Quantum phases of multi-component ultracold atom systems Walter - - PowerPoint PPT Presentation
Quantum phases of multi-component ultracold atom systems Walter Hofstetter 2/10/2005 In collaboration with: Carsten Honerkamp Max-Planck-Institute for Solid State Research, Stuttgart, Germany Krzysztof Byczuk Warsaw University, Poland
2/10/2005
Carsten Honerkamp
Max-Planck-Institute for Solid State Research, Stuttgart, Germany
Krzysztof Byczuk
Warsaw University, Poland
Dieter Vollhardt
Augsburg University, Germany
condensed matter physics
New laboratory for correlated many-body systems
atomic physics
ultracold atoms: degenerate quantum gases
Ketterle ‘95 Bose-Einstein condensate
Bosons Fermions condensate Fermi sea
Truscott et al., Science ‘01
6Li 7Li
Fermi pressure due to Pauli principle
multiple scattering channels (hyperfine states) Feshbach resonance degeneracy between open and closed channel
Cornish et al., PRL ‘00
large effective scattering length
artificial crystal for atoms standing light wave:
1d
theoretical description:
Hubbard model
Jaksch et al., ‘98
Hubbard model strongly correlated atoms
“recoil energy”
low filling per site single Bloch band approximation tight-binding basis
Jaksch et al., ‘98
random optical lattices: speckle laser quasiperiodicity (Guidoni et al., PRL ‘97) random heavy “impurity” atoms
Horak et al., PRA ‘98
Anderson localization due to impurity backscattering
random,
interactions + disorder: Anderson-Hubbard Hamiltonian
e.g. 2d metal-insulator transition in doped Si-MOSFETS
(Kravchenko et al., Pudalov et al., 1995 - )
scaling theory of localization (Abrahams et al.): no metallic state possible for 2d noninteracting electrons with disorder interplay of interaction and disorder?
delocalized, Fermi liquid localized, Mott insulator pure system (=0) at half filling n+ n=1
transition at U ~ bandwidth
disordered system, no interactions (U=0)
coherent backscattering leads to localization
return probability
extended localized states
d>2
metal what is a good criterion for localization? Fermi’s golden rule typical LDOS vanishes in insulator: order parameter
local DOS measures escape rate from given site
insulator
Schubert et al. ‘05
noninteracting
LDOS: random quantity, with probability
localized extended
close to localization: log-normal distribution
typical DOS: order parameter
mean-field theory for Anderson transition
Dobrosavljevic et al., EPL ‘03
Kotliar, Vollhardt, Physics Today 57, 53 (‘04)
interacting lattice model self-consistent local problem nonperturbative approach to disorder + interaction
effective impurity fermionic “bath”
stochastic DMFT uses typical DOS as mean field
map onto self-consistent Anderson impurity model (here: ensemble!)
impurity hybridization conduction band
start off with interacting lattice model effective action through “cavity” method
Hilbert transform yields local lattice GF self-consistency: determine local selfenergy from Dyson equation
hybridization
iterate to convergence
DMFT becomes exact as d
Kotliar, Vollhardt, Physics Today 57, 53 (‘04)
successful description of pure fermionic Mott transition
separation of energy scales: logarithmic discretization linear chain Hamiltonian iterative diagonalization non-perturbative approach
Wilson, Rev. Mod. Phys. 47, 773 (`75)
quantum impurity problems
Hofstetter, PRL 85, 1508 (`00)
bosonic and fermionic
dynamics: DM-NRG
re-entrant metallic behavior
spectral DOS as a function of interaction U and disorder interaction + disorder = delocalization
see also PRB 69, 045112 (‘04)
Detection: “metal” vs. insulator: Fermi surface/incoherent peak Mott insulator has AFM spin order Mott and Anderson insulators continuously connected
Mott transition at noninteger filling =x e.g. random impurity atoms
quarter filling x: density of defects
antiferromagnetism suppressed paramagnetic Mott insulator
electrons can only have spin 1/2:
flavor index m=1,2,3,… total particle # on site i
SU(N) Hubbard
atoms have many hyperfine states
6Li
Houbiers et al. ‘97
as=-2160a0
spin-1/2 (N=2): antiferromagnetism N>2: flavor density wave N>6: staggered flux
funktional RG:
dominant instability N=3 N=8
3-color fermions: pairing
unpaired
symmetry breaking
8+1 3+1 generators
degenerate ground state
SU(3)-triplet Leggett `97
coexistence of SC and normal Fermi liquid
SU(3) symmetric 5 gapless modes
amplitude fluct. Landau damping
SU(3) broken:
Bragg scattering experimental signature: density response
new “exotic” quantum state in cold atom system 3-color “toy model” for QCD
flavor mode 123=1+2 -23 Anderson- Bogoliubov phase mode
BEC
quantum simulations disorder exotic quantum states