Lundi 29 octobre à 14h00
Salle des séminaires, Bât. A
"Bosons de Tonks et Girardeau dans un anneau à une dimension"
Orateur : Christoph Schenke
Recent experimental activities of boson trapping on a ring geometry open the way to explore a novel topology. We focus on a tight ring trap with strong transverse confinement leading to an effectively one-dimensional motion along its circumference. We consider a strongly interacting bose gas on the ring subjected to a localized barrier potential which is suddenly set into motion. Using the time-dependent Bose-Fermi mapping  an exact solution for the dynamical evolution in the impenetrable boson (TonksGirardeau) limit is obtained. The exact solution allows to obtain the particle current, the particle current fluctuations and the drag force acting on the barrier . In the weak barrier limit the stirring drives the system into a state with net zero current and vanishingly small current fluctuations for velocities smaller than v_c=\pi\hbar /mL, with m the atomic mass and L the ring circumference. The existence of a velocity threshold for current generation indicates superfluidlike behavior of the mesoscopic Tonks-Girardeau gas, different from the nonsuperfluid behavior predicted for the TG gas in an infinite tube. At velocities approaching integer multiples of v_c, angular momentum can be transferred to the fluid and a nonzero drag force arises. At these velocities we predict the formation of a macroscopic superposition of a rotating and a nonrotating Fermi sphere of the mapped Fermi gas . We calculate the momentum distribution, time of flight images and the Wigner function of the Bose gas, the latter allowing to identify quantum interferences in the superposition. We find that the barrier velocity should be larger than the sound velocity for a better discrimination of the two components of the superposition.
 M. D. Girardeau and E. M. Wright, Phys. Rev. Lett. 84 5691 (2000)
 C. Schenke, A. Minguzzi and F. W. J. Hekking, Phys. Rev. A 85, 053627 (2012)
 C. Schenke, A. Minguzzi and F. W. J. Hekking, Phys. Rev. A 84, 053636 (2011)