Color superfluidity of neutral ultracold fermions in the presence - PowerPoint PPT Presentation

Color superfluidity of neutral ultracold fermions in the presence of color-orbit and color-flip fields Carlos A. R. Sa de Melo Georgia Institute of Technology Yukawa Institute for Theoretical Physics Kyoto, November 8 th , 2017 1

謝辞 この素晴らしいシンポジウムの主催者の皆さま、 発表させていただきましてありがとうございます。 私は日本語話せませんし、今日たくさんの外国 人の方がいらっしゃいますし、申し訳ございませ んが英語で発表をさせていただきます。 2

Acknowledgement I would like to thank the organizers for the opportunity to speak at this Symposium. Since I can not speak Japanese and many people here are from overseas, I will have to speak in English. 3

Acknowledgements Ian Spielman Doga Kurkcuoglu 4

Outline of talk 1) Motivation: color superfluidity and ultracold fermions 2) Introduction to spin-orbit and color-orbit coupling 3) Interacting fermions with color-orbit and color-flip fields 4) Spectroscopic and thermodynamic properties 5) Conclusions 5) Conclusions 5

Conclusions in pictures: color-orbit and color flip fields 6

Conclusions in pictures: color-orbit and color flip fields 7

Conclusions in words . Ultracold fermions with three internal states can exhibit very unusual color superfluidity in the presence of color-orbit and color-flip fields, where SU(3) symmetry is explicitly broken. The phase diagram of color-flip versus interaction parameter for fixed color- orbit coupling exhibits several topological phases associated with the nodal structure of the quasiparticle excitation spectrum. The phase diagram exhibits a pentacritical point where five nodal superfluid phases merge. Even for interactions that occur only in the color s-wave channel, the order parameter for superfluidity exhibits singlet, triplet and quintuplet components due to the presence of color-orbit and color-flip fields. These topological phases can be probed through measurements of spectroscopic properties such as excitation spectra, momentum distributions and density of states. 8

References for today’s talk To appear in PRA To appear in PRL 9

Outline of Talk 1) Motivation: color superfluidity and ultracold fermions 1) Motivation: color superfluidity and ultracold fermions 2) Introduction to spin-orbit and color-orbit coupling 3) Interacting fermions with color-orbit and color-flip fields 4) Spectroscopic and thermodynamic properties 5) Conclusions 10

Motivation: color superfluidity and ultracold fermions • Why studying ultracold fermions is important? • Because it allows for the exploration of several fundamental properties of matter, such as superfluidity, which is encountered in atomic, condensed matter, nuclear and astrophysics. 11

Possible phase diagram for Quantum Chromodynamics (QCD) SdM – Physics Today, October (2008) 12

QCD and ultracold fermions (UCF) with three internal states: SU(3) case • QCD – gluons mediate interactions • QCD – s-wave interactions are not controllable • QCD - quark masses are different • QCD – quarks are charged • QCD – quarks have three colors (internal states) • UCF – contact interactions • UCF – s-wave interactions are controllable • UCF – Fermi atoms masses are the same • UCF – Fermi atoms are neutral • UCF – Fermi atoms can have three internal states 13

Ultracold fermions (UCF) with two internal states: SU(2) case F = 5/2 6 Li, 40 K F = 9/2 SdM - Physics Today, October (2008) 14

Simplest example: colored fermions and single interaction channel Single channel only Red and Blue have contact interactions Green band is inert: non-interacting 15

BCS Pairing (g << E F or k F a s � 0 - ) µ = E F > 0 FERMI SEA k F E F g -k F 16

BEC Pairing (g >> E F or k F a s � 0 + ) FERMI SEA IS DEPLETED E F Weakly interacting gas of tightly bound Molecules with inert Green fermions g 2µ = -E b < 0 17

Feshbach Resonances ( B ) → s → g a a Contact B-dependent S interaction scattering length 18

Scattering Length a s BEC g * g BCS 19

E(k) = [( ε k – µ ) 2 + ∆ 2 ] 1/2 + + + + θ BEC ( µ < 0) E k + + + + + + + + k F + + + + (µ 2 + ∆ 2 ) 1/2 BCS ( µ > 0) |∆| ε k ε k µ 20

E(k) at T = 0 and k x = 0 (S-wave) µ > 0 µ < 0 Same Topology 21

QCD-like color superfluidity nearly identical to BCS-BEC crossover of SU(2) case Inert fermions Change of scale 3 / 3 2 = π n k 2 2 c F c 3 2 / 2 = π n k 3 3 c F c = n n 2 3 c c ( 3 / 2 ) 1 / 3 = k k 2 3 F c F c 2 / 2 = T k m 2 2 F c F c 2 / 2 = T k m 3 3 F c F c ( 3 / 2 ) 2 / 3 = T T 2 3 F c F c SdM, Physics Today (2008) inert Green fermions + 22

