Creation of topological states of a Bose-Einstein condensate in a plaquette

We study a square plaquette of four optical microtraps containing ultracold $^{87}$Rb atoms in F=1 hyperfine state. In a presence of external resonant magnetic field the dipolar interactions couple initial $m_F=1$ component to other Zeeman sublevels. This process is a generalization of the Einstein-de Haas effect to the case when the external potential has only $C_4$ point-symmetry. We observe that vortex structures appear in the initially empty $m_F=0$ state. Topological properties of this state are determined by competition between the local axial symmetry of the individual trap and the discrete symmetry of the plaquette. For deep microtraps vortices are localized at individual sites whereas for shallow traps only one discrete vortex appears in the plaquette. States created in these two opposite cases have different topological properties related to $C_4$ point-symmetry

Single-shot simulations of dynamics of quantum dark solitons

Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type~II excitation spectrum identified by E. H. Lieb, reproduces the dispersion relation of dark solitons in the mean-field approach. The corresponding eigenstates possess translational symmetry which can be broken in measurements of positions of particles. We analyze emergence of single and double solitons in the course of the measurements and investigate dynamics of the system. In the weak interaction limit, the system follows the mean-field prediction for a short period of time. Long time evolution reveals many-body effects that are related to an increasing uncertainty of soliton positions. In the strong interaction regime particles behave like impenetrable bosons. Then, the probability densities in the configuration space become identical to the probabilities of non-interacting fermions but the wave-functions themselves remember the original Bose statistics. Especially, the phase flips that are key signatures of the solitons in the weak interaction limit, can be observed in the time evolution of the strongly interacting bosons.Comment: 11 pages, 9 figure

Coherence properties of spinor condensates at finite temperatures

We consider a spinor condensate of 87Rb atoms in its F=1 hyperfine state at finite temperatures. Putting initially all atoms in m_F=0 component we find that the system evolves into the state of thermal equilibrium. This state is approached in a step-like process and when established it manifests itself in distinguishable ways. The atoms in states m_F=+1 and m_F=-1 start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the m_F=+1 and m_F=-1 spinor condensate components periodically loose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up.Comment: 5 pages, 4 figure

Solitons and vortices in ultracold fermionic gases

We investigate the possibilities of generation of solitons and vortices in a degenerate gas of neutral fermionic atoms. In analogy with, already experimentally demonstrated, technique applied to gaseous Bose-Einstein condensate we propose the phase engineering of a Fermi gas as a practical route to excited states with solitons and vortices. We stress that solitons and vortices appear even in a noninteracting fermionic gas. For solitons, in a system with sufficiently large number of fermions and appropriate trap configuration, the Pauli blocking acts as the interaction between particles.Comment: 4 pages, 5 figures many new result

Exact dynamics and decoherence of two cold bosons in a 1D harmonic trap

We study dynamics of two interacting ultra cold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the delta-like potential we study time evolution of initially separable state of two particles. The corresponding time dependent single particle density matrix is obtained and diagonalized and single particle orbitals are found. This allows to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.Comment: 9 figures, 5 movies available on-lin