Coherent states versus number (harmonic oscillator) states
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* The harmonic oscillator states we wrote <math>|n \rangle</math>. | * The harmonic oscillator states we wrote <math>|n \rangle</math>. | ||
| − | * We saw that hese states also arise when quantizing fields such as the electric field in a cavity and the displacement field in an elastic solid. In that case <math>n \ </math> refers to the number of quanta in the cavity or solid. In that context these are also called number states or Fock states. | + | * We saw that hese states also arise when quantizing fields such as the electric field in a cavity and the displacement field in an elastic solid. In that case <math>n \ </math> refers to the number of quanta in the cavity or solid (we called these '''photons''' and '''phonons''', respectively). In that context these are also called number states or Fock states. |
* A quantum state of a cavity that is like a classical state as much as possible should have the property that when you make a measurement you don't change the state. Since nearly all measurements of light involve destroying photons (e.g., by creating current or heat), these measurements should have the general form some operators <math> \times a </math> where <math> a \ </math> is the destruction (lowering) operator. | * A quantum state of a cavity that is like a classical state as much as possible should have the property that when you make a measurement you don't change the state. Since nearly all measurements of light involve destroying photons (e.g., by creating current or heat), these measurements should have the general form some operators <math> \times a </math> where <math> a \ </math> is the destruction (lowering) operator. | ||
Revision as of 14:45, 1 May 2006
The most wave-like state of a cavity is called a coherent state
- The harmonic oscillator states we wrote
.
- We saw that hese states also arise when quantizing fields such as the electric field in a cavity and the displacement field in an elastic solid. In that case
refers to the number of quanta in the cavity or solid (we called these photons and phonons, respectively). In that context these are also called number states or Fock states.
- A quantum state of a cavity that is like a classical state as much as possible should have the property that when you make a measurement you don't change the state. Since nearly all measurements of light involve destroying photons (e.g., by creating current or heat), these measurements should have the general form some operators
where 
is the destruction (lowering) operator.
- This means that a quantum state that is "like a classical state" (whatever that means) should be an
eigenvector of the destruction operator. Such states are called coherent states and were introduced by Roy Glauber, who was one of three people to get the Nobel Prize in Physics in 2005.
Here are two views of coherent states (both images from [1] Wikipedia):
