Strongly Interacting Fermi Gases: Universal Thermodynamics, Spin Transport, and Dimensional Crossover

Transcription

1 NewSpin, College Station, 1/16/011 Strongly Interacting ermi Gases: Universal hermodynamics, Spin ransport, and Dimensional Crossover Martin Zwierlein Massachusetts Institute of echnology Center for Ultracold Atoms at MI and Harvard

2 Ultracold atomic ermi Gases Ideal test-bed for Many-Body physics unable, resonant interactions ermi mixtures with controllable spin composition All relevant parameters precisely known I. Realize idealized models of many-body physics Benchmarking the many-body problem Need high precision to discriminate between theories - Equation of State of Unitary ermi Gas - Evolution from 3D to D II. Beyond the Standard Model Non-Equilibrium Physics, New States of Matter - Spin ransport

3 Little ermi Collider (LC) A ermi gas collides with a cloud with resonant interactions rom Magnetism to Superfluidity Harmonic rap A. Sommer, M. Ku, G. Roati, MWZ, Nature 47, 01 (011)

4 Little ermi Collider No Interactions, a=0

5 Distance [mm] Evolution without interactions ime [ms]

6 Little ermi Collider Unitary Interactions, 1/a=0

7 1.3 mm 1.3 mm irst collision initial 0 ms ime (1ms per frame)

8 Distance [mm] Later times ime [ms]

9 Distance [mm] 1.0 Much later times 450 ms ime [ms]

10 Universal Spin ransport Relaxation of spin current only due to collisions Resonant scattering cross section: ~ 1 1 k Mean free path: l ~ = interparticle spacing n k A perfect liquid Spin drag coefficient ( Collision rate) Diffusion constant: m D SD ~ nv (mean free path) ~ ~ collision time (100 m) 1 s ~ k m ~ E 1 / m

11 Universal Spin ransport Relaxation of spin current only due to collisions Resonant scattering cross section: ~ 1 1 k Mean free path: l ~ = interparticle spacing n k A perfect liquid Spin drag coefficient ( Collision rate) Diffusion constant: Spin conductivity: D s SD ~ nv ~ k m ~ E (mean free path) ~ ~ collision time n m SD 1 mv ~ k 1 / m

12 s [k /] unable spin conductivity Spin conductivity in cold ermi gases is tunable over a wide range n 1 1 spin = m m v spin ~ k 1 ck a SD 100 Giant Magneto Spin Resistance a /k a

13 Spin Diffusion vs emperature dn dn js ntot d ntot sdd Ds dx dx 5.8 m Quantum Limit of Spin Diffusion it: 6.3(3) m 3/

14 Spin Diffusion for imbalanced mixtures highly imbalanced mixture: ermi liquid Collision rate Pauli blocking Classical Regime emperature A. Sommer, M. Ku, MWZ, NJP 13, (011)

15 Spin Diffusion in Presence of Superfluid Slight imbalance: Normal + Superfluid otal density Difference density Intricate motion of normal unpaired atoms around(?) the superfluid core Lot s of Andreev reflections A. Sommer, M. Ku, MWZ, NJP 13, (011)

16 hermodynamics Equilibrium hermodynamics as baseline for non-equilibrium studies Establish Equation of State Classical gas P nk B Generally need P( n, ) Or fixing chemical potential P(, ) Or replacing n P n(, ),a,...

17 hermodynamics of the Unitary ermi Gas Spin ½ - ermi gas at a eshbach resonance Classical gas Normal state: Is it a ermi liquid? High- ermi Liquid Are there preformed pairs (pseudogap regime)? Superfluid properties: Preformed pairs? ransition temperature Critical Entropy Energy of the superfluid c Low- Superfluid

18 Density Potential Equation of State Equation of state from density distribution in a trap 4 V () r Position Local chemical potential ( r) V( r) Local density n( V) n( V, ) 0 0. he density profile provides a scan 0.0 through the equation of state - -1 Position 0 1

19 Density [10 11 /cm 3 ] Measuring density 1. Cylindrical Symmetry: Inv. Abel Get n(, z). Equidensity lines = Equipotential lines Get as we know V (, z) V ( 0, z) Experimental n(v) from single profile V [K] 1.

