Is it possible to get steady photon?

Question

When light travels from low density medium to high density medium it's speed decreases according to refractive index of medium. And light is made of moving photons . That means photons are slow downed. So it should be possible to reduce the speed of light to zero and we can get a steady photon.

Answer 1

So it should be possible to reduce the speed of light to zero and we can get a steady photon

No, photons always move with velocity c, whether in vacuum or crossing a transparent medium

Light is not made up by an addition of photons, the way a kilo of sugar is made up of sugar particles. Light is a superposition of photons in the complex quantum mechanical space. Zillions of photons make up the classical electromagnetic wave, that is slowed within a transparent medium. The individual photons follow a quantum mechanical solution "photon scattering off transparent lattice" . The superposition of those solutions in the lattice make up the classical beam.

One can say that the individual photons are not collinear with the classical ray direction, but can travel in longer paths in the lattice, building up by superposition the slower emergent beam of light in the lattice.

Answer 2

Yes there is are ways to slow down light. It falls under the broader topic of slow light and a particular technology that one may consider as an example is electrically induced transparency (EIT). One can consider this as a slow down of the photons in the sense of an effective medium.

At the microscopic level, the photons propagating through a dielectric material would be traveling from molecule to molecule, being absorbed and re-emitted all the time. However, the macroscopic effect of this rather complicated process is that the light propagates through the medium in a normal linear fashion, but slowed down by a factor given by the refractive index. One can therefore treat each photon as if it is doing the same: propagating through a linear medium at a slowed down speed.

These days there are special materials that can be manipulated by external electric fields to slow down light by EIT. In such a case, it become transparent or opaque depending on the external control. The microscopic process is still very much a quantum process that involves the interaction of photons with the atoms/molecules, but the macroscopic effect is to slow down the light (photon) so much that it effectly stops. Such materials are being considered as possible quantum memories in that they can store the quantum state of photons for some period before being released again by being allowed to propagate further.

Now, just to clear up some misconceptions, light can be expressed as quantum states in various ways depending on the nature of the light. If the light source is a laser, its quantum state is very well represented by what we call a coherent state, which is a superposition of all the different number states (Fock states). A number state has a fixed number of photons, but because the coherent state is a superposition of all the number states it does not have a well-defined number of photons. Note however that a superposition of several different single-photon states is still a single-photon states. One cannot produce multiphoton states from single photon states through a superposition. To produce a multiphoton states from single-photon states one needs to form a tensor product of the single-photon states.

Another thing, regardless of how many photons there are in a particular state, the propagation of these photons are described by the wave function of the quantum state. It is the wave function that obeys the dynamical equations. So the probability to detect a particular photon at a particular point in space and time is given by the modulus square of the wave function, which is governed by the dynamical equations.

Answer 3

There are a few things that we should clarify:

1. the EM wave always travels with speed c in vacuum when measured locally

2. photons always travel in vacuum with speed c when measured locally

3. classically the Em wave is built up by a herd of photons

4. it is the EM wavefront that slows down in media

So in your case, when light enters a media denser then vacuum, the wavefront slows down.

But the individual photons in the media always travel in the vacuum between the atoms, and these photons always travel with speed c.

So why does the wavefront slow down if the individual photons still travel at speed c? What happens is that the individual photons interact with the media's atoms and molecules, and this interaction takes time. So although the individual photons will always travel with speed c between the atoms (in vacuum), they will as a herd slow down, the wavefront will slow down.

Although the classical EM wave is built up by a herd of photons, you need QM to understand what happens at the micro level to understand why the wavefront slows down.

To understand it, let's take how you calculate the speed of light in glass. You take the time that is spent between when the wavefront enters the glass and when the wavefront exits the glass. You divide the distance (straight path) through the glass by this time. What you come up with is that the time needed for the wavefront to pass through the glass is more then what a single photon would need to pass through vacuum (in a straight path).

Now the wavefront needs more time. Why? Because as per QM, the individual photons are interacting with the media's atoms and molecules. This interaction will cause them to take path's that are longer (then the straight path). You can call this a phase shift, and because of this, the individual photons will need more time to pass through the glass.

Though, the individual photons will still travel at speed c between the atoms (in vacuum), but since the photons' path through the entire glass will be longer (then the straight path), the wavefront will slow down.

There is a very good example to see how this works, though it is not exactly the same thing. When a photon makes its way through the Sun, from the core to the surface, it will go along a not straight path, because it interacts with the dense gas in the Sun. The gas in the Sun is so dense, that it takes for the photon to pass through the gas inside the sun 100000 years to get to the surface. In this case you could even say that the speed of sound is faster then the speed of these photons in the Sun. Of course this would be a little misleading, since we are talking about individual photons in the Sun's core making their way to the surface. But this is a good example to see how a single photon's path might be altered by interacting with the dense media.

So in the case of glass the media is not so dense but still the individual photons are making their way through the glass and take longer path's. This will cause the wavefront to seem to slow down compared to the speed c.

So when you measure the speed of the EM wave passing through the glass, the distance will be the straight path, and the time will be the time needed between when the wavefront enters and exits the media. This time will be longer then in vacuum, because the time corresponds to individual photon's not straight path's. So you are dividing a straight path with a longer time (then what would be needed for the straight path) and you get a speed slower then c.

And to answer the question, there is no way to slow down the photons themselves on a straight path as they move from atom to atom, between the atoms they move with speed c (in vacuum). Even in a dense matter like the gas of the Sun they move at speed c between atoms (in vacuum) and the only thing that will seem to be slower is altogether through the dense gas if you calculate their wavefront speed (which is a little misleading here) but even that is always above 0 speed. So you can never slow down photons in vacuum. What you can say is that the wavefront seems to move slower in dense media.