Polarized Atoms Visualized by Multipole Moments  The polarization of an ensemble of atoms with angular momentum  is described by its density matrix  that has  elements. The state of polarization can be represented by a probability surface that represents the probability of finding the ensemble in the stretched state  when the quantization axis is oriented along ( ,  ). where the  are irreducible tensor operators with rank  and  . The  , called multipole moments or state multipoles, transform under rotations as the spherical harmonics  The moments  are called longitudinal moments, while the moments  are called transverse moments or coherences. An ensemble of particles with spin  can have multipole moments of rank  . The longitudinal moments can be expressed in terms of the populations  of particles in the magnetic sublevel  and conversely the sublevel populations depend on the state multipole moments according to This Demonstration visualizes the probability surfaces of ensembles with spin  that have a pure longitudinal multipole moment  in addition to the (trivial) monopole moment of value  . You can vary the value of  between its extreme values, and the corresponding populations of the sublevel populations are shown as vertical bars.   "Polarized Atoms Visualized by Multipole Moments" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/PolarizedAtomsVisualizedByMultipoleMoments/ Contributed by: Gianni Di Domenico (Université de Neuchâtel) and Antoine Weis (Université de Fribourg) |
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