20 How to get and? + -??

21 Density [10 11 /cm 3 ] How to get and? Solutions: it wings to high-temperature theory (Virial expansion, Hartree-ock, etc ) n e b e 3b e V [K] 1. hat s what we all do. 3D Bose gas (see recent Cambridge expt.) D Bose Gas: Chicago, ENS, JILA 3D Unitary ermi Gas: ENS ( fixed via 7 Li thermometer) 3 b b b : Beth, Uhlenbeck (1937), Ho, Mueller (004) b 3 : Liu, Hu, Drummond (009), Blume et al. (011) 3

22 No-fit equation of state Energy [E We want: n(, ) We know hus 0 - V d - dv Local compressibility 1 dn 1 dn n d n dv ( n, P) P d n V dv ' n( V ') Compressibility Equation of State No fit at all! V () r 0 V () r Local pressure Position [R Mark J. H. Ku, Ariel. Sommer, Lawrence W. Cheuk, Martin W. Zwierlein arxiv: (011) 0

23 No-fit Equation of State Normalize compressibility & pressure via known density: ~ d d 1 n d d V ~ P P 0 5 P P 0 n or a scale-invariant system p) ~ ~ ( ~

24 Compressibility Equation of State At =0: / 0 1/ P / P 0 0 P 0 P

25 Compressibility Equation of State Getting the temperature scale: ~1 ~ 1 ~ 5 exp ~ ~ p dp p p i i ), ( P n ), ( n / d / d P P P P

26 Compressibility Equation of State Compressibility Sudden rise and fall

27 Specific Heat C V /N At unitarity: E P 3 V CV Nk B d Heat capacity E/ Nk dp/ ne d B 3 N, V d( / ) P P Noninteracting ermi Gas /

28 Specific Heat C V /N At unitarity: E P 3 V CV Nk B d Heat capacity E/ Nk dp/ ne d B 3 N, V d( / ) P P Unitary ermi Gas /

29 At unitarity: E P 3 V CV Nk B d Heat capacity E/ Nk dp/ ne d B 3 N, V d( / ) P P 0 0 A lambda-like feature in the specific heat

30 Compressibility, Heat Capacity, Condensates Compressibility Heat Capacity Condensate raction Direct observation of the superfluid transition at C / = 0.167(13)

31 Compressibility Equation of State Going back to Density Equation of State d / d d d ~ ~ 1 ) / ( / / i i d with i i and known at high temperatures

32 Normalized Density Equation of State Energy Chemical Potential ree Energy New value for : 0.376(5)[8]

33 On resonance: 3 E PV Entropy vs emperature 1 S E PV N S 5 P Nk nk B B Critical Entropy S c 0.73(13) Nk B

34 Density and Pressure Mark J. H. Ku, Ariel. Sommer, Lawrence W. Cheuk, Martin W. Zwierlein arxiv: (011)

35 Strongly Interacting ermi Gases in coupled quasi-d layers High- c Superconductor with stacks of CuO planes Stacks of D coupled fermionic superfluids Access physics of layered superconductors Evolution of ermion Pairing from 3D to D Berezinskii-Kosterlitz-houless transition in deep D limit A.. Sommer, L. W. Cheuk, M. J.-H. Ku, W. S. Bakr, M. W. Zwierlein PRL, to appear, arxiv: (011)

36 Making quasi-d ermi gases Confine tightly in 1 direction 1D lattice (retro-reflected 1064nm) Lattice depths up to 30 E R D-ness tuned by lattice depth Deep lattice:, aspect ratio of ~1:1000

