Is all electromagnetic radiation quantized?

[harrylin]

For quite a while I have been wondering if the quantization of light may be due to the emission process. In that case, at first sight there seems to be no reason for radio waves (created with LRC circuits) to be quantized.
But perhaps I overlook something? And would there be a way to test between the two hypotheses? Links to experiments in the literature (if they exist) will be appreciated!

 

[Cthugha]

Well, a good indicator for quantized emission at some wavelength range would be the observation of antibunching if you manage to prepare a Fock state in this wavelength range. However, at long wavelengths you run into the problem of no suitable detectors being available.

I am not aware of any demonstration of antibunching in the radio wave regime, but recently it has been demonstrated in the microwave range (D. Bozyigit et al, Nature Physics 7, 154–158 (2011)) which is in my opinion already a great achievement from the experimental point of view.

 

[zonde]

D. Bozyigit et al, Nature Physics 7, 154–158 (2011)

arxiv version of this paper:
http://arxiv.org/abs/1002.3738"

 

[harrylin]

The paper by Bozyigit is very recent, and very interesting.

If I correctly understand the introduction, they analyzed radiation coming from a quantized source with a non-quantum detector. That is not what I asked for, but it is halfway towards that goal.

Thanks!

 

[Meir Achuz]

For quite a while I have been wondering if the quantization of light may be due to the emission process. In that case, at first sight there seems to be no reason for radio waves (created with LRC circuits) to be quantized.

That was Planck's original hypothesis, which he never rescinded, and so he never really believed in quantum mechanics. But all of QED requires that all EM fields be quantized.
So called "classical" fields are just the huge N limit of the quanta. This is like a liquid seeming continuous.

 

[f95toli]

Also, the radiation created by LCR circuits IS quantized; some of the circuit elements used in circuit-QED are just "ordinary" capacitors and inductors (operated at a few GHz, but that is still essentially RF): you can create a Fock state in a LC oscillator just as you would in a cavity type resonator.

 

[harrylin]

Also, the radiation created by LCR circuits IS quantized; some of the circuit elements used in circuit-QED are just "ordinary" capacitors and inductors (operated at a few GHz, but that is still essentially RF): you can create a Fock state in a LC oscillator just as you would in a cavity type resonator.

Then, according to QM, what would physically cause the quantization in an LRC circuit? Or is this free to interpretation? Different from an atom, an LRC circuit does not seem to have fixed energy levels, it seems. It's even possible to emit frequencies with such a circuit that are not exactly resonance frequencies.

 

[kof9595995]

I guess what op really want to ask is "Is all electromagnetic radiation discretized?". The modern usage of "quantization" usually refer to a set of procedures which transit a classical description to a quantum mechanical description. And discretization of energy levels in bound system is just one possible consequence of quantization.
Discretization of radiation refers to the discretized energy in a particular frequency, not that the whole frequency spectrum is discretized. So in LRC circuit the frequency spectrum is a continuum, but the energy for each frequency is not.

 

[tom.stoer]

Modern quanum field theory describes both matter and radiation fields as quantum fields, i.e. being intrinsically quantum. For electromagnetic radiation that means that a discrete or continuous frequency spectrum is due to the properties of the emission process, the quantization of the field (that it consists of single = discrete photons each with frequency f and energy E=hf) is due to the quantum nature of the photon field.

 

[PhilDSP]

The other way to look at this is to consider solutions to the Maxwell equations. Any term signifying displacement current could be considered radiation. If you require a less general description for radiation, such as displacement current within a traveling wave, then you need to look at wave solutions. The term "displacement current" means a change of E and B fields or vector potential along with the flow of energy implied by their change (as given by the Poynting vector).

From the wave solutions there is apparently no stipulation enforcing a non-continuous frequency or wavelength spectrum. However once you start working with solutions involving media, the discrete nature of a charge together with the de Broglie relations indicates that motions of two or more charges are reactively coupled in such a way to produce only quantized radiation.

 

[harrylin]

Any term signifying displacement current could be considered radiation. [..] From the wave solutions there is apparently no stipulation enforcing a non-continuous frequency or wavelength spectrum. However once you start working with solutions involving media, the discrete nature of a charge together with the de Broglie relations indicates that motions of two or more charges are reactively coupled in such a way to produce only quantized radiation.

