Dimensional BCS-BEC crossover
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1 Dimensional BCS-BEC crossover Igor Boettcher Institute for Theoretical Physics, Heidelberg University ERG 2014
2 Outline Ultracold atoms BCS-BEC Crossover 2D Experiments
3 with... Theory Experiment C. Wetterich J. M. Pawlowski S. Jochim T. K. Herbst N. Strodthoff J. Braun (Darmstadt) D. Roscher (Darmstadt) L. von Smekal (Giessen/Darmstadt) T. Enss M. Scherer S. Lammers F. Golibrzuch S. Diehl (Dresden) S. Floerchinger (CERN) M. Ries A. Wenz G. Zuern P. Murthy M. Neidig T. Lompe D. Kedar L. Bayha
4 Many-body physics with cold atoms Ultracold atoms: 10^6 atoms trapped by light (Hz-kHz) 100 nk, T/T = O(1) F Clean realizations of many-body Hamiltonians. High experimental control & accessibility. 2D pancakes
5 Many-body physics with cold atoms Li-6 a(b) Interactions between 1> and 2> atoms encoded in the s-wave scattering length a=a(b) For small a:
6 BCS-BEC Crossover superfluidity: vortices Zwierlein et al., Nature 435, (2005) C.A.R. Sà de Melo, Physics Today 61(10), 45 (2008)
7 BCS-BEC Crossover Feshbach resonance physics described by two-channel model Yukawa-type model: Key observables: Fermion propagator Boson propagator Effective potential Phase diagram Equation of state Momentum distribution
8 Functional Renormalization Group FRG setup Effective potential: Taylor expansion or resolution on a grid Boson propagator: scale-dependent derivative expansion Fermion propagator: iterative, frequency and momentum-resolved* *IB, S. Diehl, J. M Pawlowski, C. Wetterich, PRA 87, (2013)
9 Functional Renormalization Group IB, J. M. Pawlowski, C. Wetterich, PRA 89, (2014)
10 Functional Renormalization Group IB, J. M. Pawlowski, C. Wetterich, PRA 89, (2014)
11 Functional Renormalization Group Critical temperature & superfluid gap of the Unitary Fermi Gas IB, J. M. Pawlowski, C. Wetterich, PRA 89, (2014)
12 Dimensional BCS-BEC Crossover
13 Dimensional BCS-BEC Crossover Phase structure of spin-imbalanced unitary Fermi gases IB, J. Braun, T. K. Herbst, J. M. Pawlowski, D. Roscher, C. Wetterich - arxiv: see talk by Dietrich Roscher today Sarma phase in relativistic and non-relativistic systems IB, T. K. Herbst, J. M. Pawlowski, N. Strodthoff, L. von Smekal, C. Wetterich - arxiv: see talk by Tina K. Herbst today
14 Dimensional BCS-BEC Crossover Observation of pair condensation in a strongly interacting two-dimensional Fermi gas M. G. Ries, A. N. Wenz, G. Zuern, L Bayha, IB, D. Kedar, P. A. Murthy, M. Neidig, T. Lompe, S. Jochim - arxiv: Dimensional BCS-BEC crossover in ultracold Fermi gases IB, PHD thesis (2014) IB, J. M. Pawlowski, C. Wetterich (in preparation, 2014)
15 Dimensional BCS-BEC Crossover Equation of state at T=0 3 Fermi liquid Crossover parameter 3D: MF LHY 2
16 Dimensional BCS-BEC Crossover Equation of state at T=0 3 Fermi liquid Crossover parameter 3D: MF 2D: LHY MF Fermi liquid 2
17 Dimensional BCS-BEC Crossover Phase diagram 3 S=1, V=0 2
18 Dimensional BCS-BEC Crossover diagram BKT scaling is resolved Phase from FRG for all log(kfa): 3 S=1, V=0 2
19 2D experiment Jochim PI Heidelberg in-situ profiles and momentum distribution after TOF expansion trap aspect ratio ωx/ωz=1/300 => effectively 2D
20 2D experiment Superfluid/condensation transition from enhanced occupation of low-momentum states momentum distribution after TOF
21 2D experiment 2D scattering length a from magnetic field B Boltzmann fit gives T and μ Density n from in-situ image => Full thermodynamic characterization n(μ,t,a)! Nq/N T, μ
22 2D experiment BKT verified from infinite correlation length and algebraic decay of correlations below Tc
23 2D experiment Bauer, Parish, Enss FRG Understanding of the phase diagram within reach!
24 Equation of state determination Equation of state n(μ,t,a) from in-situ images local density approximation Nascimbene, Navon, Chevy, Salomon New Journal of Physics 12 (2010)
25 Equation of state determination Equation of state n(μ,t,a) from in-situ images local density approximation Thank you for your attention! Nascimbene, Navon, Chevy, Salomon New Journal of Physics 12 (2010)
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