Steady-state solutions for atomic multipole moments in an arbitrarily oriented static magnetic field

Abstract

We derive algebraic expressions for the atomic multipole moments m k,q (F ) describing the steady-state polarization of an atomic ensemble with angular momentum F in a static magnetic field of arbitrary direction and general multipole relaxation rates (k) q . The longitudinal moments m k,0 are given in terms of truncated continued fractions, while the transverse moments m k,q =0 , representing the ensemble coherence, are given by products of truncated continued fractions. The special case of isotropic relaxation leads to particularly simple and elegant expressions. Our results are relevant for all domains of physics that consider the evolution of a spin system interacting with vector-type perturbations.

Orientational effects on the amplitude and phase of polarimeter signals in double-resonance atomic magnetometry

“…Figure 2 shows the coordinate basis used to describe the laboratory frame. If the quantisation axis is parallel to the k -vector of the pump light, then non-absorbing atomic dark states are described by sums of atomic multipoles in which only m k,0 moments are non-zero, where k may be any positive integer for circularly-polarised light and k any even positive integer for linearly-polarised light [19]. Optical pumping dynamically couples multipole moments of any k, q to moments for which q = 0 in this basis.…”

Magneto-optic spectroscopy with linearly polarized modulated light: Theory and experiment

“…In the presence of a magnetic field and of relaxation mechanisms, the m k q satisfy the following equations [20]:…”

“…We use the multipole moments representation of the density matrix [21,22,30,31] operator because their transparent physical meaning allows for noticeable description of magneto-optical resonances (see for instance the discussion in [20] and references therein). Then, ρ reads…”

Dual-Axis Hanle Magnetometer Based on Atomic Alignment with a Single Optical Access

“…the 2 3 S 1 metastable level of 4 He, with F = 1 [25]). Its five components, which obey m (2) −q = (−1) q (m (2) q ) * , can be represented by the column matrix [23,24,26,27] M = (m (2) −2 , m (2) −1 , m (2) 0 , m (2) 1 , m (2) 2 ) t . This alignment is subject to several concurrent processes: preparation of the gas state by optical pumping, relaxation, evolution under the magnetic field, and optical measurement.…”