A Detecting Single Phonons: Is It Possible?

[Demystifier]

Is it possible to detect a single phonon? If yes, can it be detected at a well-defined position?

 

[Dadface]

I don't know the answer but I'm watching the thread because I think it's an interesting question. I would,however, like to offer some initial thoughts:
1. I think the observation of phonons is known of only indirectly for example by observations of things such as sound propagation and specific heat capacities.
2. Perhaps more observational details can be obtained by observing vibrations of particles that carry the vibrations from place to place. X ray diffraction techniques come to mind.
3. The concept of phonons is probably useful but I'm wondering whether they are actually real things and by that I mean whether it is possible, if only in principle, to actually observe them directly.

 

[Lord Jestocost]

I remember some "listening with a 'quantum ear'": “Local probing of propagating acoustic waves in a gigahertz echo chamber”, Nature Physics 8, 338–343 (2012)

 

[Demystifier]

3. The concept of phonons is probably useful but I'm wondering whether they are actually real things and by that I mean whether it is possible, if only in principle, to actually observe them directly.

In principle, a phonon should be possible to detect if there is an interaction of the form
$$H_{\rm int}\propto a_{\rm phonon} b^{\dagger}b + h.c.$$
where $a_{\rm phonon}$ is the destruction operator for the phonon, while $b$ and $b^{\dagger}$ are the destruction and creation operators of some quanta which can absorb and emit phonons. Can someone give an actual example of such an interaction?

Such an interaction can detect a phonon at a well-defined position if the above are local operators, i.e.
$${\cal H}_{\rm int}(x)\propto a_{\rm phonon}(x) b^{\dagger}(x)b(x) + h.c.$$
where $b(x)$ etc are Fourier transforms of the usual operators $b_k$ etc in the momentum space. Examples?

 

[Demystifier]

I remember some "listening with a 'quantum ear'": “Local probing of propagating acoustic waves in a gigahertz echo chamber”, Nature Physics 8, 338–343 (2012)

As far as I can see, this doesn't have much to do with single phonons.

 

[Dadface]

http://www.nature.com/nphys/journal/v2/n8/abs/nphys345.html?foxtrotcallback=true

Is this the sort of thing you're looking for?

 

[Demystifier]

http://www.nature.com/nphys/journal/v2/n8/abs/nphys345.html?foxtrotcallback=true

Is this the sort of thing you're looking for?

In the abstract they talk about "coherent phonons in SWNT ensembles". I'm not sure what do they mean by that, but it doesn't sound like a single phonon to me.

EDIT: Indeed, by little googling I found
https://arxiv.org/pdf/1205.6023.pdf
where Eq. (2.1) shows that coherent phonons is a state with an uncertain number of phonons. I want exactly one phonon, not an uncertain number of them.

 

[Dadface]

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.62.1057
I don't know if this is any good.

 

[TeethWhitener]

Is it possible to detect a single phonon? If yes, can it be detected at a well-defined position?

Phonons are collective lattice motions with well-defined momenta. Thus individual phonons are localized in reciprocal space, not real space.

As for detecting a phonon, why isn't Raman scattering acceptable? It involves either creation (Stokes) or annihilation (anti-Stokes) of a phonon via inelastic photon scattering. Theoretically, you could do the experiment with a single photon, though the cross section of Raman scattering is several orders of magnitude smaller than Rayleigh scattering.

 

[Demystifier]

Phonons are collective lattice motions with well-defined momenta.

Phonon (just like photon) does not need to have a well-defined momentum. A superposition of one-phonon states with different momenta is still one phonon.

 

[Demystifier]

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.62.1057
I don't know if this is any good.

Almost! In this experiment, they observe an electron that emitted a single phonon. A detection of phonon would correspond to an inverse process in which they observe an electron that absorbed a single phonon.

 

[Demystifier]

As for detecting a phonon, why isn't Raman scattering acceptable? It involves either creation (Stokes) or annihilation (anti-Stokes) of a phonon via inelastic photon scattering. Theoretically, you could do the experiment with a single photon, though the cross section of Raman scattering is several orders of magnitude smaller than Rayleigh scattering.