37 Binding Energy from 3D to D (1D lattice) BCS BEC V 0 = 0 E R Orso & Wouters. PRL (005)

38 Binding Energy from 3D to D (1D lattice) BCS BEC V 0 = 5 E R Orso & Wouters. PRL (005)

39 Binding Energy from 3D to D (1D lattice) BCS BEC V 0 = 10 E R Orso & Wouters. PRL (005)

40 Binding Energy from 3D to D (1D lattice) BCS BEC V 0 = 0 E R Orso & Wouters. PRL (005)

41 Evolution of ermion Pairing from 3D to D ~ const. Density of States: 3D D Direct consequence: Always a bound state in D R spectrum: R Spectrum: 3D: I ( th I ) ~ ( ) ( th I ) ~ ( ) ~ ( ) ( k) k k ( ) D: f ln Interactions in final state: ln ( E (( E ) / E ) b f b / E b b )

42 Evolution of ermion Pairing from 3D to D Atom transfer [a.u.] 3D V 0 = E R V 0 = 5 E R V 0 = 6 E R V 0 = 10 E R V 0 = 1 E R D V 0 = 19 E R V 0 = 0 E R R Offset [khz]

43 Atom transfer [a.u.] R Offset [khz] Evolution of ermion Pairing from 3D to D 3D Resonance d/a = 0 E R 3D BCS d/a = E R 5 E R 4 E R 6 E R 10 E R 1 E R 19 E R 5 E R 6 E R 10 E R D 0 E R 18 E R

44 Logarithmic Corrections in Spectra in D ransferred fraction [a.u.] D nature of interactions strongly influence naïve spectra MI Rf spectrum at 690 G, 18 E MI Rf spectrum at 690 G, 18 R MI it Rf spectrum at 690 G, 18 E R it th )/ th )/ it including log-corrections I Pair ( ) ~ R offset [khz] ( th ) ln ln ( E (( f E ) / E ) b f b / E b b )

45 Logarithmic Corrections in Spectra in D ransferred fraction [a.u.] D nature of interactions strongly influence naïve spectra I Pair ( ) ~ 50 ( R offset [khz] th ) ln MI Rf spectrum at 690 G, 18 E R it th )/ with gauss. convolution it including log-corrections with gaussian convolution ln ( E (( f E ) / E ) b f b / E b b )

46 Evolution of ermion Pairing from 3D to D On Resonance (in harmonic trap): E, 0.44z B th Resonance d/a = 0 3D BCS d/a = -1. 3D BCS d/a = -.7 3D D A.. Sommer, L. W. Cheuk, M. J.-H. Ku, W. S. Bakr, M. W. Zwierlein PRL, to appear, arxiv: (011)

47 Deep D regime Comparison with mean-field BEC-BCS in D Prediction: Randeria et al. (1989) Many-body bound state energy = -body bound state energy 3D BCS 3D BEC A.. Sommer, L. W. Cheuk, M. J.-H. Ku, W. S. Bakr, M. W. Zwierlein PRL, to appear, arxiv: (011)

48 Deep D regime Comparison with mean-field BEC-BCS in D Prediction: Randeria et al. (1989) Many-body bound state energy = -body bound state energy D BEC Strong Coupling D BCS Only small deviation observed between many-body and -body bound-state energy A.. Sommer, L. W. Cheuk, M. J.-H. Ku, W. S. Bakr, M. W. Zwierlein PRL, to appear, arxiv: (011)

49 Conclusion & Outlook Spin ransport in a Strongly Interacting ermi Gas Quantum Limited Diffusion Revealing the Superfluid Lambda ransition Compressibility, Density, Pressure No-it EoS Specific Heat, Chemical potential, Entropy, Energy etc. Observe transition at c =0.167(13) ermi gases in D Are those pairs superfluid? Study coherence, thermodynamics, rotation

50 BEC I BEC-BCS Crossover D ermi Gases Ariel Sommer Mark Ku Lawrence Cheuk Dr. Waseem Bakr Dr. arik Yefsah ermi I LiNaK ermi-ermi mixtures Cheng-Hsun Wu Ibon Santiago Jee Woo Park Dr. Peyman Ahmadi Dr. Sebastian Will ermi II ermi Gas Microscope homas Gersdorf akuma Inoue Melih Okan Dr. Waseem Bakr