9Vortices observed at:JILA-BoulderENS-ParisMITOxfordProduced with different techniques:Phase imprinting, rotating laser spoon, rotating magnetic trap, rotating thermal cloud, selective evaporation, decay of solitons, etc.
10A lot of physical questions: Nucleation mechanisms.Observation of density and phase.Stability, decay, precession.Shape and dynamics of a single vortex.Formation and dynamics of vortex lattices.Fast rotating condensates and giant vortices.Coreless vortices and textures in spinor condensates.Interaction with thermal atoms, solitons, surface modes.Vortex rings, vortex-antivortex pairs, etc.A lot of theoretical papers !!
11Vortex-free configurations with angular momentum ℓ≠0
19Possible route to vortex nucleation Almost spherical condensatein a rotating trap with Ω close to ω┴/√2New stable configuration, spherical, with vorticesMany quadrupole shape deformations are excitedVortices enter the condensateHighly deformed condensate with irrotational fieldComplex dynamics with nucleation of vortices at the surfaceThe deformed condensate becomes dynamically unstable
24Work done in TrentoVortex nucleation and quadrupole deformation of a rotating Bose-Einstein condensate M. Kraemer, L. Pitaevskii, S. Stringari, F. Zambelli, Laser Physics 12, 113 (2002) Consequence of superfluidity on the expansion of a rotating Bose-Einstein condensate M. Edwards, C. W. Clark, P. Pedri, L. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 88, (2002) A superfluid gyroscope with cold atomic gases S. Stringari, Phys. Rev. Lett. 86, 4725 (2001) Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates F. Dalfovo and S. Stringari, Phys. Rev. A 63, (R) (2001) Overcritical Rotation of a Trapped Bose-Einstein Condensate A. Recati, F. Zambelli, and S. Stringari, Phys. Rev. Lett 86, 377 (2001) Moment of Inertia and Quadrupole Response Function of a Trapped Superfluid F. Zambelli and S. Stringari, Phys. Rev. A 63, (2001) Free expansion of Bose-Einstein condensates with quantized vortices F. Dalfovo and M. Modugno, Phys. Rev. A 61, (2000) Pinning of quantized vortices in helium drops by dopant atoms and molecules F. Dalfovo, R. Mayol, M. Pi, and M. Barranco, Phys. Rev. Lett. 85, 1028 (2000) Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas D. Guery-Odelin and S. Stringari, Phys. Rev. Lett 83, 4452 (1999) Phase diagram of quantized vortices in a trapped Bose-Einstein condensed gas S. Stringari, Phys. Rev. Lett. 82, 4373 (1999) Quantized vortices and collective oscillations of a trapped Bose condensed gas F. Zambelli and S. Stringari, Phys. Rev. Lett. 81, 1754 (1998) Moment of Inertia and Superfluidity of a Trapped Bose Gas , S. Stringari, Phys. Rev. Lett. 76, 1405 (1996) Bosons in anisotropic traps: ground state and vortices , F. Dalfovo and S. Stringari, Phys. Rev. A 53, 2477 (1996)
25Present and next future: Most recent activity:Scissors mode in rotating condensatesScissors mode of a rotating Bose-Einstein condensate,M.Cozzini, S. Stringari, V. Bretin, P. Rosenbusch, J. Dalibard, PRA 67, (2003)Macroscopic dynamics of vortex latticesMacroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice,Marco Cozzini and Sandro Stringari, e-print cond-mat/Present and next future:More about vortex latticesStationary configurations, Collective oscillations, elastic properties, dynamics, …
41Helium droplet ↔ trapped BEC Helium is denseCondensate fraction is 10% in bulk at T=0Superfluid fraction is 100% in bulk at T=0Helium droplets are self bound (no confinement)Temperature of droplets is about K (evaporative cooling)
43Density functional calculations for helium nanodroplets: Moment of inertiaA superfluid hydrodynamic model for the enhanced moments of inertia of molecules in liquid 4He, C. Callegari, A. Conjusteau, I. Reinhard, K. K. Lehmann, G. Scoles, F. Dalfovo Phys. Rev. Lett. 83, 5058 (1999)Quantized vorticesPinning of quantized vortices in helium drops by dopant atoms and molecules , F. Dalfovo, R. Mayol, M. Pi, and M. Barranco, Phys. Rev. Lett. 85, 1028 (2000)Quantized Vortices in Mixed 3He-4He Drops, R. Mayol, M. Pi, and M. Barranco, and F. Dalfovo, Phys. Rev. Lett. 87, (2001)
45Trapped BEC with a vortex Helium droplet with a vortexF. D., R. Mayol, M. Pi, and M. Barranco, Phys. Rev. Lett. 85, 1028 (2000)←Trapped BEC with a vortexF. D. and S. Stringari,Phys. Rev. A 53, 2477 (1996)↓
47ConclusionsRotational properties and quantized vorticity are intimately connected to superfluidity.Dilute condensates in traps represent a wonderful testing ground for theories on quantum fluids.Dilute condensates and liquid helium are good friends. They look different, but they speak the same language.