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When light is emitted (or received) one photon at a time, what is the duration of each pulse? Is it related to the wavelength? Is it possible to create a laser pulse (or a radio wave) shorter than the wavelength (period of oscillations)?

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This depends on the light source, obviously - some sources produce longer pulses and other sources produce shorter pulses. However, the general rule is that the pulse duration is limited not by the wavelength but by the bandwidth of the pulse, that is, the lenfth $\Delta \omega$ of the interval of frequencies that contribute significantly to the pulse's spectrum. Generally speaking, the pulse duration $\Delta \tau$ is constrained by the bandwidth via $$ \Delta \tau \ \Delta \omega \gtrsim1, $$ which is essentially the Heisenberg uncertainty principle minus all the quantum mechanics.

In general, if you want to make a pulse with a single wavelength, then this requires you to have an infinitely long pulse. If you want to have a pulse that's shorter than the carrier wavelength $\omega_0$, then the bandwidth $\Delta \omega$ will be larger than $\omega_0$ and you will have a broad, multi-octave spectrum where your original $\omega_0$ might still be relevant to describe the finer details of the spectrum but will be essentially impossible to infer from a qualitative look at the latter.

For more details, see my answer to the closely related question How can a wavelength be defined for a laser where a photon's travel distance over a pulse duration is less than a wavelength?.

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  • $\begingroup$ Thank you for the answer and the link, +1 to both for being helpful and informative. Essentially you answer "no" to the second part of my question, because the broader spectrum would always contain wavelengths shorter than the pulse duration. Understood. My main question though is the duration of a single photon. The uncertainty principle gives one full oscillation for virtual photons (this has a deep physical meaning although unrelated here). Are you saying that the duration of a real photon is defined by the width of the spectral line (bandwidth) though the uncertainty principle? $\endgroup$ – safesphere Oct 7 '17 at 5:32
  • $\begingroup$ Photons are simply excitations of some underlying classical mode. That mode can be monochromatic but it doesn't need to be, and unless the mode lasts for infinite time (or longer than your experiment, in which case that idealization is appropriate) then the mode will be a wavepacket exactly as described here. The only difference between a classical pulse and a single-photon state is the counting statistics as brought out by e.g. Hong-Ou-Mandel interference. The same is true for a sequence of single-photon pulses, if that's what you meant by 'one photon at a time'. $\endgroup$ – Emilio Pisanty Oct 7 '17 at 9:49

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