Can We Construct a Detector for Precise Arrival Time of Monochromatic Photons?

[LarryS]

Suppose that I have a source of monochromatic light of which I can lower that intensity so that it emits one photon, say, per minute. At the other end of the beam I have some kind of photoelectric detector that records the arrival of each photon. It seems like one could construct a detector to record the arrival time of each photon. But the Heisenberg Uncertainty Principle says that because the light is monochromatic (one precise frequency) then we cannot pin down the photons in time. Does that mean that it is impossible to construct a detector to record the “precise” arrival time of monochromatic photons? Thank you in advance.

 

[DrChinese]

Suppose that I have a source of monochromatic light of which I can lower that intensity so that it emits one photon, say, per minute. At the other end of the beam I have some kind of photoelectric detector that records the arrival of each photon. It seems like one could construct a detector to record the arrival time of each photon. But the Heisenberg Uncertainty Principle says that because the light is monochromatic (one precise frequency) then we cannot pin down the photons in time. Does that mean that it is impossible to construct a detector to record the “precise” arrival time of monochromatic photons? Thank you in advance.

You can measure their arrival time to unlimited precision. The standard deviation of the sampled values for the time and the energy/frequency will still respect the HUP. In other words, as the precision of one increases the other decreases as you would expect. So you will see a spread of values. But it would be hard to derive much meaning from the measurement time values.

 

[LarryS]

You can measure their arrival time to unlimited precision. The standard deviation of the sampled values for the time and the energy/frequency will still respect the HUP. In other words, as the precision of one increases the other decreases as you would expect. So you will see a spread of values. But it would be hard to derive much meaning from the measurement time values.

Ok. That makes sense. But then what is the definition of a monochromatic laser beam of light if I can destroy the "monochromatic" property by simply measuring the photon arrival times to a high degree of accuracy?

 

[DrChinese]

Ok. That makes sense. But then what is the definition of a monochromatic laser beam of light if I can destroy the "monochromatic" property by simply measuring the photon arrival times to a high degree of accuracy?

You can measure any observable to the precision you desire. The question is what does that tell you? If you take light of precisely known wavelength, you will get a range of values in the time dimension. Those can be precisely measured (as precise as technology allows) yet there will be a distribution of values.

As to whether the light is truly monchromatic: sure it is as "real" as any observable.

 

[Cthugha]

Suppose that I have a source of monochromatic light of which I can lower that intensity so that it emits one photon, say, per minute.

First, lowering the amplitude does not change much. The state stays the same, just the amplitude is lowered.

It seems like one could construct a detector to record the arrival time of each photon.

Yes, you can. Avalanche photo diodes or streak cameras are used for that purpose.

But the Heisenberg Uncertainty Principle says that because the light is monochromatic (one precise frequency) then we cannot pin down the photons in time. Does that mean that it is impossible to construct a detector to record the “precise” arrival time of monochromatic photons? Thank you in advance.

As has been mentioned before the HUP does not say that. The power spectrum of a light source and the first order autocorrelation are Fourier transforms of each other. So a completely monochromatic light source (delta peak-like power spectrum) must have a coherence time approaching infinity. Coherence time is usually limited either by the characteristics of the light source (compare sunlight and laser light for example) or the duration of the emission. So truly monochromatic light must (theoretically) have completely constant intensity over time. So the HUP is about that timescale, but not about arrival times of individual photons. However one could argue that the detection of a photon changes and shortens the duration of the emission and must therefore also lead to deviations from true monochromaticity. If you look into a good book on quantum optics (for example Mandel/Wolf) you see that a monochromatic state does not have a well defined photon number and is an eigenstate of the photon destruction operator. So the detection of a photon does not change the state and will therefore of course also not lead to reduced coherence time or monochromaticity.

 

[Vanadium 50]

So a completely monochromatic light source (delta peak-like power spectrum) must have a coherence time approaching infinity.

Which is the key. To determine that a source is completely monochromatic, and not merely almost monochromatic takes infinite time.

 

[Bob S]

The lifetime of the "light" emission from the 14.4 KeV level in iron-57 (Meissner Effect source) is about 10^-7 sec, so the natural linewidth is about 10^-8 eV, or a fractional linewidth of about 10^-12. What is the smallest known fractional linewidth? How much better are lasers and masers?

 

[Vanadium 50]

Meissner effect source? Exclusion of flux from a superconductor? What are you talking about? Do you maybe mean the Mossbauer effect?

In any event, the question in the title is answered: it takes an infinite amount of time to determine if a source is truly monochromatic, so it's best to think of it as a limit or an approximation. Also, the question in the body of the message has been answered by Dr. Chinese.

 

[Bob S]

Meissner effect source? Exclusion of flux from a superconductor? What are you talking about? Do you maybe mean the Mossbauer effect?

In any event, the question in the title is answered: it takes an infinite amount of time to determine if a source is truly monochromatic, so it's best to think of it as a limit or an approximation. Also, the question in the body of the message has been answered by Dr. Chinese.

Thank you. I apologize for using "Meissner" when I meant "Mossbauer", as you surmised. Dr. Chinese is correct for an ideal monochromatic source. I was simply asking what the best monochromatic available "light" source was. I know that the stability of our NIST hyperfine structure frequency standards is better than 1 part in 10^15, but that does not speak to their monochromaticity (linewidth). Perhaps the monochromaticity of long lifetime metastable nuclear transitions like the 14.4 KeV transition in iron-57 is better. Maybe this question should be posted in a new thread.

 

[alexepascual]

Suppose that I have a source of monochromatic light of which I can lower that intensity so that it emits one photon, say, per minute. At the other end of the beam I have some kind of photoelectric detector that records the arrival of each photon. It seems like one could construct a detector to record the arrival time of each photon. But the Heisenberg Uncertainty Principle says that because the light is monochromatic (one precise frequency) then we cannot pin down the photons in time. Does that mean that it is impossible to construct a detector to record the “precise” arrival time of monochromatic photons? Thank you in advance.

In the case of photons, you can have different photons in the same state. Measuring the arrival time of individual photons will not change the wavelength of the beam. But if you use some kind of fast shutter to send a short pulse of light, as you make the pulse shorter, the range of wavelengths in the pulse will start getting wider. In order to have a laser that gives you a very sharp wavelength, you need in the first place to have a laser that does in the first place produce such a sharp wavelength, and in the second place, I think that you need to keep it on for some time so that the uncertainty in the time of emission gets larger. A short pulse won't do. Now with respect to absolutely monochromatic light, probably that does not exist.