I'm not sure if I correctly understand what you mean. Is the idea that any sinusoidal AC current in the coil would have a quantum ripple, proportional to the frequency of the applied signal? Would you (or anyone) have a reference for that?

 

[Q-reeus]

From the wave solutions there is apparently no stipulation enforcing a non-continuous frequency or wavelength spectrum. However once you start working with solutions involving media, the discrete nature of a charge together with the de Broglie relations indicates that motions of two or more charges are reactively coupled in such a way to produce only quantized radiation.

This implies quantization of radiation is purely due to quantization of source charge interaction energies. Not sure about that. Take a typical 1/2 lambda dipole antenna radiating at say 1 GHz. Assuming an aluminum antenna with aspect ratio (tube diameter over length) of say 20, tube thickness of say 1mm, we can find a rough estimate of the number of free conduction electrons to be ~ 4*10²⁴. Divide the Fermi energy of 11.6 eV by this number and we have something like 3*10_-23 eV per state (admittedly a crude figure that averages over the parabolic DOS for free-electron model). This is not quite a continuum of energy but too close to matter here. So if source charge energy quantization really governs field quantization, what prevents one from driving the antenna at an rms current so low photons of extremely small energy (<< E = hf) are emitted continuously? Conversely, if the field is inherently quantized as per E = hf, we might expect a photon emission only once every so many years on average. Crazy probability stuff but at least orthodox. Actually I would expect no emission at all unless the rms energy in the antenna current was at minimum comparable to that of E = hf. Don't believe in the notion of 'borrowed' energy.

 

[PhilDSP]

As I wrote that I was also thinking of two things. I believe this relates to your question Harald and to what Q-reeus brought up. It's known (within Plasma Physics) that the de Broglie relation "bottoms out" to phrase it simply. It's linear across most of its range but at very low frequencies it curves and becomes asymptotic to a specific low frequency for each particular type of particle.

The reason that happens is because conduction current gradually increases in proportion to displacement current as the momentum of the particle decreases. At a certain point the displacement current will become zero. At that point there is no radiation associated with the motion of the particle. (And therefore no photon is created)

I believe the radio frequencies might be below that frequency for electrons.

That is of course a little confusing because radio waves are self-propagating. So we might guess that radio waves are caused by electrons bound to a nucleus rather than single free electrons. Or I may be mistaken about the radio frequency being below the cutoff frequency.

The other thing I was thinking about was (but haven't had the time to really think about or look into) is whether Cherenkov radiation is considered quantized in the usual sense.

As a reference "Quantum Theory" by David Bohm explains how de Broglie theory is incorporated with atomic models and subsequently explains what restrictions on emission exist.

 

[Q-reeus]

As I wrote that I was also thinking of two things. I believe this relates to your question Harald and to what Q-reeus brought up. It's known (within Plasma Physics) that the de Broglie relation "bottoms out" to phrase it simply. It's linear across most of its range but at very low frequencies it curves and becomes asymtotic to a specific low frequency for each particular type of particle.
The reason that happens is because conduction current gradually increases in proportion to displacement current as the momentum of the particle decreases. At a certain point the displacement current will become zero. At that point there is no radiation associated with the motion of the particle. (And therefore no photon is created)...

Interesting indeed, but this 'bottoming out' would only apply to charged species within plasma environment? Also, I assume you meant to say "At a certain point the net current will become zero.", as displacement current (of an oscillating charge distribution in vacuo) is only zero at zero frequency or amplitude.

The other thing I was thinking about was (but haven't had the time to really think about or look into) is whether Cherenkov radiation is considered quantized in the usual sense.

Had the same thought on that one - there are no quantized energy levels and the spectrum at least is known to be continuous. On the other hand there is known to be subtle but confirmed QED corrections to the spectral output of accelerator synchrotron radiation. An open question for me. Will try and hunt down material by Bohm!
EDIT: Oops - when I saw Cherenkov was thinking synchrotron. As Cherenkov is only manifest in material media, hard to see anything there but collective atomic emissions.

 

[f95toli]

Then, according to QM, what would physically cause the quantization in an LRC circuit? Or is this free to interpretation? Different from an atom, an LRC circuit does not seem to have fixed energy levels, it seems. It's even possible to emit frequencies with such a circuit that are not exactly resonance frequencies.

