The property lattice of spatially separated quantum systems

Jakub Kopyciński, Wojciech R. Pudełko, Gabriel Wlazłowski

We investigate the properties of a spin-imbalanced and rotating unitary Fermi gas. Using a density functional theory, we provide insight into states that emerge from a competition between Abrikosov lattice formation, spatial phase separation, and the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. A confrontation of the experimental data [M. Zwierlein et al., Science 311, 492 (2006)] with theoretical predictions provides a remarkable qualitative agreement. In the case of gas confined in a harmonic trap, the phase separation into a superfluid core populated by the Abrikosov lattice and a spin-polarized corona is the dominant process. Changing confinement to a boxlike trap reverts the spatial location of the component: gas being in the normal state is surrounded by superfluid threaded by quantum vortices. The vortex lattice no longer exhibits the triangular symmetry, and the emergence of exotic geometries may be an indirect signature of the FFLO-like state formation in the system.

Boris Ischi

L. E. Reichl

Fabio Lingua

This thesis investigates bosonic mixtures in ultra-cold atom systems. We mainly focus on mixtures of two bosonic twin-species trapped in optical lattices, paying particular attention to the properties of spatial separation. The study is carried out by means of the path-integral quantum Monte Carlo by the two-worm algorithm and by analytical calculations where the complexity of the system allows it. The mixture is trapped in a square optical lattice at different filling and temperature conditions. We explore the ground-state phase diagram showing that various quantum phases can arise depending on the interplay between intra- and inter-species interactions. Demixed phases, characterized by spatial separation of the two species, are studied in details determining under which conditions they can be stabilized. The influence of temperature, filling factor and harmonic trap on phase separation is also investigated. An interesting dependence of the degree of demixing from temperature has been found, suggesting new ways to measure the temperature of a two-component bosonic mixture. We also study spatial phase separation in the simple case of a two-component mixture in a double-well potential both numerically and by means of the Bogoliubov approximaton. We show that even in this simple case the main features of the mixing/ demixing phase transitions are observed, and that the transition is characterized by a spectral collapse of the energy eigenvalues reflecting the dramatic change of algebraic structure of the model.

Petr Hájíček, J. Tolar

C. M. Chandrashekar, Sandeep K. Goyal, Subhashish Banerjee

We present a scheme for generating entanglement between two spatially separated systems from the spatial entanglement generated by the interference effect during the evolution of a single-particle quantum walk. Any two systems which can interact with the spatial modes entangled during the walk evolution can be entangled using this scheme. A notable feature is the ability to control the quantum walk dynamics and its localization at desired pair lattice sites irrespective of separation distance resulting in a substantial control and improvement in the entanglement output. Implementation schemes to entangle spatially separated atoms using quantum walk on a single atom is also presented.