I am new to the Optical Bloch Equation (OBE) and because of my background in NMR, I found the approach used by Erwin Hahn in the attached paper very fascinating and easy to follow. It has helped with understanding concepts used in
(1) the Springer Handbooks of Atomic, Molecular, and Optical Physics and
(2) the Atom-Photon Interactions by Claude Cohen-Tannoudji and Gilbert Grynberg.
However, I found out (possibly due to my limited knowledge in this area) that contemporary OBEs are slightly different (in terms of terminology) from OBEs as presented by E.L. Hahn.
Therefore, I would like experts to kindly explain some terms in the attached paper. These terms are 'po' (equivalent to NMR magnetic moment on page 24); the term equivalent to gyromagnetic ratio (on page 24) which is equal to 2po/Planck constant (which also appears before the applied field term in the last equation on page 26); and 'N' and 'g' (in the integrals 2a and 2b on page 26).
I want to know what these four terms stand for in optics and how they can be measured in the laboratory.
I understand that 'N(po)u' is a component of the polarization in the system where 'u' is the Bloch vector in the x direction.
Hi Michael
The answers to your questions are
(1) p0 is simply the electric dipole moment (fundamental charge times the expectation value of the position vector r between the two states involved in the transition projected along the incident electric field direction)
(2) the equivalent of the gyromagnetic ratio (p0/planck constant) doesn't really have a strong physical meaning as far as know. The gyromagnetic ratio is the ratio of the magnetic moment to the angular momentum, the most similar ratio in an optical transition would be the ratio of the electric dipole moment to the fundamental unit of angular momentum, plancks constant.
(3) N is just the number of atoms/unit volume
(4) g represents the lineshape function - effectively the probability per unit frequency that a photon of frequency detuned from line center (omega0) by an amount deltaomega0 will interact with the atom to cause a transition.
Hope this helps
Michael
Prof. Belsley,
I would be very grateful if you could kindly explain how g would look like according to the Optical Bloch Differential equation just before equation 2a (in terms of T1 and T2 times) for:
1. Lorentzian lineshape
2. Maxwellian lineshape
Thanks!
Dear Michael
The u and v terms in these equations represent the in phase and in quadrature components of the induced polarization (or coherences in the language of density matrices).
If I am interpreting what is written correctly the g function in the integral is there to take into account inhomogeneous broadening effects, not homogeneous broadening like that due to lifetime (T1) or collisional dephasing (T2*). If only these were present than no integral would be needed.
Perhaps the most common example is of inhomogeneous broadening is Doppler broadening due to the Maxwell_Boltzmann distribution of velocities this goes like exp(-mc^2*(omega-omega0)^2/2kT*omega0^2) with a normalization constant that I can never remember. Localized crystal fields in solids can give rise to similar effects.
The T1 and T2 times are usually put in by hand to describe the decay of populations (-w/T1) and the coherences (-u/T2 and -v/T2) respectively as in the equations at the top of page 26.
Best regards
Michael
Thank you so much Prof. Belsley. I particularly enjoyed the last two paragraph of your response. Thanks!
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