# Polarization in Rabi oscillations

• I
• Malamala
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.f

#### 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!

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.

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?

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.

TSny
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.

##\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.

Malamala