Coherent states versus number (harmonic oscillator) states
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===The most wave-like state of a cavity is called a coherent state === | ===The most wave-like state of a cavity is called a coherent state === | ||
| − | The harmonic oscillator states we wrote <math>|n \rangle</math>. | + | # The harmonic oscillator states we wrote <math>|n \rangle</math>. |
| − | These states also arise when quantizing fields such as the electric field in a cavity and the | + | # These 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 | 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. | quanta in the cavity or solid. 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 | + | # 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 | 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 | 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. | some operators <math> \times a </math> where <math> a \ </math> is the destruction (lowering) operator. | ||
| − | This means that a quantum state that is "like a classical state" (whatever that means) should be an | + | # 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 | 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. | by Roy Glauber, who was one of three people to get the Nobel Prize in Physics in 2005. | ||
Revision as of 14:43, 1 May 2006
The most wave-like state of a cavity is called a coherent state
- The harmonic oscillator states we wrote
.
- These 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. 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):
