Spin-imbalanced quasi-2d Fermi gases. Ilya Arakelyan JETLab NC State University

Transcription

1 Spin-imbalanced quasi-d ermi gases Ilya Arakelyan JTLab NC State University

2 JTLab Group PI: J.. Thomas Graduate Students: Willie Ong Chingyun Cheng Jayampathi Kangara Support: ARO DO NS AOSR Graduated Student: Yingyi Zhang

3 Outline Introduction Creating layered quasi-two dimensional ermi gases: Meaning of quasi-d? xperiments Radio-frequency spectroscopy of quasi-d ermi gases: ailure of dimer and D-BCS theories D ermi-polaron model Thermodynamics of quasi-d ermi gases: Density, pressure, and temperature in spin-imbalanced mixtures Phase transition of spin-imbalanced mixtures to a balanced core

4 Creating a Quasi-D ermi Gas CO laser: Standing wave Mirror ~1000 atoms/site, 5.3 mm spacing Individual optical imaging

5 x (µm) Atoms in Standing Wave Trap z (µm)

6 Two-Dimensional Gas h z sin z 1 e m U 0 m D Transverse ermi nergy 0 h N 0 True D if: m 0 h z m 0 h h z 3D if: m 0 h z

7 Quasi-Two-Dimensional Gas h z m 0 True D if: h z Quasi-D if: h z

8 Quasi-D ermi Gases Search for high temperature superconductivity in layered materials: In copper oxide and organic films, electrons are confined in a quasi-two-dimensional geometry Complex, strongly interacting many-body systems Phase diagrams are not well understood xotic superfluids in spin-imbalanced systems nhancement of the superfluid transition temperature compared to true D materials: Heterostructures and inverse layers Quasi-D organic superconductors Intercalated structures and films of transition metals

9 energy Optically-Trapped 6 Li Atoms 6 Li ermi Gas B =3/ =1/ Magnetic field,g

10 Radio requency Spectroscopy Bare Atom Picture b (a s,ν trap ) - dimer binding energy

11 R 1-to-13 spectrum at 70 G Bare atomic transition Calculated dimer binding energies: Bound to free transition b khz b 13.9 khz

12 R 1-to-13 spectrum at 83 G Bare atomic transition Bound to bound transition b 1 = 7.5 khz b 13 = 0.81 khz Dimer theory fails!

13 Many-body physics? BCS Theory in Two Dimensions BCS-Two dimensions: (Randeria 1989) Predicts radio-frequency transition with frequency ω: ħω = Gap equation: b = μ + μ μ + μ h b Dimer Spectrum! No many-body effects on the spectrum!

14 ermi-polaron Gas (Chevy) 1 0, p 0 S kq, q - k S ;1 0 polaron k q kq single spin down cloud of particle-hole pairs

15 Comparison of Polaron Model with Measurements h dimer b 1 b 13 hpolaron p 1 p 13 B(G) ν z (khz) ν meas (khz) ν dimer (khz) ν polaron (khz)

16 Thermodynamics Spin Imbalance n Measure Column Density: c ( x) dy nd ( x y Transverse Density Profiles: n ( ) ) D

17 Column Densities versus N /N 1 Majority state: N per site b = D dimer binding energy Minority state: N N 1 = D ideal gas ermi energy 83 G G b b

18 Quasi- D ermi Gas Temperature T U T U n D n n e e T R N n ~ ]/ ~ ~ [ ~ )] / ( ~ ~ [ ) ( ln ~ ) ( m m Normalization determines µ 0 ) ( ) ( y x dy n x n c it Column Density: n nh z m m 0 ) ( ) ( ) ( n n D n n Total D-Density

19 Quasi-D ermi Gas Spatial Profiles / b =.1 it n = 0 only / b = 6.6 N /N 1 = 0.1 N /N 1 = 0.5 N /N 1 = 1 it n = 0,1, n = 0 contribution T/T = 0.1 T/T = 0.18 T/T = 0.14

20 Majority and Minority Radii b = D dimer binding energy = D ideal gas ermi energy Ideal gas Thomas-ermi radius - Majority b 6.6 b 0.75

21 Majority and Minority Radii b 6.6 m b b 0.75 Ideal gas D-BCS balanced

22 D-Polaron Thermodynamics 1 1 ree energy density of imbalanced gas: f n n n () 1 1 p Polaron energy: 1 h m n 1 p( ) ym( q 1 1 q1 b y m 1) ( q 1 ) log(1 q Ideal ermi gas 1 ) Minority Polaron nergy Klawunn and Recati 011 Chemical potentials: f n 1 = μ 1 = μ 10 U ρ, f n = μ = μ 0 U(ρ) Pressure: p n1m 1 nm f

23 Majority and Minority Radii b 6.6 b 0.75 Ideal gas Polaron model D-BCS balanced

24 Predicted Density Profiles / b = 0.75 N /N 1 = 0.5 n D n ideal Minority Majority

25 Transition to a Balanced Core? Balanced Core D-Profile: n D ( ) A[ R] [ R1 ](1 / R 1 ) balanced core ρ < R N /N 1 = 0.35 / b = 0.75 data model

26 D-Central Density Ratio b b b Polaron model Ideal gas Transition to balanced core: Not predicted!

27 Summary BCS theory for a true D system fails in the quasi-d regime. D polaron model explains several features of the density profiles in the quasi-d regime. D polaron model with the analytic approximation is too crude to predict the transition to a balanced core. Measurements with imbalanced mixtures provide the first benchmarks for predictions of the phase diagram for quasi-d ermi gases.