Weak distinction and the optimal definition of causal continuity

Causal continuity is usually defined by imposing the conditions (i) distinction and (ii) reflectivity. It is proved here that a new causality property which stays between weak distinction and causality, called feeble distinction, can actually replace distinction in the definition of causal continuity. An intermediate proof shows that feeble distinction and future (past) reflectivity implies past (resp. future) distinction. Some new characterizations of weak distinction and reflectivity are given.Comment: 9 pages, 2 figures. v2: improved and expanded version. v3: a few misprints have been corrected and a reference has been update

Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons

The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaron-like composite object consisting of the impurity clothed by a co-moving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio $m_i/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact solution for arbitrary $m_i/m$ and impurity-boson interaction strength.Comment: 4 pp., 2 figures, revtex4; error in Eq.(6) corrected and derivation simplifie

Phase separation in a boson-fermion mixture of Lithium atoms

We use a semiclassical three-fluid model to analyze the conditions for spatial phase separation in a mixture of fermionic Li-6 and a (stable) Bose-Einstein condensate of Li-7 atoms under cylindrical harmonic confinement, both at zero and finite temperature. We show that with the parameters of the Paris experiment [F. Schrek et al., Phys. Rev. Lett. 87 080403 (2001)] an increase of the boson-fermion scattering length by a factor five would be sufficient to enter the phase-separated regime. We give examples of configurations for the density profiles in phase separation and estimate that the transition should persist at temperatures typical of current experiments. For higher values of the boson-fermion coupling we also find a new phase separation between the fermions and the bosonic thermal cloud at finite temperature.Comment: 8 pages, 4 figures, new version of Fig. 4 and typos correcte

Interaction-enhanced flow of a polariton persistent current in a ring

We study the quantum hydrodynamical features of exciton-polaritons flowing circularly in a ring-shaped geometry. We consider a resonant-excitation scheme in which the spinor polariton fluid is set into motion in both components by spin-to-orbital angular momentum conversion. We show that this scheme allows to control the winding number of the fluid, and to create two circulating states differing by two units of the angular momentum. We then consider the effect of a disorder potential, which is always present in realistic nanostructures. We show that a smooth disorder is efficiently screened by the polariton-polariton interactions, yielding a signature of polariton superfluidity. This effect is reminiscent of supercurrent in a superconducting loop.Comment: 7 pages, 4 figure

Pairing of a harmonically trapped fermionic Tonks-Girardeau gas

The fermionic Tonks-Girardeau (FTG) gas is a one-dimensional spin-polarized Fermi gas with infinitely strong attractive zero-range odd-wave interactions, arising from a confinement-induced resonance reachable via a three-dimensional p-wave Feshbach resonance. We investigate the off-diagonal long-range order (ODLRO) of the FTG gas subjected to a longitudinal harmonic confinement by analyzing the two-particle reduced density matrix for which we derive a closed-form expression. Using a variational approach and numerical diagonalization we find that the largest eigenvalue of the two-body density matrix is of order N/2, where N is the total particle number, and hence a partial ODLRO is present for a FTG gas in the trap.Comment: 4 pages, 3 figures, revtex