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Locked mixing of species in a 1D Bose-Fermi mixture

Locked mixing of species in a 1D Bose-Fermi mixture. ICREA Workshop on disorder in cold atoms Barcellona, Spain, 25 th January 2007. M. Rizzi 1 , A. Imambekov 2 R. Fazio 1,3 , E. Demler 2. 1 Scuola Normale Superiore – Pisa, Italy 3 SISSA – Trieste, Italy.

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Locked mixing of species in a 1D Bose-Fermi mixture

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  1. Locked mixing of speciesin a 1D Bose-Fermi mixture ICREA Workshop on disorder in cold atoms Barcellona, Spain, 25th January 2007 M. Rizzi1, A. Imambekov2 R. Fazio1,3, E. Demler2 1 Scuola Normale Superiore – Pisa, Italy 3 SISSA – Trieste, Italy 2 Harvard University – Cambridge, MA

  2. B as F-F force carriers • Fs dressed by Bs, … BFMs in nature Mixed statistics effects in ideal model systems exp. feasible and tunable! Ultracold gases as a toolbox Disorder & metastability See next talk by T.Roscilde Experimental setups via sympathetic cooling G. Modugno, F. Ferlaino, et al., Phys. Rev. A 68 011601 (2003) K. Gunter, T. Stoferle, et al., Phys. Rev. Lett. 96, 180402 (2006) S. Ospelkaus, C. Ospelkaus, et al., Phys. Rev. Lett. 96, 180403 (2006) Interests about Bose-Fermi mixtures

  3. 1D Model Hamiltonian In the continuum: In a lattice formulation: At low enough fillings, good approximation: Realistic 87Rb-40K tf = 87/40 tb=1 and n ~ 1/4

  4. MIXED PHASE Boson physics ruled by UBB Fermions slightly perturb it Weak UBF ~ 0 SEPARATED PHASE Bosons live where Fermions do not Separation surfaces Strong UBF> 0 COLLAPSED PHASE Bosons collapse in small region Fermions Mott there / free outside Strong UBF< 0 MP Stability criterion: positively defined Naive Phase diagram

  5. “Locked Mix” B& F spread Dni very small ! “Usual Mixed” B & F spread Dni not small “Collapsed” tight B peak F free + peak L.Pollet, C. Kollath, et al., cond-mat/0609604 Population profiles

  6. Stability of Locked Mixing Not only a matter of fine tuning densities, but stable at least locally !

  7. In the “usual” mixed phase: quasi-long range order for both B & F as individuals ! In the novel “locked” mixing regime: short range individual correlations, power law only for composite BF-ons ! L.Pollet, M. Troyer, et al., Phys. Rev. Lett. 96, 190402 (2006) Correlation functions

  8. Phase Diagram Sketch Open questions: UBB treshold to get Locked Mixing / Single LL ? Experimental detection? What happens in parabolic traps?

  9. Summary • Parameters for 87Rb - 40K mixtures, low filling • Population profiles: • emergence of a novel “locked mixed” phase • between “usual mixed” and “collapsed” • stability against defects • Correlation functions: • - “usual mixed” are 2 interacting LLs • - “locked mixed” is 1 composite LL • Phase diagram sketch: • locking only for great enough UBB • Work in progress, suggestions are welcome  More info about the open source DMRG code used here available at http://www.qti.sns.it

  10. Simplest estimate as independent liquids: MF phase boundary Mixing-demixing BUT “F (B) induced” B-B (F-F) interactions are too ! • Indeed MF predictions fails in these cases: • exactly solvable case gBF = gBB, mF = mB : mixing always stable! • if gBF = gBB, nF = nB then g = mF gBF / n h2 ~ 5 (MF valid for g < 1) • if gBB = 0 then induced stability has been shown … Numerical investigations are thus worth to be done … (DMRG) Mixing-Demixing: MF approach

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