Theoretically, yes. But I would like to know if something like that has been done in practice.

 

[DrDu]

How about Mössbauer effect, specifically the phonon sideband?

 

[atyy]

Maybe

https://www.nature.com/nature/journal/v464/n7289/full/nature08967.html
Qyantum ground state and single-phonon control of a mechanical resonator
A. D. O’Connell, M. Hofheinz, M. Ansmann, Radoslaw C. Bialczak, M. Lenander, Erik Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, John M. Martinis & A. N. Cleland

https://arxiv.org/abs/1410.1047
Phonon counting and intensity interferometry of a nanomechanical resonator
Justin D. Cohen, Sean M. Meenehan, Gregory S. MacCabe, Simon Groblacher, Amir H. Safavi-Naeini, Francesco Marsili, Matthew D. Shaw,Oskar Painter

 

[David Olivier]

Plain thermal agitation can be construed as a sea of incoherent phonons, can't it? If so, if you have a molecule that, when excited above a certain threshold, emits a photon, and you maintain a collection of such molecules at a certain temperature such that once in a while the threshold is crossed and a photon is emitted, then it would seem that you have detected a single phonon ‑ namely, the phonon that, added to all others, made the molecule cross that threshold.

 

[Andy Resnick]

Is it possible to detect a single phonon? If yes, can it be detected at a well-defined position?

I think so- not at a well-defined position, but at a well-defined momentum (phonons don't have well-defined positions).

http://www.nature.com/nature/journal/v530/n7590/full/nature16536.html

 

[Mech_Engineer]

So-called "photon counting" systems do exist, although it does require careful management of your signal to noise ratio. Photon Multiplier Tubes have historically been one method to achieve single photon counting this due to their high gain and high sensitivity.

More reading: Hamamatsu PMT Handbook- Chapter 6: Photon Counting

One modern technology for single photon counting is the "superconducting nanowire single-photon detector," see here:

https://en.wikipedia.org/wiki/Superconducting_nanowire_single-photon_detector
https://www.nist.gov/news-events/news/2013/02/high-efficiency-fastest-single-photon-detector-system

 

[DrDu]

(phonons don't have well-defined positions).

I don't see why not. A photon is a quantum of atomic displacement. It is not required that this quantum is in an eigenstate of energy or momentum.

 

[jtbell]

So-called "photon counting" systems do exist

This thread is about phonons, not photons.

 

[David Olivier]

This thread is about phonons, not photons.

Ah. I thought it was about phodons.

 

[Andy Resnick]

I don't see why not. A photon is a quantum of atomic displacement. It is not required that this quantum is in an eigenstate of energy or momentum.

Phonons are quantized displacements of a crystal (an ordered array of many atoms); a good discussion is in Coleman's "Introduction to Many Body Physics", chapter 2.4.

 

[DrDu]

Phonons are quantized displacements of a crystal (an ordered array of many atoms); a good discussion is in Coleman's "Introduction to Many Body Physics", chapter 2.4.

Yes. I mean, if they aren't eigenstates of energy and crystal momentum, they are time dependent phonons but phonons nevertheless.

 

[Mech_Engineer]

This thread is about phonons, not photons.

My bad! Carry on...

 

[M Quack]

Measurements of the phonon dispersion curves (energy vs. momentum) are very standard in neutron inelastic scattering and to a lesser extent in inelastic x-ray scattering. In these experiments you detect single neutrons and x-ray photons. Each neutron/photon enters the sample will a well-defined energy and momentum (direction), and comes back out with different energy and momentum. The difference is taken up by the phonon, i.e. a phonon is created in the process (or another elementary excitation, e.g. a magnon in a magnetically ordered crystal) . So with each x-ray photon or neutron you measure a single phonon. You need x-rays or thermal neutrons rather than visible light for this because the momentum transfer is on the order of the reciprocal lattice unit.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1994/press.html
http://iopscience.iop.org/article/10.1088/0034-4885/63/2/203/meta

"Thermal diffuse scattering" of x-rays or neutrons is also caused by phonons, but in that case you do not measure the phonon's energy.