We show that the general quantum state of synthetically spin-orbit coupled ultra cold bosonic atom whose condensate was experimentally created recently ( Y. J. Lin {it et al.}, Nature, {bf 471}, 83, (2011)), shows entanglement between motional degree
s of freedom ( momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provides a unique opportunity to verify fundamental principle like quantum non-contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such atom-laser system and how that influneces quantities like entanglement entropy, violation of Bell like Inequality etc. We also discuss the implication of our result in testing the quantum non-contextuality and Bells Inequality vioaltion by macroscopic quantum object like Bose-Einstein Condensate of ultra cold atoms.
The surface states of the three dimensional (3D) Topological Insulators are described by two-dimensional (2D) massless dirac equation. A gate voltage induced one dimensional potential barrier on such surface creates a discrete bound state in the forb
idden region outside the dirac cone. Even for a single barrier it is shown such bound state can create electrostatic analogue of Shubnikov de Haas oscillation which can be experimentally observed for relatively smaller size samples. However when these surface states are exposed to a periodic arrangement of such gate voltage induced potential barriers, the band structure of the same got nontrivially modified. This is expected to significantly alters the properties of macroscopic system. We also suggest that in suitable limit the system may offer ways to control electron spin electrostatically which may be practically useful.
We start by reviewing the concept of gauge invariance in quantum mechanics, for Abelian and Non-Ableian cases. Then we idescribe how the various gauge potential and field can be associated with the geometrical phase acquired by a quantum mechanical w
ave function while adiabatically evolving in a parameter space. Subsequently we show how this concept is exploited to generate light induced gauge field for neutral ultra cold bosonic atoms. As an example of such light induced Abelian and Non Abelian gauge field for ultra cold atoms we disucss ultra cold atoms in a rotating trap and creation of synthetic spin orbit coupling for ultra cold atomic systems using Raman lasers.
An analysis of electron transport in graphene is presented in the presence of various arrangement of delta-function like magnetic barriers. The motion through one such barrier gives an unusual non specular refraction leading to asymmetric transmissio
n. The symmetry is restored by putting two such barriers in opposite direction side by side. Periodic arrangements of such barriers can be used as Bragg reflectors whose reflectivity has been calculated using a transfer matrix formalism. Such Bragg reflectors can be used to make resonant cavities. We also analyze the associated band structure for the case of infinite periodic structures.
Magnetic dipole-dipole interaction dominated Bose-Einstein condensates are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from large spin limit to obtain an effective minimal Hamiltoni
an; a version extended from a non-linear sigma model. By solving the Gross-Pitaevskii equation we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.
