Superfluid-insulator transitions of the Fermi gas with near-unitary ...
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential Eun-Gook Moon1, Predrag Nikolić2 and Subir Sachdev1
Harvard University1, Rice University2
Introduction and motivation Fermionic superfluids in the unitary limit Pairing strength: weak-BCS, strong-BEC Universal behavior in the crossover region Many-body strongly correlated systems Universality => collective effects, no microscopic scales Novel phases (FFLO, supersolid, exotic Mott insulator...) Simulation of electronic condensed matter systems Evidence for superfluidity of ultracold fermions in an optical lattice J.K.Chin, D.E.Miller, Y.Liu, C.Stan, W.Setiawan, C.Sanner, K.Xu, W.Ketterle Nature 443, 961 (2006) Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Field theory at unitarity Sp(2N) generalization of the two-channel model
Quantum critical point Zero-density Feshbach resonance Relevant perturbations: T, μ, ν, h, V(x) Universality: quantum critical region (broad Feshbach resonance)
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Large-N expansion Effective theory of Cooper pairs/molecules Wiggly lines: Φ and Φ† New molecule bare propagator: “bubble diagram” 1 /N New molecule bare vertices: N Perturbation theory generates a 1 /N expansion
The limit N→ ... mean-field
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Unitarity in optical lattices: T=0 2nd order superfluid-insulator phase transition at T=0, h=0 Band insulators deep in BCS limit Mott insulators deep in BEC limit Crossover at unitarity
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Universal critical lattice depth Mean-field theory Diagonalize in continuum space near unitarity Single-band Hubbard-like models available only deep in BCS or BEC limits... Fix density - completely filled bands
At unitarity: Our result: VC~ 70 Er MIT experiment: VC~ 6 Er
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Finite temperatures Superfluid-normal transitions at T=0.6EF Thermal fluctuations destroy superfluid in the bands Transition at small V possible at unitarity Relation to the experiment?
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Conclusions T=0 superfluid-insulator transitions in a lattice, near unitarity universal phase diagram, reminiscent of Mott phase diagram calculation of the universal critical lattice depth no single-band tight-binding approximations smooth evolution from band to Mott insulator T>0 superfluid-normal transitions lower critical lattice depth than at T=0 possible agreement with experiment, T~Ef
Eun Gook Moon, Predrag Nikolić, Subir Sachdev; Phys. Rev. Lett. 99, 230403 (2007) Predrag Nikolić and Subir Sachdev; Phys. Rev. A 75, 033608 (2007) Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Harvard University1, Rice University2
Introduction and motivation Fermionic superfluids in the unitary limit Pairing strength: weak-BCS, strong-BEC Universal behavior in the crossover region Many-body strongly correlated systems Universality => collective effects, no microscopic scales Novel phases (FFLO, supersolid, exotic Mott insulator...) Simulation of electronic condensed matter systems Evidence for superfluidity of ultracold fermions in an optical lattice J.K.Chin, D.E.Miller, Y.Liu, C.Stan, W.Setiawan, C.Sanner, K.Xu, W.Ketterle Nature 443, 961 (2006) Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Field theory at unitarity Sp(2N) generalization of the two-channel model
Quantum critical point Zero-density Feshbach resonance Relevant perturbations: T, μ, ν, h, V(x) Universality: quantum critical region (broad Feshbach resonance)
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Large-N expansion Effective theory of Cooper pairs/molecules Wiggly lines: Φ and Φ† New molecule bare propagator: “bubble diagram” 1 /N New molecule bare vertices: N Perturbation theory generates a 1 /N expansion
The limit N→ ... mean-field
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Unitarity in optical lattices: T=0 2nd order superfluid-insulator phase transition at T=0, h=0 Band insulators deep in BCS limit Mott insulators deep in BEC limit Crossover at unitarity
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Universal critical lattice depth Mean-field theory Diagonalize in continuum space near unitarity Single-band Hubbard-like models available only deep in BCS or BEC limits... Fix density - completely filled bands
At unitarity: Our result: VC~ 70 Er MIT experiment: VC~ 6 Er
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Finite temperatures Superfluid-normal transitions at T=0.6EF Thermal fluctuations destroy superfluid in the bands Transition at small V possible at unitarity Relation to the experiment?
Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
Conclusions T=0 superfluid-insulator transitions in a lattice, near unitarity universal phase diagram, reminiscent of Mott phase diagram calculation of the universal critical lattice depth no single-band tight-binding approximations smooth evolution from band to Mott insulator T>0 superfluid-normal transitions lower critical lattice depth than at T=0 possible agreement with experiment, T~Ef
Eun Gook Moon, Predrag Nikolić, Subir Sachdev; Phys. Rev. Lett. 99, 230403 (2007) Predrag Nikolić and Subir Sachdev; Phys. Rev. A 75, 033608 (2007) Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential
Predrag Nikolić
