Consider the emission of a photon when an atom decays from an excited state to its ground state. In most cases, this emitted photon is depicted as a small wave-packet being expelled by the atom in a well-defined direction. However, quantum optics tell us that photons are essentially associated with the amplitude of plane wave modes forming an electromagnetic field. Therefore, the small wave-packet representation seems rather suspicious…
What does the emitted photon really "look" like then ?
Assuming that the emitted photon has a corresponding wavelength much larger than the size of the atom, the atom should essentially behave as a small electric dipole. Therefore, considering lifetime broadening, it seems to me that the photon should propagate away from the atom as a pulsed dipolar emission. Is this correct ?
Best Answer
@G.Smith is absolutely right writing
So let me add my dime. Actually I wouldn't talk about what is really happening. Rather, about how quantum mechanics describes a photon. It has some peculiarities, deriving from its vanishing mass. But apart that, a photon has a state, which will be different according to how it was emitted, from where, and so on.
If we consider the usual case of an atom in an excited state which emits a photon by jumping to a lower energy state, most often it will be an electric dipole transition and the photon will have a state the kind @Andrew Steane depicted. What I want to emphasize is that in such state the photon has a momentum vector totally undetermined as to its direction, even though probability is not the same in all directions, being maximum in the equatorial plane and zero at the poles.
On the contrary momentum magnitude is very well defined, like energy (for a photon $E=cp$). Not exactly defined however. As already remarked photon state isn't a stationary one, but with a time dependence, say exponentially decaying. Translating into the frequency-energy domain, photon energy has a Lorentzian spread around an average value, generally small for atomic transitions.
But strange things may sometimes happen, e.g. quantum beats (see wikipedia article "quantum beats"). If the atom was preparared in a superposition of two nearby states, when it decays it emits a photon in a superposition of different energy eigenstates. This state exhibits an oscillating behaviour, revealed by an oscillating probability of detection at different times. (Of course this cant't be seen with a single atom. An ensemble of atoms must be prepared in the same state at the same time.)
So it is not a matter of tastes in describing a photon. It is that - like every quantum system - it can be revealed through different apparatuses, measuring different observables. E.g. if the detector is a CCD or the like, we will be measuring photon's position. If it's sent on a grating its wavenumber (i.e. its energy) is measured and so on. This is QM.