Quantum Optics from the Opposite Direction: QED Limits on Laser Intensities

Most of the time, when we talk about seeing quantum effects from light, we talk about extremely weak beams-- looking at intensities where one photon more or less represents a significant change in the intensity of the light. Last week, though, Physics Buzz wrote up a paper that goes in the other direction: they suggest a limit on the maximum strength of a laser pulse due to quantum effects, specifically the creation of particle-antiparticle pairs.

This is a little unusual, in that most of the time when people talk about really intense lasers, they end up discussing them as an oscillating electromagnetic field, in a very classical sense. The idea is that once you have a large enough intensity, the effect of adding or subtracting one photon from the beam is completely negligible, so you can talk about it as a more-or-less classical field. And, in fact, the paper in question takes this approach for looking at the effects of the laser field after the pair creation. But it's a useful reminder that quantum effects become important not just when you look at really small amounts of energy, but also when you try to pack a large amount of energy into a really small space.

The paper itself is kind of difficult to read-- English is almost certainly not the first language of anybody involved in the writing-- but the basic idea is that an ultra-intense laser pulse, or the "collision" of two pulses, can lead to the production of electron-positron pairs out of the vacuum, converting a small amount of the light energy into mass. (This builds on earlier experiments at SLAC which collided intense laser pulses with high-energy electrons to create a similar effect; this new paper, as I understand it, involves the creation of the electron-positron pairs from light alone.)

Once a single pair has been created, they look at its behavior in the large electric field of the original laser pulse. This will tend to accelerate the electron and positron in opposite directions, and for sufficient laser intensity, the acceleration can be rather dramatic. We know from Maxwell's equations, though, that an accelerating charged particle gives rise to radiation. If the laser field is strong enough, the accelerating electron and positron will emit radiation themselves, and the light produced from their motion can, in turn, produce more electron-positron pairs, which are then accelerated, and so on.

Every one of these steps chips away at the energy of the initial laser pulse. The energy to create the initial pair has to come from the laser, and the energy gained by the accelerating particles also comes from the laser. At high enough initial pulse energy, the creation of a single pair triggers a "cascade," an exponentially growing collection of particles begetting other particles, all of them stealing energy from the initial pulse, until it's gone, or at least down below the threshold intensity needed to start making pairs that make other pairs. This would place a hard limit on the maximum intensity of a laser pulse.

This isn't really a quantum optical effect in the usual sense of requiring a quantum model for the behavior of the light pulse-- as I said, their calculation just uses an oscillating electric field to produce the effects-- but it does involve both light and quantum effects, so it's not too big a cheat to call this a quantum optical effect. And while this is very much a theoretical paper, the pulse intensities where they expect these effects to start showing up should be attainable by some ultra-high-power lasers that are currently under development, so it may soon be possible to see quantum effects using nothing but bright light and empty space. Which is pretty cool, no matter what you call it.

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When they say the effect will be seen at upcoming laser facilities, I guess the point is that the new generation of lasers is below the critical field strength, but not too far below, so that pair-creation is rare, but happens enough to be studied? Surely no one would have planned to build a laser that actually reaches Schwinger-strength electric fields....

I think the key claim is that the level where this should start to appear is lower than previously believed. Thus, the laser systems under development might be able to trigger these cascades at intensities that are lower than expected. So the development may have begun thinking this wouldn't be attainable.

The paper is very preliminary, though-- it's pretty much a toy model, needing further development.

The paper gives ~10^25 W/cm^2 as the critical intensity. We're still pretty far from that in the optical regime. I wouldn't hold my breath about seeing pair production any time soon, at least with light of UV wavelengths and longer.

Question: How does this conserve rest mass? In a laser, all the light is going in (roughly) the same direction, so it has no rest mass. If an electron/positron pair is produced, the pair has rest mass.

Question: How does this conserve rest mass?

It doesn't, because rest mass is not a conserved quantity. Energy and momentum are conserved (yes, photons do have momentum), but E = mc^2, so if you have mc^2 of energy lying around, you can convert it to mass m, or you can liberate it by conversion from mass m.

By Eric Lund (not verified) on 18 Aug 2010 #permalink

No, I'm pretty sure rest mass is a conserved quantity. The key word is *rest* mass, which is the total mass-energy in the center of mass frame. In a closed system, the center of mass frame is an inertial frame and mass-energy is conserved.

You can't cause two photons going in the same direction to undergo pair production. If it were possible, then the reverse reaction would also be possible. That is, you could have an electron/positron pair produce two photons which go in the same direction. This obviously doesn't conserve momentum. There exists some reference frame where the electron/positron pair has net zero momentum. There does not exist a reference frame where the photons have zero momentum.

What you're talking about is what most people would call "energy conservation", miller; calling the invariant mass of a two-photon system its "rest mass" is a little nonstandard.

You're right that two photons moving in the same direction are kinematically incapable of annihilating. But the initial pair creation event here isn't something you can understand perturbatively in terms of scattering any small number of photons. It happens even in a completely uniform homogeneous electric field. It's a nonperturbative effect that can be understood as a semiclassical tunneling process.

miller: It's conservation of momentum and energy that's at issue here, and were it true that

In a laser, all the light is going in (roughly) the same direction, so it has no rest mass.

then pair production would indeed violate conservation of momentum, energy or both.

However, while the light in a laser beam travels in one direction, the light in the laser cavity itself travels in two opposite directions, so pair production is possible.

http://en.wikipedia.org/wiki/Laser