Polarization in Rabi oscillations

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Discussion Overview

The discussion centers on the feasibility of driving Rabi oscillations between two quantum states characterized by the quantum numbers ##(J=0,m_J=0)## and ##(J=1,m_J=1)## using fixed laser polarization. Participants explore the implications of polarization on the transitions between these states and the conditions necessary for Rabi oscillations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether Rabi oscillations can occur with a fixed polarization, noting the need for right-circularly polarized light to drive the transition from ##(J=0,m_J=0)## to ##(J=1,m_J=1)## and the potential issue of remaining in the ##(J=1,m_J=1)## state if the polarization is not changed.
  • Another participant agrees that, ignoring spontaneous emission, the atom would remain in the ##(J=1,m_J=1)## state indefinitely if the polarization is not altered.
  • A subsequent post seeks clarification, suggesting that Rabi oscillations in an ideal two-level system may require linearly polarized light to facilitate transitions in both directions.
  • One participant asserts that a single polarization can couple the two states, emphasizing that the transition from ##(J=1,m_J=1)## to ##(J=0,m_J=0)## is a case of stimulated emission rather than absorption.
  • Another participant challenges the notion that Rabi oscillations involve both stimulated transitions and absorption, arguing that the necessity of opposite polarizations for the transitions suggests that full ##2\pi## Rabi oscillations may not be possible with a fixed polarization.
  • A technical clarification is provided regarding the use of ##\sigma^+## light for both absorption and emission, indicating that the same polarization is involved in both processes.
  • A note is made about the terminology, suggesting that ##\sigma^+## and ##\sigma^-## polarizations should be used instead of left and right-handed, as the latter depends on the light's propagation direction.

Areas of Agreement / Disagreement

Participants express differing views on the ability to achieve Rabi oscillations with fixed polarization, with some asserting it is not possible while others suggest that it may be feasible under certain conditions. The discussion remains unresolved regarding the implications of polarization on Rabi oscillations.

Contextual Notes

There are assumptions regarding the ideality of the two-level system and the neglect of spontaneous emission and other states, which may affect the conclusions drawn about the transitions and Rabi oscillations.

Malamala
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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!
 
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Malamala said:
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.
 
Twigg said:
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?
 
Malamala said:
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.
 
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DrClaude said:
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.
 
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