Superfluidity with disorder in a thin film of quantum gas
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Disordered superfluid thin films with cold atoms ππΏ ππ S. Krinner, D. Stadler, J. Meineke, J.-P. Brantut and T. Esslinger Institute for Quantum Electronics, ETH Zürich Motivation Two – dimensional superconducting thin films Superconductor – Insulator Quantum Phase Transition Control Parameter: • Disorder Strength • Film Thickness • Magnetic Field Mechanism: Bosonic vs Fermionic A. Goldman, N. Markovic; Physics Today 51, 11 (1998) V. Ganthmaker, V. Dolgopolov, Physics-Uspekhi 53, 1 (2010) Experimental Setup Degenerate Fermi Gas • Atom number: 105 6Li atoms • Temperature: 0.2 TF Experimental Setup Degenerate Fermi Gas • Atom number: 105 6Li atoms • Temperature: 0.2 TF • Tunable Interactions Experimental Setup Geometry: Mesoscopic two-dimensional channel connected to two reservoirs ππΏ ππ J.-P. Brantut et al., Science 337, 1069 (2012) Inducing a chemical potential bias Symmetric position Inducing a chemical potential bias Symmetric position Shift trap (slow) Inducing a chemical potential bias Symmetric position Shift trap (slow) Evaporative cooling Inducing a chemical potential bias Symmetric position Shift trap (slow) Evaporative cooling Shift trap back (fast) Projection of a disordered potential ππΏ ππ Tuning parameter: Disorder strength Length scales π Disorder: Correlation length π Length scales π Disorder: Correlation length π BEC: Molecule pair size d βͺ π Length scales π Disorder: Correlation length π Unitary Fermi Gas: pair size d ~ π BEC - Resistance of disordered thin film S. Krinner et al., PRL 110, 100601 (2013) BEC - Breakdown of superfluid flow S. Krinner et al., PRL 110, 100601 (2013) BEC - Breakdown of superfluid flow π = 0.29 ππ π = 400 ππΎ π = 3500 π0 S. Krinner et al., PRL 110, 100601 (2013) BEC - Breakdown of superfluid flow Classical Percolation Threshold: π/π = 1.92 S. Krinner et al., PRL 110, 100601 (2013) π = 0.29 ππ π = 400 ππΎ π = 3500 π0 Transport properties – Unitary Fermi Gas Transport properties – Unitary Fermi Gas π = 0.72 ππ π = 550 ππΎ π=∞ Transport properties – Unitary Fermi Gas Percolation threshold for pairs π = 0.72 ππ π = 550 ππΎ π=∞ Insitu observation of a disordered Fermi Gas 20μm Increasing disorder strength Insitu observation of a disordered Fermi Gas V H V H V Increasing disorder strength H Percolation analysis Percolation analysis Level π Percolation analysis Level π Percolation analysis Level π Percolation analysis Level π Percolation analysis Level π Percolation analysis Level π Percolation analysis Level π π/π = 1.4 Percolation analysis Level π π/π = 1.4 π/π = 0.2 Percolation analysis Percolation analysis Fragmented Regime Smooth Regime Pair percolation threshold Conclusion – Unitary Fermi Gas Increasing Disorder (arXiv soon) Outlook: Thermoelectricity J.-P. Brantut et al., arXiv: 1306.5754 Lithium Team J.-P. Brantut S. Krinner D. Stadler J. Meineke T. Esslinger We acknowledge fruitful discussions with: J. Blatter, T.Bourdel, A. Georges, T. Giamarchi, V. Josse, C. Kollath, P. Lugan, C. Mueller, L.Pollet, T. Roscilde, D. Shahar, V. Shenoy, A. Zheludev and W. Zwerger. Summary 1) Transport measurements: Classical Percolation Threshold: π/π = 1.92 S. Krinner et al., PRL 110, 100601 (2013) 2) Insitu study Percolation threshold for pairs Length scales π Disorder: Correlation length π = 0.72 μπ Unitary Fermi Gas: Pair size d ~ ππ −1 ~ π Coherence length ξ ~ ππ −1 ~ π Disorder-induced breakdown of superfluid flow Classical Percolation Threshold: π/π = 1.92 S. Krinner et al., arxiv:1211.7272 (2012), accepted in PRL Length scales Outlook Strongly correlated transport through projected structures Current flow Exponential decay of atom number imbalance Δπ = πleft − πright C π = π πΆ = 170ms 0.1 R 0 0.4 0.8 time (s) π 1 Δπ = Δπ ππ‘ π πΆ Finite resistance although transport through channel is ballistic!? Conduction as transmission Conduction is transmission from one reservoir to another (Landauer) ππΏ ππ Conduction as transmission Conduction is transmission from one reservoir to another (Landauer) ππΏ ππ Contact resistance: Reflection at the contacts Conduction as transmission Conduction is transmission from one reservoir to another (Landauer) ππΏ ππ Contact resistance: Reflection at the contacts Dissipation takes place deeply inside the reservoirs J.-P. Brantut et al., Science 337, 1069 (2012) Why do we not see Josephson oscillations? Length scales : Channel: ~ 30 µm Coherence length: ~ 1µm Time scales : Transport time: ~20 ms Chemical potential diff.: ~ 3 kHz The current has no chance to reverse Disorder-induced breakdown of superfluid flow Disorder-induced breakdown of superfluid flow Drift velocity Density independent quantity: Drift velocity: vd= πΌ/ππ Disorder-induced breakdown of superfluid flow Classical percolation threshold Classical Percolation Threshold: π/π = 1.92 Disorder-induced breakdown of superfluid flow π π΅πΈπΆ πππΌπΉ πΆπ΅πΈπΆ = π ππΌπΉ ππ΅πΈπΆ πΆππΌπΉ Correlation energy Δ§2/ππ2 Classical Percolation Threshold: π/π = 1.92 S. Krinner et al., arxiv:1211.7272 (2012) Thermodynamics External parameter (gate potential V) LDA: Gibbs-Duhem: Intensive quantity (temp. T, pressure P) π(π) = π0 − π(π) → ππ = −ππ π π, π0 ππ = ππ → π = − π(π, π0 ) ππ measure • Transform gate potential into pressure «pressure thermometer» Ku et. al., Science 335, 563-567 (2012) What is Resistance ? Normal conductor Limit of ballistic conductor R≠0 R=0 U I= R R→0 ? I→∞ Landauer Approach What is Resistance ? Landauer Approach – Conduction as Transmission π π π − ππ R=0 • Conduction is transmission from one reservoir to the other. • Prediction: finite resistance for a perfect conductor ! Imry, Landauer Rev. Mod. Phys. 71, S306–S312 (1999) Ohmic conduction • Current at each point in time • Slope gives cond. G • 2 different confinements 3.2 and 3.9 kHz Ultracold Fermi gases: Vortices Current 101 Years ago… Resistance «Mercury practically zero» Delft, Kes Physics Today 63, 38-42 (2010) Temperature • Kamerlingh-Onnes observes «unmeasurably small resistance» ο Discovery of «superconductivity» • But: no such measurements in ultracold Fermi gases! Looking in-situ Intrinsic transport property Thermodynamic scale Drift velocity Pressure ππ = πΌ/ππ π=− π(π, π0 ) ππ Ku, Science 335, 563-567 (2012) Nascimbène, Nature 463, 1057-1060 (2010) Looking in-situ Intrinsic transport property Thermodynamic scale Drift velocity Normalized Pressure ππ = πΌ/ππ π π0 Ideal 2d Fermi gas Ku, Science 335, 563-567 (2012) Nascimbène, Nature 463, 1057-1060 (2010)