That is asking the wrong question. All forms of electromagnetic radiation is quantized, it is just that we only see the effects of these in carefully prepared experiments where we work with few or single photons. Note that it is possible to e.g. quantize the usual equations for microwave transmission lines.
Also, an LC resonator made from discrete elements does have discrete energy levels when operated at low enough temperatures, in the linear regime it is described using the usal equation for a quantum mechanical oscillator.
The reason the temperature matters is because unless the thermal energy is lower than hf (in real experiments we want to have kbT<<hf) the energy levels will be so smeared that the levels overlap. In practice this means that one has to operated the circuits at mK temperatures and microwave frequencies (usually a few GHz).

 

[PhilDSP]

Yes, I meant to say that the frequency stays at the single value at the cutoff point regardless of how much slower that particle travels under the cutoff point. So presumably there would be no quantization for any momentum changes below that point (for the slow moving electron). It could still interact with a different particle species to produce quantization.

 

[f95toli]

So if source charge energy quantization really governs field quantization, what prevents one from driving the antenna at an rms current so low photons of extremely small energy (<< E = hf) are emitted continuously? Conversely, if the field is inherently quantized as per E = hf, we might expect a photon emission only once every so many years on average.

if you drive it at low enough energy the distribution will be Poissionian (and the photons will of course have an energy hf), this is no different than experiments where heavily attenuated sources of light are used to create "few photon sources" (which BTW are not "true" single photons sources since they are not generating Fock states).

Another good example is the maser, the performance of masers is inherently limited by the fact that they are operated at quite low energies (- 90 dBm or so); at this power level (which is routinely used in commercial microwave equipment so it is no way extremely low) a large portion of the noise in the signal comes from shot-noise; this noise is due the "discrete nature" of the photons, analogues to shot noise in electrical circuits (this is why masers are bad short-time frequency references, but good at long times).

 

[Q-reeus]

...if you drive it at low enough energy the distribution will be Poissionian (and the photons will of course have an energy hf), this is no different than experiments where heavily attenuated sources of light are used to create "few photon sources"...

OK, but will any emission occur if source energy per cycle drops much below single photon energy (at a given frequency of operation)? I would imagine a reasonably sharp threshold akin to photoelectric effect.

Another good example is the maser, the performance of masers is inherently limited by the fact that they are operated at quite low energies (- 90 dBm or so); at this power level (which is routinely used in commercial microwave equipment so it is no way extremely low) a large portion of the noise in the signal comes from shot-noise; this noise is due the "discrete nature" of the photons...

Yes that is quite convincing. On the lighter side, I suppose you are aware of the stories (promoted chiefly by a certain Frenchman) claiming crop-circles are a product of the US and/or UK military using high powered 'death-ray' masers carried by high altitude balloons. Seems not all masers are born equal!

 

[_PJ_]

I think the answer lies at the heart of why Quantum Mechanics is so strange compared to classical.

Everything can be considered in either Quantum or Classical terms. However, depending on what you wish to measure, you might get ludicrous or inaccurate results.

according to QM, what would physically cause the quantization in an LRC circuit? Or is this free to interpretation? Different from an atom, an LRC circuit does not seem to have fixed energy levels, it seems.

Regardless of the energy levels of the circuit, electrons and photons when considered as quantum entities, DO only have discrete energies, defined by Planck's constant.
For a QM interpretation of the system, everything MUST be considered within the Quantum framework. This would therefore assume non-definite probabilities of uncertainty, superposition of states before and entanglement after interaction.

 

[harrylin]

As I wrote that I was also thinking of two things. I believe this relates to your question Harald and to what Q-reeus brought up. It's known (within Plasma Physics) that the de Broglie relation "bottoms out" to phrase it simply. It's linear across most of its range but at very low frequencies it curves and becomes asymptotic to a specific low frequency for each particular type of particle.

The reason that happens is because conduction current gradually increases in proportion to displacement current as the momentum of the particle decreases. At a certain point the displacement current will become zero. At that point there is no radiation associated with the motion of the particle. (And therefore no photon is created)

I believe the radio frequencies might be below that frequency for electrons.

That is of course a little confusing because radio waves are self-propagating. So we might guess that radio waves are caused by electrons bound to a nucleus rather than single free electrons. Or I may be mistaken about the radio frequency being below the cutoff frequency.

The other thing I was thinking about was (but haven't had the time to really think about or look into) is whether Cherenkov radiation is considered quantized in the usual sense.

As a reference "Quantum Theory" by David Bohm explains how de Broglie theory is incorporated with atomic models and subsequently explains what restrictions on emission exist.

