Undergrad Zeeman effect sign of circular polarization

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The discussion focuses on the relationship between circular polarization and the Zeeman effect, specifically regarding the wavelengths of CCW and CW polarized emissions. It is clarified that when the magnetic field points toward the observer, CCW polarized emission corresponds to higher wavelengths than CW polarized emission. The energy levels are influenced by the uniform magnetic field, with the energy formula provided to explain the transitions. The transition associated with the σ+ line has a higher frequency due to a change in magnetic quantum number, while the σ- line corresponds to a lower frequency. Overall, the analysis confirms that the direction of the magnetic field significantly affects the observed polarization and energy levels.
Khashishi
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I'm unsure about the sign of the circular polarization.
Assume the magnetic field is pointed toward the observer.
In the Zeeman effect spectrum, is the CCW polarized emission at higher or lower wavelength than the CW polarized emission.

I think the CCW polarized emission is higher, and this is reversed if we change the direction of the magnetic field.
 
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In the picture below ##\sigma^-## line has higher energy than ##\sigma^+##.
 

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  • Zeeman effect longitudinal.png
    Zeeman effect longitudinal.png
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I don't see any indication of energy or direction of magnetic field in that picture.
 
Sorry I forgot to mention that the field is uniform pointing in the positive z direction.
The explanation about the energy is given in the text, there I took the snapshot of the picture only. In the presence of uniform magnetic field the energy level is given by
$$
E = E_n +\mu_B B_z(m_l+2m_s)
$$
The frequency corresponding to down-transition ##n\to n'## is then ##\nu = (E-E')/\hbar = \frac{E_n-E_{n'}}{\hbar} - \frac{\mu_B B_z}{\hbar}(m_{l'}-m_l) = \nu_{nn'} - \frac{\mu_B B_z}{\hbar}\Delta m_l## where ##E>E'## and ##\Delta m_l = m_{l'}-m_l##. The ##\sigma^+## line which is defined to be the transition with ##\Delta m_l = -1## hence has higher frequency than ##\sigma^-## line which is defined by ##\Delta m_l = 1##.
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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