Saturday, September 01, 2007

What is laser light?

It is sometimes said that laser light consists of a bunch of photons in the same state. In fact, if a laser is treated as a 'coherent' state of a quantized harmonic oscillator, as is often the case, then this statement is quite false.

The popular science literature often claims that light consists of photons, but according to quantum field theory, photons are merely the excitation quanta of the quantized free electromagnetic field. There are states of the quantized free electromagnetic field in which there are definite numbers of photons present, but there are also states in which there is an indefinite number of photons. Such states can be described as non-particle states of the quantized free electromagnetic field.

Laser light of energy E=hν can be represented by a coherent state |α> of a quantized, frequency ν harmonic oscillator, as follows:



The states denoted as |n> are the energy eigenstates, state |n> consisting of n photons of energy E=hν.

The state |α> is coherent by virtue of the fact that it is an eigenstate of the annihilation operator â:



The eigenvalue is a complex number α = |α|e, and this complex number specifies the phase θ and amplitude |α| of the energy E=hν laser light. The states |n> are eigenstates of the number operator, hence these states are states in which a definite number of photons exist. However, the coherent state is clearly a superposition of these states, and is not itself an eigenstate of the number operator.

Hence, laser light is a non-particle state of the quantized free electromagnetic field.

3 comments:

Clare said...

Well, Gordon I tried reading this in my head and then out loud but the old brain just couldn't make any sense of it, I'm afraid.

I reckon I'm going to have to stick with the duality (?) of photons and waves. Thanks for having a go, though!

Gordon McCabe said...

Never read physics out loud, Clare: you risk summoning a demon from the n+1th dimension.

Arjen Dijksman said...

Hello Gordon,

I think it's of interest to keep both perspectives, photons and field. You might see it the other way round: the excitation quanta of the quantized electromagnetic are merely photons. States where there are an indefinite number of photons are described by the coherent state statistics |α>, meaning that the laser beam sends bunches of coherent photons. The number of photons in a single bunch obeys the statistics of the Glauber equation you gave: undetermined but Poisson-distributed around |α|.