The Effect of Time-Varying Electric Fields on a 2-Level Ion System

[Malamala]

Hello! If I have an ion which can be treated as a 2 level system, in a time varying electric field (the variation of the field doesn't need to be on or close to resonance, but for simplicity we can assume it is an oscillatory field) can I simply separate the problem into a center of mass motion and an internal 2 level system motion. Basically the ion would move up and down under the influence of the field, but in the ion's rest frame we would just have a normal time varying field, as if the ion wouldn't move at all. Would this work or am I missing some coupling between the internal and external degrees of freedom? Thank you!

 

[DrClaude]

You mean like in a Paul trap?

 

[LuisP]

Yes, it would work as long as the electric field is homogenous, meaning, the value and direction of the electric field is the same everywhere where the ion is embedded. If there is inhomogeneity, then electron cloud and ion core may be pulled differently.
If electric field is very strong, then you may have other effects.

 

[Malamala]

Yes, it would work as long as the electric field is homogenous, meaning, the value and direction of the electric field is the same everywhere where the ion is embedded. If there is inhomogeneity, then electron cloud and ion core may be pulled differently.
If electric field is very strong, then you may have other effects.

@DrClaude yes. My question was in general but indeed that would be a physical implementations of the system.

@LuisP I assume you mean homogenous in space, as in for a given moment in time, the field in a region completely enclosing the ion is constant in space? What would be the requirements for this? Is a light wavelength much bigger than the atomic size enough?

 

[DrClaude]

@DrClaude yes. My question was in general but indeed that would be a physical implementations of the system.

I was asking because the answer of course depends on the strength of the field. There is of course the Stark effect, but for a typical Paul trap it can be neglected in most cases (an exception might be if you are using the ion as an atomic clock, where even small effects must be accounted for).

@LuisP I assume you mean homogenous in space, as in for a given moment in time, the field in a region completely enclosing the ion is constant in space? What would be the requirements for this? Is a light wavelength much bigger than the atomic size enough?

Are you talking about electric fields (as mentioned in the OP) or electromagnetic fields? These are different beasts. (To be clear: an electric field is what is created by two charged electrodes, while people usually use "electromagnetic field" to talk about electromagnetic radiation.)

 

[Malamala]

I was asking because the answer of course depends on the strength of the field. There is of course the Stark effect, but for a typical Paul trap it can be neglected in most cases (an exception might be if you are using the ion as an atomic clock, where even small effects must be accounted for).
Are you talking about electric fields (as mentioned in the OP) or electromagnetic fields? These are different beasts. (To be clear: an electric field is what is created by two charged electrodes, while people usually use "electromagnetic field" to talk about electromagnetic radiation.)

Well in the original post I mentioned an oscillatory electric field (like sinusoidal). You can't have this without a sinusoidal magnetic field being created, right? So the ion will see both anyway. What I had in mind specifically was something along the line of having 2 plates to which I apply a time varying field (with a phase difference of $\pi$ between them) at a given frequency (on the order of kHz). So basically it is like an RF field applied to the ion. I am not sure I totally understand the difference you make between the 2 cases.