# Displacement in phase space

1. Nov 23, 2014

### naima

Hi PF

I read the definition of the displacement operator:
$D(\lambda) = e^{\lambda a^\dagger - \lambda ^* a}$
but i did not find how this operator can be implemented say in a cavity with a photonic state inside.
Could you give me links?
thanks.

2. Nov 23, 2014

### vanhees71

Have a look at this:

http://en.wikipedia.org/wiki/Coherent_states

Note that the application of this "displacement operator" to the vacuum does not create a photon Fock state (i.e., a state with definite photon number) but a coherent state!

3. Nov 23, 2014

### naima

Danke Vanhees71
I read in this wiki
""...letting the unitary displacement operator D(α) operate..."
The problem is not to let it operate. The problem is to prepare a device which will enable an experimentalist to displace a sate by $\alpha$
I read the external links at the end of the article but i did not find any device's
description. I think that it needs pulses but with which interaction?

Last edited: Nov 23, 2014
4. Nov 24, 2014

### vanhees71

I only know that lasers produce coherent states. How you prepare a given coherent state in detail, I cannot say :-(.

5. Nov 24, 2014

### strangerep

Mandel & Wolf (sect. 11.13, p568) give a derivation of the field produced by a time-dependent classical current, and show (iiuc) that it's a coherent state. As the current changes, the state changes continuously, but it's always a coherent state. I.e., changing the current is equivalent (in that case) to acting with a $D(\alpha)$--like operator.

Last edited: Nov 24, 2014
6. Nov 25, 2014

### naima

7. Nov 25, 2014

### naima

Suppose that, using a pulse during t, i displace the vacuum to a gaussian centered around a point P in the phase space. This point will rotate in this plane. At a given moment the gaussian will be centerd around -P. If i apply the same pulse will the atom return to its vacuum?
If yes how can we know when we have to light the atom ?

Edit
As i have many copies of the ground state |g> i can vary the $\Delta t$ between two pulses and for which it returms to |g> and know the rotation period.

Last edited: Nov 25, 2014