We theoretically investigate in-medium two- and three-body correlations in one-dimensional spinless fermions with attractive two-body
p-wave interaction. By investigating the variational problem of two- and three-body states above the Fermi sea, we elucidate the fate of the in-medium two- and three-body cluster states. The one-dimensional system with the strong
p-wave interaction is found to be stable against the formation of three-body clusters even in the presence of the Fermi sea, in contrast to higher-dimensional systems that suffer the strong three-body loss associated with the trimer formation. Our results indicate that the weak two-body coupling side is more sensitive to the residual three-body interaction than the strong-coupling side. By including the dimensionless three-body coupling such that the universality associated with the scattering length is maintained, we find that an in-medium three-body state similar to a squeezed Cooper triple appears.
We consider propagation of light pulses detuned from the atomic resonance in a dense two-level medium and the photonic structures with it. The large density of the medium is important for decreasing the spatial scale of nonlinear effects such as pulse compression, though it does not provide any fundamentally new phenomena as compared to dilute media. Frequency detuning decreases the effectivity of nonlinear phenomena such as pulse compression and dispersion-spreading compensation as well. We propose simple logic gates based on interaction between two pulses in one-dimensional nonlinear photonic crystal. We found that frequency detuning is necessary to obtain ultrafast AND gates, while OR and NOT gates can be realized in the system without detuning.
We study general features of the excitation spectrum of a system of one-dimensional chiral spinless fermions with short-range interactions. We show that the nature of the elementary excitations of such a system depends strongly on the nonlinearity of the underlying dispersion of the fermions. In the case of quadratic nonlinearity, the low-momentum excitations are essentially fermionic quasiparticles and quasiholes, whereas the high-momentum ones are classical harmonic waves and solitons. In the case of cubic nonlinearity, the nature of the elementary excitations does not depend on momentum and is determined by the strength of the interactions. At a certain critical value of the interaction strength, the excitation spectrum changes qualitatively, pointing to a dynamic phase transition in the system.