A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a specific case of unstructured electron waves. Unlike all precedent investigations, the present study describes structured electron states which are not plane waves along the magnetic field direction. In the weak-field limit, our solution (unlike the existing theory) is consistent with the well-known equation for free twisted electron beams. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted. Distinguishing features of the quantization of the velocity and the effective mass of the Laguerre-Gauss and Landau electrons in the uniform magnetic field are analyzed.

Spin-exchange collisions in alkali or alkali-noble gas vapors are at the basis of quantum sensing, nucleon structure studies, tests of fundamental symmetries, and medical imaging. We here show that spin-exchange collisions in hot alkali vapors naturally produce strong bipartite entanglement, which we explicitly quantify using the tools of quantum information science. This entanglement is shown to have a lifetime at least as long as the spin-exchange relaxation time, and to directly affect measurable spin noise observables. This is a formal theoretical demonstration that a hot and dense atomic vapor dominated by random spin-exchange collisions can support long-lived bipartite and possibly higher-order entanglement.

Counterpropagating (CP) solitons generated in high-Q microcavities not only offer useful dual-comb sources, but also provide a new platform to study soliton interactions. Here, we demonstrate and theoretically explain a manifestation of soliton trapping that occurs between CP solitons in a silica microcavity introducing a Kerr soliton dimer. In conventional soliton trapping, the group velocities of two solitons can be synchronized by a Kerr-effect-mediated interaction. The solitons can then copropagate with a fixed temporal delay. However, as shown here, when counterpumping a microcavity using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counterclockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion around a locked average relative displacement with an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the CP solitons. Our observation provides insights on coherently pumped soliton dimers in microcavities.

We show that the threshold condition for two pump photons to convert into a pair of the sideband ones in Kerr microresonators with high-quality factors breaks the pump laser parameter space into a sequence of narrow in frequency and broad in power Arnold tongues. Instability tongues become a dominant feature in resonators with the finesse dispersion parameter close to and above one. As pump power is increased, the tongues expand and cross by forming a line of cusps, i.e., the threshold of complexity, where more sideband pairs become unstable. We elaborate theory for the tongues and threshold of complexity, and report the synchronisation and frequency-domain symmetry breaking effects inside the tongues.