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Quantum impurity problem in ultracold gases: from dark solitons to quantum ferromagnets Dimitri M Gangardt MUARC – Midlands Ultra Cold Atoms Research Centre In collaboration with Alex Kamenev, University of Minnesota Phys. Rev. Lett. 102, 070402 (2009), arXiv:0908.4513 Experiments in 1D atoms in each tube 1 dimensional regime Short-range interactions Impurity in 1D 1 impurity of mass M making its way through the liquid.... Questions: How to characterise its interactions with background Dissipative processes Motion under slow external fields (harmonic trap) Bose spinor gas Magnetically trapped Untrapped S. Palzer et al. PRL 2009 Constructing effective action Impurity Bose Liquid co-moving frame is TOTAL momentum Renormalised collective dispersion Minimise the total energy of impurity + liquid for given total momentum ground state of Control parameters: velocity , background chemical pot. Dispersion periodicity 'superfluid' argument Transfer momentum quantum No change to internal state! Total momentum Total energy Periodic dispersion to each particle Dispersion periodicity 'umklapp' argument Assume no (quantum, thermal) fluctuations: perfect lattice Periodic zone with period contains contribution of all excitations with Phonons Phase-density representation for slow fields Close to equibrium + interactions Real processes: dissipation and viscous friction One phonon processes - Landau criterion Superfluid at two phonon processes Viscosity coefficient In 3 dimensions depends crucially on coupling with phonons In 1 dimension Landau & Khalatnikov, 1949 Baym & Ebner, 1967 Castro Neto & M.P.A Fisher, 1996 Impurity – phonon coupling Coupling to density Coupling to (super) velocity Galilean transformation: Gauge transformation Choose to eliminate linear couplings: Integrating out phonons Quantum interference – possible cancellation Effective coupling Number of particles expelled by the impurity Integrable cases Integrability ? Mechanism of relaxation? 3-body collisions No dissipation No decay of supercurrents Even at Dark Soliton Phase drop : Number of part. expelled can be obtained in the limit Experiments. Life-Time Lifetime ~300ms ● Finite lifetime due to background fluctuations (phonons) ● Absent at T=0 (Landau criterion) ● Absent for integrable case 1D fermions with spin ½ Spin -1 excitation above a (metastable) ferromagnetic state Castella, Zotos '93 (Gaudin '67, Young '67) Perturbation around integrability Weakly interacting bosons Strong interactions Concluding remarks ● Impurity in 1D – model to study nonequilibrium many body quantum dynamics. ● Universal coupling to phonons ● Dissipation is important. Mechanism of dissipation ● ● ● Sensitive to parameters. Absence of dissipation for integrable systems even at nonzero temperature Can be applied to study excitation dynamics in nearly integrable systems. Lifetime of quasiparticles Experiments....