Commensurate-Incommensurate phase transition in cold atomic gases Commensurate-Incommensurate phase transition in cold atomic gases 05/03/2010 SISSA, Trieste Marcello Dalmonte, Dipartimento di Fisica, Alma Mater Studiorum- Università di Bologna e Sezione INFN, Bologna
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Commensurate-Incommensurate phase transition in cold atomic gases
Commensurate-Incommensurate phase transition in cold atomic gases
05/03/2010SISSA, Trieste
Marcello Dalmonte,Dipartimento di Fisica, Alma Mater Studiorum-
Università di Bologna e Sezione INFN, Bologna
Journal club on...Journal club on...
And complementary information and experiments:●W. Zwerger, arXiv:cond-mat/0211314v2;●T. Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004);●D. Clément et al., Phys. Rev. Lett. 102, 155301 (2009).
Cold atoms in 1 DCold atoms in 1 D
1D gas of bosons with contact interactions
with dimensionless interaction strength:
+optical lattice
Cold atoms and optical lattices: the deep lattice case
Cold atoms and optical lattices: the deep lattice case
D. Jaksch et al., PRL98D. Jaksch et al., PRL98
When , atoms occupy the lowest vibrational level in each well
Bose-Hubbard model
SF
MI
Phase transition point:
Weak optical lattice: what happens?Weak optical lattice: what happens?
Treat the lattice as a perturbation if the system is strongly interacting!
Lieb-Liniger model + perturbation
+ optical lattice
Lieb-Liniger modelLieb-Liniger model
T. Kinoshita et al., Science(2004); B. Paredes et al., Nature(2004).T. Kinoshita et al., Science(2004); B. Paredes et al., Nature(2004).
E. Haller et al., in preparationE. Haller et al., in preparation
In excellent agreementwith BKT predictions
even at V=2
Confrms BH numerical predictions
Add-ons: spectrum and gap scalingAdd-ons: spectrum and gap scaling
lattice depth0.7 Er1.0 Er1.4 Er2.1 Er
Very good accordancewith Zamolodchikov
formula for V<1
Open questions and suggestionsOpen questions and suggestions
What happens when both models break down?
Gap scaling away from weak coupling?
●Dynamical properties of the sine-Gordon and PT models●Thermalization properties●Commensurate-incommensurate transition in 2D and 3D●Finite-size effects?