Those are a lot of directions to look into... and I now realize that although I often heard "David Bohm", I never really looked at his theory!

@ Q-reeus, yes also the mechanism of synchrotron radiation seems to challenge the claim that all radiation is emitted in wave packets of energy E=hf.

 

[harrylin]

That is asking the wrong question. All forms of electromagnetic radiation is quantized, it is just that we only see the effects of these in carefully prepared experiments where we work with few or single photons.

The question is what evidence there is for such claims; I don't understand the value of begging the question.

Note that it is possible to e.g. quantize the usual equations for microwave transmission lines.
Also, an LC resonator made from discrete elements does have discrete energy levels when operated at low enough temperatures, in the linear regime it is described using the usal equation for a quantum mechanical oscillator.
The reason the temperature matters is because unless the thermal energy is lower than hf (in real experiments we want to have kbT<<hf) the energy levels will be so smeared that the levels overlap. In practice this means that one has to operated the circuits at mK temperatures and microwave frequencies (usually a few GHz).

Certainly you don't imply that the LC resonator of a radio station that is sending out at frequency f, sends out photons of E=hf as function of its temperature...

 

[harrylin]

Yes, I meant to say that the frequency stays at the single value at the cutoff point regardless of how much slower that particle travels under the cutoff point. So presumably there would be no quantization for any momentum changes below that point (for the slow moving electron). It could still interact with a different particle species to produce quantization.

Thanks for the clarification!
Apparently this question is still fully open for scientific investigation.

 

[harrylin]

I guess what op really want to ask is "Is all electromagnetic radiation discretized?". The modern usage of "quantization" usually refer to a set of procedures which transit a classical description to a quantum mechanical description. And discretization of energy levels in bound system is just one possible consequence of quantization.
Discretization of radiation refers to the discretized energy in a particular frequency, not that the whole frequency spectrum is discretized. So in LRC circuit the frequency spectrum is a continuum, but the energy for each frequency is not.

Thanks for the precision, I noticed that indeed some people misunderstood my question in the way that you indicated. Indeed, I meant with "quantized radiation" not that people describe it as discrete lumps but that the radiation occurs as discrete lumps. It may be possible to set up experiments to test that claim for true radio waves.

 

[PhilDSP]

To clarify the confusion regarding the hf cutoff frequency (my own): the cutoff frequency will be approached as the group velocity of the wave approaches zero. In other words the cutoff frequency is reached when the particle is stationary. In that case the conductance current is equal to the negative of the displacement current so that the net energy flow vanishes if the currents occupy the same region in space. Therefore no radiation occurs.

Those results are valid for any particle with mass and one charge in an environment with no heat and no magnetic field.

This actually reaches deep into Maxwell theory. The primary principle is that the medium is polarizable. That is, that the movement or displacement of a charge stresses the equilibrium of the medium causing the medium to issue a counter current in the opposite direction.

I'm currently writing a book that among other things re-examines the foundation of physics. It's very gratifying to be able to trace the chain of deductions from the beginning all of the way into the most sophisticated modern concepts. Ideas or observations will be gladly received!

 

[kof9595995]

Thanks for the precision, I noticed that indeed some people misunderstood my question in the way that you indicated. Indeed, I meant with "quantized radiation" not that people describe it as discrete lumps but that the radiation occurs as discrete lumps. It may be possible to set up experiments to test that claim for true radio waves.

Actually I don't know if the spectrum of LRC circuit is a continuum or not, but I'd like to emphasis that whether frequency is discretized or not doesn't matter, because that's not what we mean by "radiation is quantized".
If you want to ask whether frequency is discretized, then you are perfectly correct, i.e. it depends on the nature of the emission process, and you should investigate further about LRC emission.

 

[f95toli]

Certainly you don't imply that the LC resonator of a radio station that is sending out at frequency f, sends out photons of E=hf as function of its temperature...

No, what I meant was that if you make a resonator out of an inductor and an capacitor, it will only have discrete levels (=behave as a quantum harmonic oscillator) if the level spacing is larger than the thermal energy (otherwise the levels become smeared). In practice this means that the resonance frequency must be in the GHz range and temperature in the mK range (you also need its quality factor to relatively large, meaning R should be small)

Again, this is not "in theory". There are plenty of experiments where circuits like these are made to behave "quantum mechanically".