Recently a scheme has been proposed for detection of the structured light by measuring the transmission of a vortex beam through a cloud of cold rubidium atoms with energy levels of the Λ-type configuration [N. Radwell et al., Phys. Rev. Lett. 114, 123603 (2015) ]. This enables observation of regions of spatially dependent electromagnetically induced transparency (EIT). Here we suggest another scenario for detection of the structured light by measuring the absorption profile of a weak nonvortex probe beam in a highly resonant five-level combined tripod and Λ (CTL) atom-light coupling setup. We demonstrate that due to the closed-loop structure of CTL scheme, the absorption of the probe beam depends on the azimuthal angle and orbital angular momentum (OAM) of the control vortex beams. This feature is missing in simple Λ or tripod schemes, as there is no loop in such atom-light couplings. One can identify different regions of spatially structured transparency through measuring the absorption of probe field under different configurations of structured control light.

We propose a scheme to exchange optical vortices of slow light using the phenomenon of electromagnetically induced transparency in a four-level double-$\mathrm{\Lambda }$ atom-light coupling scheme illuminated by a pair of probe fields as well as two control fields of larger intensity. We study the light-matter interaction under the situation where one control field carries an optical vortex, and another control field has no vortex. We show that the orbital angular momentum (OAM) of the vortex control beam can be transferred to a generated probe field through a four-wave-mixing process and without switching on and off of the control fields. Such a mechanism of OAM transfer is much simpler than in a double-tripod scheme in which the exchange of vortices is possible only when two control fields carry optical vortices of opposite helicity. The losses appearing during such OAM exchange are then calculated. It is found that the one-photon detuning plays an important role in minimizing the losses. An approximate analytical expression is obtained for the optimal one-photon detuning for which the losses are minimum while the intensity of generated probe field is maximum. The influence of phase mismatch on the exchange of optical vortices is also investigated. We show that in presence of phase mismatch the exchange of optical vortices can still be efficient.

We study the manipulation of slow light with an orbital angular momentum propagating in a cloud of cold atoms. Atoms are affected by four co-propagating control laser beams in a double tripod configuration of the atomic energy levels involved, allowing us to minimize the losses at the vortex core of the control beams. In such a situation the atomic medium is transparent for a pair of co-propagating probe fields, leading to the creation of two-component (spinor) slow light. We study the interaction between the probe fields when two control beams carry optical vortices of opposite helicity. As a result, a transfer of the optical vortex takes place from the control to the probe fields without switching off and on the control beams. This feature is missing in a single tripod scheme where the optical vortex can be transferred from the control to the probe field only during either the storage or retrieval of light.

We consider transfer of optical vortices between laser pulses carrying orbital angular momentum in a cloud of cold atoms characterized by the $\mathrm{\Lambda }$ configuration of the atom-light coupling. The atoms are initially prepared in a coherent superposition of the lower levels, creating a so-called phaseonium medium. If a single vortex beam initially acts on one transition of the scheme, an extra laser beam is subsequently generated with the same vorticity as that of the incident vortex beam. The absorption of the incident probe beam takes place mostly at the beginning of the atomic medium within the absorption length. The losses disappear as the probe beam propagates deeper into the medium where the atoms are transferred to their dark states. The method is extended to a tripod atom-light coupling scheme and a more general ($n+1$)-level scheme containing $n$ ground states and one excited state, allowing for creation of multiple twisted light beams. We also analyze generation of composite optical vortices in the scheme using a superposition of two initial vortex beams and study lossless propagation of such composite vortices.

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f$\beta${} noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/f$\beta${} noise, and provides further insights into the origin of 1/f$\beta${} noise.

We propose a procedure to achieve a complete energy conversion between laser pulses carrying orbital angular momentum (OAM) in a cloud of cold atoms characterized by a double-$\mathrm{\Lambda }$ atom-light-coupling scheme. A pair of resonant spatially dependent control fields prepare atoms in a position-dependent coherent-population-trapping state, while a pair of much weaker vortex probe beams propagate in the coherently driven atomic medium. Using the adiabatic approximation we derive the propagation equations for the probe beams. We consider a situation where the second control field is absent at the entrance to the atomic cloud and the first control field goes to zero at the end of the atomic medium. In that case the incident vortex probe beam can transfer its OAM to a generated probe beam. We show that the efficiency of such an energy conversion approaches the unity under the adiabatic condition. On the other hand, by using spatially independent profiles of the control fields, the maximum conversion efficiency is only $1/2$.