Is it possible to confine a photon in less than its* wavelength?

Question

*(Its, or associated. That is somehow the question).

I can think of, at least in principle, a perfectly reflecting optical cavity with dimension comparable to the wavelength of the electromagnetic wave associated to a photon. Say, a kind of internally reflecting sphere with diameter of a wavelength or smaller (or a comparable cube etc for that is matter).

Would be possible for that photon to exist inside that object?

How this relates to the "size of a photon", where now size stands for the spread of the probability to find it (sort of "De Broglie wave for a photon") and what would change in this respect if the photon won't be confined?

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I ended up to this while thinking about the meaning of the various jiggling arrows we draw when depicting photons arriving at a place, motivated by the common widespread feeling of getting lost when asked what it really means. In other words by thinking of a wave that, tough interacting as a point particle, must conveys information about an oscillating em field. It seems it needs at least a wavelength (in that medium) to do so. I hope that the question above is more clear than the motivation that drove me to write it.

Answer 1

Confining a photon to a region smaller than its wavelength is not only conceivable in principle, it is current experimentally achievable reality.

In particular in plasmonics, people build cavities that confine the electromagnetic field to such tiny regions for a time of multiple oscillation periods. Here is a review from 2010: "Review on subwavelength confinement of light with plasmonics" Journal of Modern Optics 57, 1479(2010) and a lot more work in this direction has been done recently. Another nice example is are "picocavities" such as in the more recent paper Science 354, 726-729 (2016).

So with regards to the question

Would be possible for that photon to exist inside that object?

we can give a clear "yes!" answer.

With regards to the more conceptual question on the size of a photon, the confined photon can be described as a superposition of various field degrees of freedom. So there is no conceptual problem here. Whether it is a single photon or not depends on which quantum state precisely you excite in the system.

In the case of plasmonics, specifically, one actually does not have a purely photonic excitation, but an excitation of the electrons in the confining cavity material is mixed in. This mixed excitation is called a plasmon.

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Since there have been some comments on whether a plasmonic excitation qualifies as a photonic excitation or not, I decided to include a second example that avoids this discussion altogether: "Experimental realization of deep-subwavelength confinement in dielectric optical resonators" Hu et al., Science Advances 4, 2355 (2018). This paper (as one can see already from the title) experimentally realizes subwavelength confinement of the electromagnetic field in an all-dielectric photonic crystal cavity made of silicon. So this is purely based on refractive scattering of photons inside the resonantor.

This example unambiguously qualifies as "confining photons to less than their wavelength" without the definition discussion in the case of plasmonic resonators.

Answer 2

A photon does not in general have an exact wavelength. Because of the property of the Fourier Transform known as the Heisenberg Uncertainty Relation, if the photon doesn't have infinite spatial extent, then it must have finite (non-zero) spectral extent. In my work in ultrafast laser physics, we regularly make pulses that are few cycle, and some people make only single cycle duration pulses. The primary limitation to getting such a short pulse is how broad you can get your spectrum to be (how precisely you can control the spectral phase is also very important).

Now, I spoke of wavelength, but you may know that photons carry an energy determined by their frequency. This frequency is related to the wavelength, and there is also an Uncertainty Relation for energy and duration.

If you're still not convinced because I haven't really addressed the quantum aspect of the situation, consider the infinite well problem, which is known to all students of quantum mechanics. You learn what the eigenstates are, but those aren't all possible states. You can also have a linear superposition of any or all of those states, and in fact it's possible to represent any function that is zero on the boundaries and is well behaved as such a superposition. In other words, you can propose a function with an arbitrarily narrow peak, and you are guaranteed to be able to represent that as a superposition of states.

The Schroedinger equation in this problem only models a single particle. So this amounts to saying you can confine the particle to an arbitrarily small spatial extent, it just means that the particle will be in a superposition of states.

I will note, in this potential, the peak will not last in general, it will rapidly blow up, but it is certainly possible to do this if your potential and wavefunction are right, and this is evidenced by coherent states

The other answer, by Wolpertinger, addresses that it has actually been accomplished, what I'm trying to add is some more explanation for why this is actually not surprising.

Answer 3

How a photon is created?

I am not referring to photons being sent into the cavity from outside. It simply will not fulfil the situation you describe.

To use a photon, you have to create one. If you accelerate an electron along the surface of the mirror, the electric field of the electron turns into a magnetic field. Given enough space in front of the mirror, the magnetic field converts back into an electric field and the propagation of such a packet of energy is what we call a photon. When it hits another surface, the photon is reflected or absorbed.

Conclusion: Below the distance of one wavelength, the photon does not occur. There is simply a transfer of energy from one side of the cavity to the other.

What about modulated radiation?

Normally you don't accelerate a single electron. Normally we accelerate a large number of electrons together. And we do that periodically, accelerating the electrons back and forth.

The resulting phenomenon is very different from single electron radiation. The emitted common fields (depending on the shape of the emitter, it can be an electric or a magnetic antenna (and nothing other than an antenna is your surface)) induces a common excitation of surface electrons on the other side of the cavity. These in turn emit a common field (attenuated by energy losses, of course). With cavity walls of calculated thickness, or better layers of composite materials, these energy losses can be reduced.

The interesting thing about a light-plasmon-light transformation is the possibility of modulating EM radiation, focusing it and using it for computing tasks alongside today's PCs.