Abstract A cavity filled with a medium displaying electromagnetically induced transparency is shown to exhibit coexistence of complex transverse structures often leading to pattern competition. Because of multi-stability of the solutions, the asymptotic state in such a cavity crucially depends on the values of the control parameters and the initial conditions. The pattern competition can result in coexisting regions of pattern structures of different geometry separated by stable or metastable fronts. Here we propose a selection technique based on external periodic modulations for directing the system to a single pattern state of choice and thus removing the separation fronts. The control technique takes the system close to sub-sections in the phase space providing the operator with the choice of the final state from different multi-stable solutions. We extend the use of the technique to stationary or drifting structures composed of regions made of a single pattern state with different orientations. In this case the regularization to a pattern with a single orientation is associated with the removal of defects. The harmonic signal technique has not been used previously to control a spatio-temporal system where the multi-stability is due to the coupling of nonlinearity and diffraction.
Abstract A cavity filled with a medium displaying electromagnetically induced transparency is shown to exhibit coexistence of complex transverse structures often leading to pattern competition. Because of multi-stability of the solutions, the asymptotic state in such a cavity crucially depends on the values of the control parameters and the initial conditions. The pattern competition can result in coexisting regions of pattern structures of different geometry separated by stable or metastable fronts. Here we propose a selection technique based on external periodic modulations for directing the system to a single pattern state of choice and thus removing the separation fronts. The control technique takes the system close to sub-sections in the phase space providing the operator with the choice of the final state from different multi-stable solutions. We extend the use of the technique to stationary or drifting structures composed of regions made of a single pattern state with different orientations. In this case the regularization to a pattern with a single orientation is associated with the removal of defects. The harmonic signal technique has not been used previously to control a spatio-temporal system where the multi-stability is due to the coupling of nonlinearity and diffraction.
Spatially periodic and localized structures in the transverse plane of a medium displaying electromagnetically induced transparency in an optical cavity and under the action of two pumps are investigated. The system supports a multitude of different complex spatial structures depending on the chosen initial condition. We explore regimes of multistable patterns, filaments, stable defects, scrolling structures, nested patterns, fronts, and the spontaneous occurrence of multiple cavity solitons. To simulate realistic conditions of operation, we replace periodic boundary conditions with pumps of finite size. Many of the multistable features are recovered apart from the scrolling of patterns with defects.
We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.
Summary form only given. Stationary localized structures (LS) and localized patterns have been predicted in passive resonators in regimes where the homogeneous steady states exhibit a subcritical Turing (or modulational) instability. These solutions consist of bright or dark spots in the transverse profile of the intracavity field amplitude. They can be either spatially independent and randomly distributed or clusters forming well-defined spatial patterns in the transverse plane orthogonal to the propagation axis. We consider an optical cavity with plane mirrors filled with resonant two-level atoms and driven by a coherent plane-wave injected signal. We focus on the purely absorptive limit where the two-level atoms are in resonance with the injected field. In this system, two type of LS may be generated, depending on the magnitude of the critical wave number associated with the modulational instability: circular localized bright spots or a stationary localized single stripe. Both types of LS can form for the same value of parameters.
We investigate pattern formation in a finite chain of bosonic modes whose dynamics is governed by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. The model combines local parametric driving and nonlinear damping with nonlocal dissipative couplings between modes that work on different discrete spatial scales. In the classical limit, these mechanisms generate a reaction-diffusion-like dynamics, allowing the emergence of Turing-type instabilities. The key aspect of the analysis is the coexistence and competition of different unstable spatial modes. Depending on the range of parameters, the system may select different stationary nonuniform configurations, oscillatory wave-like states, or regimes in which multiple modes interact before a dominant pattern is established, thus providing a mechanism for pattern selection. We compare the deterministic bifurcation scenario, generated by a reaction-diffusion-like system derived from semiclassical drift dynamics, with the quantum dynamics, derived via the GKSL master equation, using phase-space methods and reduced Wigner functions. The results show how Turing instabilities, mode competition, and pattern selection can be extended to multimode open quantum systems, providing a bridge between nonlinear dynamical systems, dissipative quantum mechanics, and spatial self-organization.
Abstract We study electromagnetically induced transparency (EIT), which is affected by cavity optomechanics in different atomic configurations ( V and Λ ). The cavity mode is depicted as a probe field, and a classical driving field is applied to the atomic medium as the control laser in each system. Interaction between the cavity mode, atomic media and the oscillating mirror of the cavity can change the susceptibility of the atomic ensemble. Equations of motion demonstrate a system of nonlinear equations for each system. Nonlinearity of equations is a result of interaction between the cavity mode and atomic transitions. The equations are solved via a perturbation method. The results show two different aspects of atom-assisted optomechanics in V -type system: a common transparency window and an amplifying process in a transparency window that does not occur in the Λ configuration, notable as a considerable difference between the proposed systems. It is shown that classical field detuning leads to different changes in the susceptibility of both systems; other values of cavity detuning, except in the resonant case, can guarantee the occurrence of EIT in the system. For the initial value of the cavity field, a negative region appears in absorption spectrum of the V -type atomic ensemble. Meanwhile, the Λ configuration does not show a such process. According to our results, in the appearance of the transparency window, the position of movable mirror changes significantly.