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

Color superfluidity of neutral ultracold fermions in the presence

• f color-orbit and color-flip fields

Carlos A. R. Sa de Melo Georgia Institute of Technology

Yukawa Institute for Theoretical Physics Kyoto, November 8th, 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

• pportunity 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

Doga Kurkcuoglu Ian Spielman

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

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-

• rbit 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. .

Conclusions in words

8

References for today’s talk

9 To appear in PRA To appear in PRL

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 1) Motivation: color superfluidity and ultracold fermions

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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)

12 SdM – Physics Today, October (2008)

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

14

(2008) October Today, Physics

• SdM

K Li, 40

6

F = 9/2 F = 5/2

Simplest example: colored fermions and single interaction channel

15 Single channel

• nly Red and Blue

have contact interactions Green band is inert: non-interacting

BCS Pairing (g << EF or kFas 0-)

kF

• kF

FERMI SEA g EF

µ = EF > 0

16

BEC Pairing (g >> EF or kFas 0+)

FERMI SEA IS DEPLETED EF

Weakly interacting gas of tightly bound Molecules with inert Green fermions

g

2µ = -Eb< 0

17

Feshbach Resonances

) (B a a g

S s →

→

B-dependent scattering length Contact interaction 18

Scattering Length

as g g* BCS BEC

19

E(k) = [(εk – µ)2 + ∆2]1/2

εk Ek BCS (µ > 0) BEC (µ < 0) (µ2 + ∆2)1/2 |∆| εkµ

+ + + + + + + + + + + + + + + +

kF θ

20

E(k) at T = 0 and kx = 0 (S-wave)

µ > 0 µ < 0

Same Topology

21

QCD-like color superfluidity nearly identical to BCS-BEC crossover of SU(2) case

fermions Green inert (2008) Today Physics SdM, +

22

c F c F c F c F c F c F c F c F c c c F c c F c

T T m k T m k T k k n n k n k n

3 3 / 2 2 2 3 3 2 2 2 3 3 / 1 2 3 2 2 3 3 3 2 3 2 2

) 2 / 3 ( 2 / 2 / ) 2 / 3 ( 2 / 3 / scale

• f

Change = = = = = = = π π

fermions Inert

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 2) Introduction to spin-orbit and color-orbit coupling

23

Raman process and spin-orbit coupling

            − + Ω Ω + − 2 2 ) ( 2 2 2 2 ) (

2 2

δ δ m m

R R

k k k k

24

spin-orbit detuning Raman coupling

            Ω − +       −       − − Ω + + 2 2 2 2 2 2

2 2 2 2

m k k m k i k m k i m k

R x R x R R

k k δ δ

25

Rb

87

SU(2) rotation to new spin basis: σx σz; σz σy ; σy σx

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

26

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

27

Raman Process Yb K, Li,

173 40 6

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

28

Kinetic energies of Red, Green and Blue fermions Color-orbit and Color-Zeeman fields Color-flip field

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

29

Colored fermions are a correlated three band system

30 Example of Fermi Surface

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 3) Interacting fermions with color-orbit and color-flip fields

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

spin-orbit detuning Raman coupling

            Ω − +       −       − − Ω + + 2 2 2 2 2 2

2 2 2 2

m k k m k i k m k i m k

R x R x R R

k k δ δ

33

Rb

87

Zeeman and Spin-Orbit Hamiltonian

z z y y x x

h h h σ k σ k σ k 1 k k H ) ( ) ( ) ( ) ( ) ( Matrix n Hamiltonia − − − = ε

34

2 2 2 eff eff eff

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( k k k k k k k k k k

z y x

h h h h h h + + = + = − =

⇓ ⇑

ε ε ε ε

05 . ) ( 71 . ) ( ) ( = = =

F z F x F y x

h k k h h ε ε k k k

2 2 2 2

) ( ) ( ) ( ) (

x z x z

vk h vk h + + = + − =

⇓ ⇑

k k k k ε ε ε ε

Energy Dispersions in the ERD case

Can have intra- and inter-helicity pairing.

35

Bring Interactions Back (real space)

Kinetic Energy Contact Interaction Spin-orbit and Zeeman

36

Bring interactions back: Hamiltonian in initial spin basis

↑ k

ψ

↓ k

ψ

+ ↓ −k

ψ

+ ↑ k

ψ

+ ↓ k

ψ

+ ↑ −k

ψ

↑ −k

ψ

↓ −k

ψ

z

h K − =

↑

) ( ) ( ~ k k ξ

z

h K + =

↓

) ( ) ( ~ k k ξ

37

Bring interactions back: Hamiltonian in the helicity basis

⇑

Φk

⇓

Φk

+ ⇑ −

Φ k

+ ⇓ −

Φ k

+

⇑

Φ

k

+

⇓

Φ

k

⇑ −

Φ k

⇓ −

Φ k

38

Excitation Spectrum

Can be zero

) ( ) ( ) (

eff k

k k h − =

⇑

ξ ξ ) ( ) ( ) (

eff k

k k h + =

⇓

ξ ξ

39

Excitation Spectrum (ERD)

US-2 US-1 d-US-0 i-US-0 = 0

40

Phase diagram for finite spin-orbit coupling and changing Zeeman field

41

d-US-0 i-US-0 US-2 US-1 gapped gapless Triple-point: US-0/US-1/US-2

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

43 Pair operator

No color-orbit and no color-flip fields

44 KE is SU(3) invariant 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! NOT VERY INTERESTING, JUST CROSSOVER!

Add color-orbit and color-flip fields (near zero temperature)

45

bands quasihole 3 and cle quasiparti 3 has Spectrum

Hamiltonian Blocks

46

Mixed (rotated) color basis

47

Zero color-orbit coupling

48

not! is field flip

• color

but zero, is coupling

• rbit
• Color

Ω

gapped. fully are

• ther two

the nodes,

• f

surface a has bands cle quasiparti three the

• f

One

inert. completely is band color mixed

• ne

zero is field flip

• color

When Ω

Non-zero color-orbit coupling

49

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 4) Spectroscopic and thermodynamic properties

50

Non-zero color-orbit coupling

51

R3 R1

point cal pentacriti and Quintuple

Color compressibility near quintuple point

52

2 / 1 , 2

) ( ] / [ λ α κ κ µ κ

c Rm R V T

n n Ω − Ω − = ∂ ∂ =

−

R1 R2 R4 R5 R3

Color compressibility near gapless R1 to fully gapped FG line

53

) ( ln ] / [

, 2

λ κ κ µ κ

c R V T

n n Ω − Ω = ∂ ∂ =

−

R1 FG

Momentum distributions

• f original colors

54 N3

R3 R1 FG

Order parameter tensor (mixed color basis)

55

Order parameter tensor (total pseudo-spin basis)

56

SINGLET AND QUINTET PAIRING

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

57

Conclusions in pictures: color-orbit and color flip fields

58

Conclusions in pictures: color-orbit and color flip fields

59

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-

• rbit 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. .

Conclusions in words

60

THE END

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