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Journal of Optics B Quantum and Semiclassical Optics

Magnetic field control over microscopic symmetry properties of an optical pattern-forming system: experiment

Andreas Aumann, E. Große Westhoff, T. Ackemann, Wulfhard K. Lange

Published Jun 1, 2000• 8 citations
Publisher

Abstract

We study the selection between hexagonal and square polarization patterns in a sodium vapour cell with optical feedback provided by a single mirror. Scanning an external magnetic field, a transition sequence from squares via negative hexagons, squares, and positive hexagons again to squares is observed close to the instability onset. Well above threshold the hexagons give way to squares in a secondary bifurcation. These observations demonstrate how the macroscopic symmetries of optical patterns can be controlled by manipulating the microscopic symmetries of the light-matter interaction. The key to this control is the vectorial degrees of freedom of the optical pattern-forming system.

DOI
10.1088/1464-4266/2/3/332

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We study the selection between hexagonal and square polarization patterns in a sodium vapour cell with optical feedback provided by a single mirror. Scanning an external magnetic field, a transition sequence from squares via negative hexagons, squares, and positive hexagons again to squares is observed close to the instability onset. Well above threshold the hexagons give way to squares in a secondary bifurcation. These observations demonstrate how the macroscopic symmetries of optical patterns can be controlled by manipulating the microscopic symmetries of the light-matter interaction. The key to this control is the vectorial degrees of freedom of the optical pattern-forming system.
The occurrence of polarization instabilities in alkaline vapours and their coupling with spatial degrees of freedom are considered. We discuss experiments in which a laser beam is transmitted through a vapour cell without external feedback or with feedback by a single mirror. In both cases a lateral separation of the light field into domains of orthogonal circular polarization is found. Without feedback, relatively simple structures like rings or two spots are obtained. With feedback, more complicated polarization patterns result from spontaneous symmetry breaking. We emphasize the crucial role of the polarization ellipticity of the input beam. Changing this control parameter we observe a transition from positive to negative hexagons in one of the circular polarization components, while simultaneously the opposite transition occurs in the other one. The transition is mediated by square patterns occurring for linear input polarization. This metamorphosis is governed by symmetry principles and therefore provides an example of the ease of influencing the symmetry properties of systems consisting of multilevel atoms interacting with a vector light field.
Laser driven cold atoms in front of a retro-reflecting mirror exhibit self-organization above pump threshold. It was recently demonstrated how this system can be used to mimic a transverse lattice of interacting spins. The spontaneously formed lattice breaks both translational and rotational symmetries of the initial homogeneous spin state. By applying a constant longitudinal magnetic field of |Bz| ~ 100 mG a switching between antiferromagnetic square and ferri-magnetic hexagonal pattern ordering can be induced. We study the coupling between this magnetic field and modulations in the atomic magnetization.
The use of polarization degrees of freedom in optimizing the conditions for optical pattern formation is investigated by discussing the particular example of single-mirror feedback systems. It is demonstrated that in a quasi-scalar saturable medium pattern formation may be completely suppressed by the interplay of saturation and diffusion. This effect takes place for the optical pumping nonlinearity between Zeeman ground states in alkaline vapour cells. It is shown that these limitations can be circumvented by introducing additional polarization components either in the input beam or in the feedback beam. The latter is achieved by introducing polarization-changing elements such as a quarter-wave plate in the feedback loop. In the optimized scheme, pattern formation is obtained with rather low thresholds. Thus, investigations with a rather high aspect ratio and far beyond threshold become feasible.
It is shown that a simple system without a cavity exhibits optical bistability with no hysteresis but with symmetry-breaking or pitchfork bifurcation. The optical system is composed of a cell containing atoms with spin in the ground state, a $\frac{\ensuremath{\lambda}}{8}$ plate and a mirror, and an incident light beam linearly polarized and nearly resonant with the atomic absorption line. The system has a positive-feedback loop for the rotation of polarization through competitive optical pumping by ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ circularly polarized components. When the intensity of the incident light exceeds a critical value, symmetry breaking occurs and its polarization is subject to rotation in the clockwise or anticlockwise sense. Correspondingly, atomic spin polarization is produced spontaneously in a direction parallel or antiparallel to the incident beam. This new type of optical bistability is found to be explained well in context with the cusp catastrophe, as well as the ordinary one with hysteresis. It is also found that, in the presence of a transverse magnetic field, self-sustained spin precession occurs, which results in the steady-state modulation of the light polarization at about the Larmor frequency. Experimental evidence of the symmetry breaking and pitchfork bifurcation is obtained by using sodium vapor.
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.