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Quantum Monte Carlo methods applied to ultracold gases Stefano Giorgini

Quantum Monte Carlo methods applied to ultracold gases Stefano Giorgini Istituto Nazionale per la Fisica della Materia Research and Development Center on Bose-Einstein Condensation Dipartimento di Fisica – Universit à di Trento. BEC CNR-INFM meeting 2-3 May 2006.

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Quantum Monte Carlo methods applied to ultracold gases Stefano Giorgini

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  1. Quantum Monte Carlo methods applied to ultracold gases Stefano Giorgini Istituto Nazionale per la Fisica della Materia Research and Development Center onBose-Einstein Condensation Dipartimento di Fisica – Università di Trento BEC CNR-INFM meeting 2-3 May 2006

  2. QMC simulations have become an important tool in the study of dilute ultracold gases • Critical phenomena Shift of Tc in 3D Grüter et al. (´97), Holzmann and Krauth (´99), Kashurnikov et al. (´01) Kosterlitz-Thouless Tc in 2D Prokof’ev et al. (´01) • Low dimensions Large scattering length in 1D and 2D Trento (´04 - ´05) • Quantum phase transitions in optical lattices Bose-Hubbard model in harmonic traps Batrouni et al. (´02) • Strongly correlated fermions BCS-BEC crossover Carlson et al. (´03), Trento (´04 - ´05) Thermodynamics and Tc at unitarity Bulgac et al. (´06), Burovski et al. (´06)

  3. Continuous-space QMC methods Zero temperature • Solution of the many-body Schrödinger equation Variational Monte Carlo Based on variational principle energy upper bound Diffusion Monte Carlo exact method for the ground state of Bose systems Fixed-node Diffusion Monte Carlo (fermions and excited states) exact for a given nodal surface  energy upper bound Finite temperature • Partition function of quantum many-body system Path Integral Monte Carlo exact method for Bose systems

  4. Low dimensions + large scattering length

  5. g1D>0 Lieb-Liniger Hamiltonian (1963) g1D<0 ground-state is a cluster state (McGuire 1964) 1D Hamiltonian if g1D large and negative (na1D<<1) metastable gas-like state of hard-rods of size a1D Olshanii (1998) at na1D  0.35 the inverse compressibility vanishes gas-like state rapidly disappears forming clusters

  6. Power-law decay in OBDM Correlations are stronger than in the Tonks-Girardeau gas (Super-Tonks regime) Peak in static structure factor Breathing mode in harmonic traps TG mean field

  7. Universality and beyond mean-field effects Equation of state of a 2D Bose gas • hard disk • soft disk • zero-range for zero-range potential mc2=0 at na2D20.04 onset of instability for cluster formation

  8. -1/kFa BCS-BEC crossover in a Fermi gas at T=0 BEC BCS

  9. Equation of state beyond mean-field effects confirmed by study of collective modes (Grimm) BEC regime: gas of molecules [mass 2m - density n/2 – scattering length am] am=0.6 a (four-body calculation of Petrov et al.) am=0.62(1) a (best fit to FN-DMC)

  10. QMC equation of state Frequency of radial mode (Innsbruck) Mean-field equation of state

  11. JILA in traps Momentum distribution Condensate fraction

  12. Static structure factor (Trento + Paris ENS collaboration) ( can be measured in Bragg scattering experiments) at large momentum transfer kF k  1/a crossover from S(k)=2free molecules to S(k)=1free atoms

  13. New projects: • Unitary Fermi gas in an optical lattice(G. Astrakharchik + Barcelona) d=1/q=/2 lattice spacing Filling 1: one fermion of each spin component per site (Zürich) Superfluid-insulator transition single-band Hubbard Hamiltonian is inadequate

  14. S=20 S=1

  15. Bose gas at finite temperature(S. Pilati + Barcelona) Equation of state and universality T  Tc T  Tc

  16. Pair-correlation function and bunching effect Temperature dependence of condensate fraction and superfluid density (+ N. Prokof’ev’s help on implemention of worm-algorithm) T = 0.5 Tc

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