Experimental Demonstration of a Synthetic Lorentz Force by Using Radiation Pressure.

Synthetic magnetism in cold atomic gases opened the doors to many exciting novel physical systems and phenomena. Ubiquitous are the methods used for the creation of synthetic magnetic fields. They include rapidly rotating Bose-Einstein condensates employing the analogy between the Coriolis and the Lorentz force, and laser-atom interactions employing the analogy between the Berry phase and the Aharonov-Bohm phase. Interestingly, radiation pressure - being one of the most common forces induced by light - has not yet been used for synthetic magnetism. We experimentally demonstrate a synthetic Lorentz force, based on the radiation pressure and the Doppler effect, by observing the centre-of-mass motion of a cold atomic cloud. The force is perpendicular to the velocity of the cold atomic cloud, and zero for the cloud at rest. Our novel concept is straightforward to implement in a large volume, for a broad range of velocities, and can be extended to different geometries.

Fermi-bose transformation for the time-dependent Lieb-Liniger gas.

Exact solutions of the Schrödinger equation describing a freely expanding Lieb-Liniger gas of delta-interacting bosons in one spatial dimension are constructed. We demonstrate that for any interaction strength the system enters a strongly correlated regime during such expansion. The asymptotic form of the wave function is shown to have the form characteristic for "impenetrable-core" bosons. Exact solutions are obtained by transforming a fully antisymmetric (fermionic) time-dependent wave function that obeys the Schrödinger equation for a free gas. This transformation employs a differential Fermi-Bose mapping operator that depends on the strength of the interaction and the number of particles.

Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wave packet.

The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.

Incoherent white-light solitons in nonlinear periodic lattices.

We predict the existence of lattice solitons made of incoherent white light: lattice solitons made of light originating from an ordinary incandescent light bulb. We find that the intensity structure and spatial power spectra associated with different temporal frequency constituents of incoherent white-light lattice solitons (IWLLSs) arrange themselves in a characteristic fashion, with the intensity structure more localized at higher frequencies, and the spatial power spectrum more localized at lower frequencies; the spatial correlation distance is larger at lower frequency constituents of IWLLSs. This characteristic shape of incoherent white-light lattice solitons reflects the fact that diffraction is stronger for lower temporal frequency constituents, while higher frequencies experience stronger effective nonlinearity and deeper lattice structure.

Incoherent matter-wave solitons and pairing instability in an attractively interacting Bose-Einstein condensate.

The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.

Random-phase solitons in nonlinear periodic lattices.

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.

Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media.

We analytically demonstrate the existence of white light solitons in logarithmically saturable noninstantaneous nonlinear media. This incoherent soliton has elliptic Gaussian intensity profile, and elliptic Gaussian spatial correlation statistics. The existence curve of the soliton connects the strength of the nonlinearity, the spatial correlation distance as a function of frequency, and the characteristic width of the soliton. For this soliton to exist, the spatial correlation distance must be smaller for larger temporal frequency constituents of the beam.

Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion.

We consider n small regions (referred to as the holes) on a chaotic attractor and study the average lifetime it takes for a randomly initiated trajectory to land in their union. The holes are thought of as n possible escape routes for the trajectory. The escape route through one of the holes may be considerably reduced by other holes, depending on their positions. This effect, referred to as shadowing, can significantly prolong the average lifetime. The main result of this paper is the construction and analysis (numerical and theoretical) of the many-hole interactions. They are interpreted as the amount of shadowing between the holes. The "effective range" of these interactions is associated with the largest Lyapunov exponent. The shadowing effect is shown to be very large when the holes are located on n points of an unstable periodic orbit. Considerable attention is paid to this case since it is of interest to the field of controlling chaos.

Bursts in the chaotic trajectory lifetimes preceding controlled periodic motion

The average lifetime [tau(H)] it takes for a randomly started trajectory to land in a small region (H) on a chaotic attractor is studied. tau(H) is an important issue for controlling chaos. We point out that if the region H is visited by a short periodic orbit, the lifetime tau(H) strongly deviates from the inverse of the naturally invariant measure contained within that region [&mgr;(N)(H)(-1)]. We introduce the formula that relates tau(H)/&mgr;(N)(H)(-1) to the expanding eigenvalue of the short periodic orbit visiting H.