Application of projection techniques to the optical Bloch vector equation

Authors

  • Edgardo R. Gutierrez Jr. ⋅ PH National Institute of Physics, University of the Philippines Diliman and World Center for Fluid Dynamics, University of the Philippines Los Baños

Abstract

An exact formal solution to the problem of the two level atom under an arbitrarily time- dependent field was recently proposed by Muriel using the Method of Iterated Projections (MIP). The starting equation was the quantum Liouville equation for the density matrix operator:
iħ∂ρ/∂t = [H,ρ],
where
H = H0 + Hint = ħ[(ωg + ωe0 − (ωg − ωez]/2 − pE(t)σx.
By defining the following
sx = ρ12 + ρ21,
sy = i(ρ12 − ρ21),
sz = ρ11 − ρ22,
one may arrive at the optical Bloch vector equation
ds/dt = Ω x s,
where s = (sx, sy, sz) and the torque vector Ω = (Ωx, Ωy, Ωz) with
Ωx(t) = −2pE(t)/ħ,
Ωy = 0,
Ωz = ω = ωe − ωg.

In this paper, we show the consistency of the proposed solution by using the same method (MIP) to the Bloch equation.

Downloads

Published

1995-10-21

How to Cite

[1]
ER Gutierrez, Application of projection techniques to the optical Bloch vector equation, Proceedings of the Samahang Pisika ng Pilipinas 13, SPP-1995-TP-01 (1995). URL: https://proceedings.spp-online.org/article/view/SPP-1995-TP-01.