Scattering in the ultrastrong regime: nonlinear optics with one photon

The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using matrix product states. It is found that the scattering is strongly influenced by the single- and multiphoton dressed bound states present in the system. In the ultrastrong coupling regime a new channel for inelastic scattering appears, where an incident photon deposits energy into the qubit, exciting a photon-bound state, and escaping with a lower frequency. This single-photon nonlinear frequency conversion process can reach up to 50% efficiency. Other remarkable features in the scattering induced by counterrotating terms are a blueshift of the reflection resonance and a Fano resonance due to long-lived excited states.

Seeing topological order in time-of-flight measurements

In this Letter, we provide a general methodology to directly measure topological order in cold atom systems. As an application, we propose the realization of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentum-space Skyrmions.

Dynamics of quasicollapse in nonlinear Schrodinger systems with nonlocal interactions

We study the effect of nonlocality on some dynamical properties of a self-focusing nonlocal nonlinear Schrodinger system. Using a combination of moment techniques, time dependent variational methods, and numerical simulations, we present evidence in support of the hypothesis that nonlocal attractively interacting condensates cannot collapse under very general forms of the interaction. Instead there appear oscillations of the wave packet with a localized component whose size is of the order of the range of interactions. We discuss the implications of the results to collapse phenomena in Bose-Einstein condensates.

Dipole-mode vector solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by the soliton-induced waveguides. These solitons, which appear as a consequence of the vector nature of the two-component system, are more stable than the previously found optical vortex solitons and represent a new type of extremely robust nonlinear vector structure.

Stable and unstable vortices in multicomponent bose-einstein condensates

We study the stability and dynamics of vortices in two-species condensates as prepared in the recent JILA experiment [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)]. We find that of the two possible configurations, in which one species has vorticity m = 1 and the other one has m = 0, only one is linearly stable, which agrees with the experimental results. However, it is found that in the unstable case the vortex is not destroyed by the instability, but may be transferred from one species to the other or display complex spatiotemporal dynamics.