Inversion-symmetry breaking in spin patterns by a weak magnetic field

Abstract

Laser-driven cold atoms near a plane retroreflecting mirror exhibit self-organization above a pump threshold. We analyze the properties of self-organized spin patterns in the ground state of cold rubidium atoms. Antiferromagnetic patterns in zero magnetic field give way to ferrimagnetic patterns if a small longitudinal field is applied. We demonstrate how the experimental system can be modeled as spin-1 atoms diffractively coupled by the light reflected by the mirror. The roles of both dipolar and quadrupolar magnetization components in determining the threshold and symmetry variations with a weak longitudinal magnetic field are examined. Although the magnetic structures correspond dominantly to a lattice of magnetic dipoles, the symmetry breaking to ferrimagnetic structures in a finite field is mediated by the coupling to a homogenous quadrupole (alignment), which is not possible in a spin-1/2 system. Our study provides a basis for further exploration of instabilities in driven multilevel systems with feedback.

Self-Organization in Cold Atoms Mediated by Diffractive Coupling

“…The difference can be easily explained by stray magnetic fields. The optical density in the Strathclyde experiment is measured to be b 0 = 27, giving nominally |φ lin | = 0.96 at δ = −7Γ, but we find a more robust agreement between theory and experiment assuming b 0 = 30 [50], giving |φ lin | ≈ 1.1. Thresholds predicted are on the order of a few mW/cm 2 depending on exact parameters.…”

“…Structures due to the electronic 2-level nonlinearity were identified in [48]. Spontaneous magnetic ordering of dipolar and quadrupolar nature was demonstrated in [49,50] and [51], respectively, the latter providing also a first demonstration of a spontaneously structured atomic coherence.…”

“…If a magnetic field of the order of a few tens of mG (the exact value depends on other parameters as intensity), the squares give way to hexagonal patterns [49][50][51]. For B z > 0, these are hexagonally coordinated peaks (like the ones displayed in Figure 3) for the σ + component and the orientation w and honeycombs in the σ − component.…”

“…Due to the counterpropagation, there is a longitudinal grating at wavelength scale formed in the cloud. We assume that the residual atomic motion, although small, is sufficient to wash out the effects of this grating and to add the forward and backward intensity to calculate P. With this assumption, a good qualitative and even semi-quantitative agreement between experiment and theory has been obtained for optomechanical and optical pumping nonlinearities [44,49,50]. (For the electronic nonlinearity, this assumption is questionable and the grating has been included in the treatment in [55], but it is instructive and qualitatively correct to develop the theory without the grating.)…”

Inversion Symmetry Breaking in Cold Atomic Spin Patterns

“…Our experimentally measured variation of pattern thresholds and symmetries with B z is compared to the results of both numerical calculations in the full model and analytical calculations in a reduced model allowing for perturbations only in the spin dipole [2]. The reduced model shows that inversion symmetry of the system is broken at small |B z | by nonlinear Faraday rotation caused by coupling of the homogeneous parts of light induced quantum coherence and spin dipole.…”