Undergrad Polarization in Rabi oscillations

[Malamala]

Hello! I have 2 levels, with quantum numbers $(J=0,m_J=0)$ and $(J=1,m_J=1)$ and I am a bit confused about whether I can drive Rabi oscillations between them with a fixed laser polarization. Assuming I start in the $(J=0,m_J=0)$, I would need right-circularly polarized light to drive that transition, however once the electron gets to the $(J=1,m_J=1)$ (basically after a $\pi$-pulse), will the electron come back to the initial state if I keep applying the right-circularly polarized light? Given that this situation is equivalent to starting in $(J=1,m_J=1)$, I would need a left-circularly polarized light to drive this transition. So will the electron just stay in $(J=1,m_J=1)$ forever (ignoring other states and lifetimes) unless I change the polarization? Thank you!

 

[Twigg]

So will the electron just stay in (J=1,mJ=1) forever (ignoring other states and lifetimes) unless I change the polarization?

Yep. If you ignore spontaneous emission (and other states), then the atom will stay in the J=0, mJ=0 state forever.

 

[Malamala]

Yep. If you ignore spontaneous emission (and other states), then the atom will stay in the J=0, mJ=0 state forever.

Thank you! I assume you meant $J=1, m_J=1$, right? So the only way to get Rabi oscillations (in an ideal 2 levels system) is to use a linearly polarized light, such that the transition can happen both ways?

 

[DrClaude]

Hello! I have 2 levels, with quantum numbers $(J=0,m_J=0)$ and $(J=1,m_J=1)$ and I am a bit confused about whether I can drive Rabi oscillations between them with a fixed laser polarization. Assuming I start in the $(J=0,m_J=0)$, I would need right-circularly polarized light to drive that transition, however once the electron gets to the $(J=1,m_J=1)$ (basically after a $\pi$-pulse), will the electron come back to the initial state if I keep applying the right-circularly polarized light? Given that this situation is equivalent to starting in $(J=1,m_J=1)$, I would need a left-circularly polarized light to drive this transition. So will the electron just stay in $(J=1,m_J=1)$ forever (ignoring other states and lifetimes) unless I change the polarization? Thank you!

No, it a single polarization of light that couples the two states. the $(J=1,m_J=1) \rightarrow (J=0,m_J=0)$ transition is stimulated emission, not absorption.

 

[Malamala]

No, it a single polarization of light that couples the two states. the $(J=1,m_J=1) \rightarrow (J=0,m_J=0)$ transition is stimulated emission, not absorption.

But my question is about Rabi oscillations. Don't Rabi oscillations involve both stimulated transition and absorption? As far as I can see, to go from $(J=0,m_J=0)$ to $(J=1,m_J=1)$ you need the opposite polarization relative to going from $(J=1,m_J=1)$ to $(J=0,m_J=0)$. So it seems like you can't have a full, $2\pi$ Rabi oscillation between these 2 levels if your polarization is either left or right handed, as you'd get stuck in one of the 2 levels after a $\pi$ pulse.

 

[DrClaude]

$\Delta m= +1$ on absorption requires $\sigma^+$ light while $\Delta m= -1$ on emission is $\sigma^+$ light. It is the same polarization in both cases.

By the way, you should talk about $\sigma^+$ and $\sigma^-$ polarizations, not left and right handed, as the latter depend on the direction of propagation of the light.