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Ljup čo Hadžievski

Ljup čo Hadžievski. VINČA Institute of Nuclear Sciences University of Belgrade. Periodic density patterns in dipolar Bose-Einstein condensates trapped in deep optical lattice. Aleksandra Maluckov, Goran Gligori ć, Boris Malomed, Tilman Pfau. GOAL.

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Ljup čo Hadžievski

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  1. Ljupčo Hadžievski VINČA Institute of Nuclear Sciences University of Belgrade Periodic density patterns in dipolar Bose-Einstein condensates trapped in deep optical lattice Aleksandra Maluckov, Goran Gligorić, Boris Malomed, Tilman Pfau

  2. GOAL Search forthe stable periodic structures in 1D dipolar Bose-Einstein condensates trapped in deep optical lattices

  3. OUTLINE • Bose-Einstein condensates (BEC) • Dipolar BEC in optical lattice • Gross-Pitaevskii equation • Dipolar BEC in a cigar-shaped potential (1D) • Dipolar 1D BEC ina deep optical lattice • Results • Double periodic patterns • Triple periodic patterns • Conclusion

  4. Boze-Ajnštajnkondenzati Bose-Einstein condensation is a pure quantum phenomena consisting of the macroscopic occupation of a single-particle state by an ensemble of identical bosons in thermal equilibrium at finite temperature 1925. -The occurrence of these phenomena was predicted (Einstein-Bose) 1995. -The first successful experimental creation of BECs in dilute alkali gases Dipolar BEC: Significant magnetic or electrical moment of particles 2005. - The BEC of Chromium atoms 2008. - The BEC of polar molecules

  5. Gross-Pitaevskii equation number of atoms Feshbach resonance characteristic range of magnetic fields mass of atom resonant magnetic field s-wave scattering length Applied magnetic field Nonlinearity management Attractive contact interaction Repulsive contact interaction

  6. Dipolar BEC 3D Gross-Pitaevskiiequation Dipolar contribution

  7. Dipolar BECin a cigar-shaped potential (1D) Gross-Pitaevskii equationwith the cubic nonlinearity (GPE) Nonpolynomial nonlinear Schrödinger equation (NPSE) Repulsive contact interaction Attractive contact interaction

  8. z z Attractive DD interaction Repulsive DD interaction Discrete1D model of dipolar BEC - deep optical lattice - + + + + + + Discrete Gross-Pitaevskii (DGP) equation (tight-binding approximation) ) - - - - - - Non-local nonlinearity Local nonlinearity Attractive contact interaction Repulsive contact interaction

  9. Discrete1D model of dipolar BEC - deep optical lattice - Conserved quantities Hamiltonian Norm Stationary solutions

  10. Results optical lattice Uniform T1 Two-periodic Patterns T2 =2T1 Three-periodic T3 =3T1

  11. Two-periodic patterns Analytical solutions + Linear stability analysis Stability diagrams Uniform Bifurcation diagrams Two-periodic =-5 =-2 t =-0.55

  12. Three-periodic patterns Analyt./num. solutions + Linear stability analysis Stability diagrams Uniform Bifurcation diagrams Three-periodic =-5 =-2 t=-1.45

  13. Energy =-5 =-2 Three-periodic structures are energetically favorable Existence and stability are confirmed with the direct numerical simulations More details in Phys. Rev. Lett. 108, 140402 (2012)

  14. CONCLUSION Stable DPP and TPP patterns exist only in the dipolar BEC with repulsive contact and repulsive DD interaction + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - • Challenges: • Experimental verification? (The range of the BEC parameters are experimentally achievable) • Stable 2D patterns? Isotropic DD interaction Anisotropic DD interaction

  15. Dipolar2D BECin a deep optical lattice + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - Isotropic DD interaction IDD Anisotropic DD interaction ADD

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