have that, it’s relatively easy to convert that into a measurement of how much time the atoms spent interacting with the laser.

They end up with a number that’s definitely not zero— between 0.55ms and 0.69ms— that agrees well with one of the quantum methods for predicting tunneling time, and disagrees with a “semiclassical” model very badly. It’s always nice to get this kind of discrimination between models; their method also gives them a nice way to separate out the perturbation that comes from making the measurement from the “clock” they’re using, which is a nice bonus.

As a fellow cold-atom guy, I find this experiment very impressive and convincing, and there’s potential to extend this to other cool tunneling-related measurements, maybe even tracking the atoms as they move through the barrier. Physicists being physicists, though, I expect the argument over what, exactly, this all means will continue— I’d be a little surprised if zero-tunneling-time partisans gave up without finding some feature of this system to claim as a loophole.

Arcane disputes aside, though, it’s worth taking a step back to note how absolutely incredible it is that we can even have a sensible conversation about something as arcane as the amount of time a tunneling atom spends in places where classical physics says it can’t possibly be. The technology we’ve developed for probing the weirdest of quantum phenomena over the last few decades is mind-boggling, and continues to get better all the time.


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