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Normal holograms are, if I understand correctly, what happens when coherent light is passed through something that manipulates the photon's wave functions to be what would have been present had they been reflected off a real 3d object.

Is it possible, in principle, to do that with something other than light? In particular, I'm thinking of electrons when I ask this. Are electron-holograms possible?

(I'm imagining an electron microscope and some sort of nanoscale filter instead of a laser and photographic film, but this is just speculative).

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  • $\begingroup$ Would an answer drawn from the same Physics Stock room where we get the massless, inelastic string and the frictionless pulleys be acceptable or is the question practical in nature? $\endgroup$ – dmckee --- ex-moderator kitten Feb 7 '15 at 0:05
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    $\begingroup$ @dmckee It's that bad? Oh well. I'm curious about it in practice, but if it's only possible with unreasonable simplification, that's worth knowing too. $\endgroup$ – BenRW Feb 7 '15 at 10:14
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Yes, electron holography is possible and it is an exciting, growing research field within strong field physics. The nicest way to do this is via laser-induced holography, where you use a strong laser field to ionize a molecule and then drive the photoelectron back to the ion to make it recollide. The initial experiments looked at the way the wavefunction was scattered off of the molecular ion to try and reconstruct its shape, a principle now called laser-induced electron diffraction.

Laser-induced electron holography, on the other hand, is now also possible. Here the electron wave is now stable enough so that the scattered wavefunction will visibly interfere with the non-scattered part, and this creates a complicated hologram in the far-field photoelectron spectrum. The dream here is to simply read off a photoelectron spectrum and re-transform it back to image aspects of the target molecule: the positions of the nuclei, the electronic density, and hopefully even the ionized orbital itself. As the field develops, it has become clear that this is a bit of a tall order, because the motion of electrons in strong fields can be very complex, but we can at least perform TDSE simulations which match the measured holograms. Holographic imaging of molecules is still some way away.

The sort of picture you get out of this looks like this:

enter image description here

where the targets are noble gas atoms, imaged in

Y. Huismans et al.Time-Resolved Holography with Photoelectrons. Science 331 no. 6013 (2011), pp.61, hal-00553330.

For a nice review, see

Atomic and Molecular Photoelectron Holography in Strong Laser Fields. Xue-Bin Bian and André D. Bandrauk. Chinese J. Phys. 52 (2014) p. 569.

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There is nothing in particular quantum mechanical about the general principle of holography. There is , for example, such a thing as acoustical holography, which is entirely explainable in terms of classical wave interference and diffraction. Lasers are used in "traditional" optical holography because they provide a fixed frequency source of light.

Acoustical holography involves "imaging" the sound field produced by a vibrating object , such as a car engine. In acoustical holography, measurements are made in the "near field" of a sound source (i.e., close enough that interference and diffraction between sound waves generated by different parts of the object are important). Instead of a photographic plate, acoustical holography uses a planar array of microphones to sample the magnitude and phase of the sound field produced by the source, at a particular frequency. Reconstruction of the sound field of the source from the data is done by mathematical back-propagation from the data collected on the array.

Here is a link to an article

that goes into a bit more detail about how acoustical holography works.

I can't comment on your specific question (electron holography) since that's outside my expertise, but as you probably know, it's the wave properties of electron propagation (de Broglie wavelength) that make electron microscopy possible. So given the proper setup to capture the magnitude and phase of the electron wave field caused by scattering off an extended source, it should be possible in principle to do electron holography.

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    $\begingroup$ Note that normal holography with light has little to do with quantum mechanics. You do need a laser to produce sufficiently coherent light, but even then the state of the light is fully classical (i.e. the only quantum mechanical aspects of the light are the amplitude and phase uncertainties, whose effects are equivalent to classical noise). The holography itself is a wave-mechanical phenomenon and it fits completely inside the classical EM of Maxwell's equations. $\endgroup$ – Emilio Pisanty Feb 9 '15 at 12:22
  • $\begingroup$ @EmilioPisanty that's a really interesting note. I had no idea it was purely classical. Thanks! $\endgroup$ – BenRW Feb 9 '15 at 22:25
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Yes this can (and has) been done with electrons. It is a common way to produce wavepackets of free electrons with orbital angular momentum. People use holography to make light beams with orbital angular momentum, the beam has a dark patch in the middle, and some interesting phase circulation around the dark inner tube. And they can make identical beams for electrons (with a dark patch in the middle, and some interesting phase circulation around the dark inner tube) using identical, holographic, techniques. The diffraction gratings look exactly the same when you are trying to get the exact same effect. Except the spacing is different because the wavelength is different to be in line with the de-Broglie wavelength of the electrons.

All you need to do is etch some material so that it is thinner in some parts than others so that there is a phase difference between transmission through the etched part and transmission through the unetched part (transmission diffraction). Holography assumes a coherent beam, so you also need electron optics to get a nice beam, but again, it's already been done.

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  • $\begingroup$ Note for the OP that may be worth mentioning: the discontinuous phase in the phase plate is not essential to holography: it's particular to the creation of beams with orbital angular momentum. I can imagine wondering whether the phase defect were an essential part of the holography process if I read articles on this without knowing anything else. +1 BTW $\endgroup$ – Selene Routley Feb 8 '15 at 7:50
  • $\begingroup$ @WetSavannaAnimalakaRodVance Thanks, I was trying to make it clear that it is just like the holographic techniques for making light with orbital angular momentum, the diffraction gratings look exactly the same (except for the size of the spacing). So its definitely holography with electrons, and it is definitely just like with light. I'll edit it. $\endgroup$ – Timaeus Feb 8 '15 at 16:18

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