Outline of Talk 1) Motivation: color superfluidity and ultracold fermions 2) Introduction to spin-orbit and color-orbit coupling 2) Introduction to spin-orbit and color-orbit coupling 3) Interacting fermions with color-orbit and color-flip fields 4) Spectroscopic and thermodynamic properties 5) Conclusions 23

Raman process and spin-orbit coupling ( k k ) 2 − δ Ω   + R   2 2 2 m   ( k k ) 2 Ω + δ −   R   2 2 2 m   24

SU(2) rotation to new spin basis: σ x � σ z ; σ z � σ y ; σ y � σ x 87 Rb spin-orbit k 2 2 + Ω δ k k   + − −   i k R R   detuning   x 2 2 2 m m     k 2 2 δ + Ω k k Raman    −  − i R k R   x 2 2 2  m m  coupling     25

Experimental phase diagram for 87 Rb: bosons with two internal states (spin-1/2) 26

Case with three internal states: color-orbit and color flip fields 6 Li, 40 K, 173 Yb Raman Process 27

Case with three internal states color-orbit and color-flip fields Kinetic energies of Red, Green and Blue fermions Color-orbit and Color-Zeeman fields Color-flip field 28

Case with three internal states: color-orbit and color flip fields 29

Colored fermions are a correlated three band system Example of Fermi Surface 30

Outline of Talk 1) Motivation: color superfluidity and ultracold fermions 2) Introduction to spin-orbit and color-orbit coupling 3) Interacting fermions with color-orbit and color-flip fields 3) Interacting fermions with color-orbit and color-flip fields 4) Spectroscopic and thermodynamic properties 5) Conclusions 31

Start with SU(2) case • For simplicity and to gain insight let me start first with the SU(2) case: two colors or simple peudospin-1/2 fermions. • How spin-orbit and Zeeman fields change the crossover from BCS to BEC as interactions are tuned? 32

87 Rb k 2 2 + Ω δ spin-orbit k k   + − −   i k R R     x 2 2 2 m m detuning     k 2 2 δ + Ω k k    −  − i R k R Raman   x 2 2 2  m m  coupling     33

Zeeman and Spin-Orbit Hamiltonian Hamiltonia n Matrix H ( k ) ( k ) 1 ( k ) ( k ) ( k ) = ε − − − h h h 0 x x y y z z σ σ σ ( ) ( ) ( ) k k k ε = ε − h eff ⇑ ( ) ( ) ( ) k k k ε = ε + h eff ⇓ 2 2 2 ( ) ( ) ( ) ( ) k k k k = + + h h h h eff x y z 34

Energy Dispersions in the ERD case ( k ) 0 = h x ( ) k h k y 0 . 71 = x ε k F F ( ) k h 0 . 05 = z ε F 2 ( k ) ( k ) 2 ε = ε − + h vk z x Can have intra- and ⇑ inter-helicity pairing. 2 ( k ) ( k ) 2 ε = ε + + h vk z x ⇓ 35

Bring Interactions Back (real space) Kinetic Energy Spin-orbit and Zeeman Contact Interaction 36

Bring interactions back: Hamiltonian in initial spin basis ψ ψ + + ψ ψ ↑ ↓ k k − k ↓ − k ↑ + ψ ↑ k + ψ ↓ k ψ − k ↑ ψ − k ↓ ~ ~ ( k ) ( k ) ( k ) ( k ) = ξ − = ξ + K h K h z z ↑ ↓ 37

Bring interactions back: Hamiltonian in the helicity basis Φ k Φ k Φ k + + Φ k − − ⇓ ⇑ ⇓ ⇑ + Φ k ⇑ + Φ k ⇓ Φ k − ⇑ Φ k − ⇓ 38

Excitation Spectrum Can be zero ( k ) ( k ) eff k ( ) ξ = ξ − h ⇑ ( k ) ( k ) eff k ( ) ξ = ξ + h ⇓ 39

Excitation Spectrum (ERD) US-1 US-2 i-US-0 d-US-0 = 0 40

Phase diagram for finite spin-orbit coupling and changing Zeeman field gapped d-US-0 i-US-0 gapless US-2 US-1 Triple-point: US-0/US-1/US-2 41

Now look at SU(3) case • Let me analyze the SU(3) case: three colors or pseudo-spin-1 fermions. • How color-orbit and color-flip fields change the crossover from BCS to BEC as interactions are tuned? 42

SU(3) invariant kinetic energy and three identical interaction channels Pair operator 43

No color-orbit and no color-flip fields KE is SU(3) invariant NOT VERY INTERESTING, JUST CROSSOVER! Can go to a mixed color basis where only two mixed colors pair and the third one is inert as a result of SU(3) invariance! 44