# How can we detect matter waves?

The DeBroglie wavelength associated with a moving object is $$\lambda = \frac hp$$

For an object of mass 200 grams traveling with a velocity 20 m/s, it is in the order of $$10^{-34}$$ m. Is current technology capable of detecting matter waves of such small orders? Or are we limited to subatomic particles only? Also, is there any real-life application to these waves?

• Maybe my answer here may help in understanding "matter waves" physics.stackexchange.com/questions/251473/… Jan 22 at 13:55
• I've hidden some comments that should have been posted as answers to the question. To post a brief answer, post an answer but don't write very much in the box. Please use comments to clarify and improve the question, or to provide relevant links.
– rob
Jan 22 at 14:41
• The largest objects we have seen diffraction with have been molecules with about 2000 atoms (about 25000 AMU). It gets progressively harder with larger objects. Jan 23 at 15:28

The standard experiment to detect wavelike phenomena is to is to induce diffraction/interference effects by having the wavelike object interact with some other object whose length scale is comparable to the wavelength. The example that everyone jumps to first is the double slit experiment, where you pass the wavelike object through two barriers whose width and separation are both comparable to the wavelength. But you can also get diffraction and interference from single slits, from diffraction gratings, and from other systems with various degrees of exotic-ness.

There are two major problems with trying to observe diffraction with a macroscopic object like a three-gram paperclip. The more intuitive problem is that, if you tossed a paperclip through some hypothetical aperture with a width of $$10^{-34}\rm\,m$$, the paperclip would just bounce off rather than passing through. (This isn't in principle a fatal flaw, because you could do a diffraction analysis on the reflected beam of paperclips.)

The more important issue is that you can't really observe an interference pattern from the detection of a single transmitted object. In order to measure the locations of destructive and constructive interference, you have to run your measurement on many transmitted objects. When you shine a laser pointer on a staple, you are sending a gazillion photons with identical wavelengths onto the wall across the room. The constructive-interference locations are bright, and the destructive-interference locations are dark. The famous counterintuitive observation is that the pattern appears even if the the photons are transmitted so infrequently that there is never more than one photon in your interferometer at the same time during the duration of your experiment. But you still have to observe many transmissions to build up the pattern.

And now we come to the heart of the issue for macroscopic matter-wave experiments: in order to repeat the same transmission experiment, so that you are filling in the same pattern with every repetition, each of the objects you test must be indistinguishable from the others. For microscopic objects this is relatively straightforward. Every electron is identical, so a beam of electrons with a narrow momentum spread will generate an interference pattern. Every rubidium-87 atom in its ground state, or every rubidium-87 atom in its lowest excited state with quantum numbers $$^2P_{1/2}$$ (or whatever the lowest excited state actually is), is indistinguishable from every other rubidium-87 atom with the same quantum numbers, so you can study matter interference in rubidium vapors.

But when you start to get into big floppy molecules, you have vibrational states whose excitations energies are comparable to room temperature. If you tried to do a diffraction experiment with some carbon polymer whose spectrum includes sub-milli-eV vibrational states, and your source of polymer molecules is at room temperature so that the typical excitation energy is $$k_B\cdot300\rm\,K\approx25\,meV$$, those polymer molecules are no longer indistinguishable, and the different interference patterns from the different excitation "species" will all wash out from each other.

A three-gram aluminum paperclip (aluminum, unlike iron, has only one stable isotope; a steel paperclip isn't just iron anyway) is still a mosaic of different crystal domains whose boundaries migrate under thermal motion. The quantum-mechanical description of heat in a crystal is in terms of collective vibrations called "phonons." As the size of the crystal tends towards infinity, the spectrum of phonons becomes continuous. There's just no way to get a paperclip cold enough to put the entire paperclip in a well-defined quantum state, so it's impossible to construct a "beam" of indistinguishable paperclips.

• The "matter" wave title seems misleading, the principle is also about detection ... which invokes the EM field. All these interference type experiments need to consider the "self interference" of the EM field. Jan 23 at 6:02
• I'm not sure I understand your comment. It's totally possible to wave-interference measurements with matter particles such as electrons, atoms, or molecules (with the caveats in the answer). The precision-measurements community does interesting work with neutron interferometers. Can you clarify why you think the electromagnetic field must be involved?
– rob
Jan 23 at 6:08
• I have cherry picked this paper vixra.org/pdf/1212.0130v1.pdf. And quote this from page 6 "But from the perspective of the NQP, these experiments actually proved nothing about matter waves of the beam, but rather about the spatial Fourier transform of the measuring device, which restricted the momentum transfer in the measurement." NQP = New Quantum Paradigm. Jan 23 at 15:19
• I don't think they have to be identical particles. A particle interferes with itself when it diffracts. If the black-body radiation wavelength is much longer than the (between-slit distance, d)*sqrt(photons emitted) no which-slit info is betrayed (equivalently, the joint wave-function of particle + photons has enough spread in the "position of photons directions" that shifting the "left slit blob", in a photon direction, by d will not prevent the "left slit" and "right slit" blobs from overlapping and thus interfering). I think this means a little radiation is OK. Jan 23 at 15:54
• @PhysicsDave That paper is deeply flawed. If you'd like to have a conversation about it, let's do in Physics Chat. You can make a dedicated room if you'd like. A fair discussion of the linked paper would be easier with some back-and-forth, and this comment thread isn't the right place for that.
– rob
Jan 23 at 16:02

To simplify Rob's answer to the essential: what we are detecting are not "matter waves". We are detecting individual quanta of energy. A single quantum does not show any kind of wave phenomena. Only an ensemble of quanta does.

How we deliver these quanta of energy is completely irrelevant, but the ensembles have to be in a coherent state, i.e. the amount of energy that we are measuring has to be (roughly) the same every single time. This is much easier accomplished with microscopic systems that have very few internal states (or only one) than with compound macroscopic "objects" that have a myriad of very closely spaced excitation energies which are much larger than the quanta of (kinetic) energy that we are trying to measure.

• Thanks for this: to paraphrase Pascal, I didn't have time to make my answer shorter. I might suggest to rephrase "a single quantum doesn't show any wave phenomenon," since the wavelike description certainly does predict the evolution of the system, even when only a single quantum is present.
– rob
Jan 22 at 17:13
• @rob I didn't know how to answer the question succinctly, that's why I only left a comment. Your practical example with the Rubidium atoms was very helpful in clarifying what the "essence" of the phenomenon is. I agree that there is a non-trivial tension between the single quantum vs. ensemble view. I have not found a good way of explaining it, yet, not even in the case of classical electrodynamics where "coherence without self-interaction" is the consequence/source of the boundary value solution. It's in the the solution theory of the equations, but not easily intuitively accessible IMHO. Jan 22 at 22:48

Quick answer is no. That is, no experimental method using current technology will be sufficiently stable to show that a 200 gram object moving at 20 m/s is wavelike.

It is normally assumed that it would be possible in principle, i.e. the laws of nature allow, that there could be an experiment showing evidence of wave-like interference of such an object. However there are some issues with gravitational and other effects (interactions with the quantum vacuum) which make this not known for sure.