On Defect-Mediated Transitions in Bosonic Planar Lattices

We discuss the finite-temperature properties of Bose-Einstein condensates loaded on a 2D optical lattice. In an experimentally attainable range of parameters the system is described by the XY model, which undergoes a Berezinskii-Kosterlitz-Thouless (BKT) transition driven by the vortex pair unbinding. The interference pattern of the expanding condensates provides the experimental signature of the BKT transition: near the critical temperature, the k=0 component of the momentum distribution sharply decreases

Entanglement and sensitivity in precision measurements with states of a fluctuating number of particles

The concepts of separability, entanglement, spin-squeezing and Heisenberg limit are central in the theory of quantum enhanced metrology. In the current literature, these are well established only in the case of linear interferometers operating with input quantum states of a known fixed number of particles. This manuscript generalizes these concepts and extends the quantum phase estimation theory by taking into account classical and quantum fluctuations of the particle number. Our analysis concerns most of the current experiments on precision measurements where the number of particles is known only in average.Comment: Published versio

Macroscopic Superpositions of Phase States with Bose-Einstein Condensates

Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology

A Multi-path Interferometer with Ultracold Atoms Trapped in an Optical Lattice

We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $\Delta g\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-square fit of the average density to the interference pattern, the sensitivity still scales like $M^{-1}$ for linear potentials and can be further improved by preparing a properly correlated initial state in the lattice.Comment: 11 pages, 3 fugire

Phase oscillations in superfluid 3He-B weak links

Oscillations in quantum phase about a mean value of $\pi$, observed across micropores connecting two \helium baths, are explained in a Ginzburg-Landau phenomenology. The dynamics arises from the Josephson phase relation,the interbath continuity equation, and helium boundary conditions. The pores are shown to act as Josephson tunnel junctions, and the dynamic variables are the inter bath phase difference and fractional difference in superfluid density at micropores. The system maps onto a non-rigid, momentum-shortened pendulum, with inverted-orientation oscillations about a vertical tilt angle $\phi = \pi$, and other modes are predicted