Dipolar Fermi gases. Gora Shlyapnikov LPTMS, Orsay, France University of Amsterdam. Outline

Transcription

1 Dipolar Fermi gases Introduction, Gora Shlyapnikov LPTMS, Orsay, France University of Amsterdam Outline Experiments with magnetic atoms and polar molecules Topologcal p x +ip y phase in 2D Bilayer systems of dipolar fermions. BCS-BEC crossover Concluding slide Reisenburg, July 29, 2016 p. 1

2 Dipolar gas Polar molecules or atoms with a large magnetic moment Dipole-dipole interaction V d = d 1 d2 R 2 3( d 1 R)( d 2 R) R 5 1 R 3 d 1 d 2 R long-range, anisotropic repulsion attraction Different physics compared to ordinary atomic ultracold gases Alkali-atom molecules d from 0.6D for KRb to 5.5D for LiCs p. 2

3 Atoms with large µ Remarkable experiments with Cr atoms (µ = 6µ B d 0.05 D) T. Pfau group (Stuttgart) Effects of the dipole-dipole interaction in the dynamics Stability diagram of trapped dipolar BEC Spinor physics in chromium experiments at Villetaneuse, B. Laburthe-Tolra Bubble structure of bosonic Dy in Stuttgart Now dysprosium (µ = 10µ B, (B. Lev)) and erbium (µ = 7µ B, (F. Ferlaino)) are in the game p. 3

4 Fermionic atoms with large µ ermionic Er (Innsbruck) quantum degeneracy, deformation of the Fermi surface Fermionic Dy (Stanford) and Cr (Villetaneuse) quantum degeneracy p. 4

5 Polar molecules. Creation of ultracold clouds Photoassociation ransfer of weakly bound KRb fermionic molecules to the ground rovibrational state U(R) JILA, D. Jin, J. Ye groups KRb Feshbach state R n cm 3 T 200nK E F Ground-state LiCs molecules at Heidelberg Ground-state RbCs molecules in Innsbruck Ground-state KRb bosonic molecules in Tokyo Experiments with NaK (MIT, Munich),KCs (Innsbruck), NaRb (HongKong), LiRb (Vancouver) p. 5

6 Ultracold chemistry Ultracold chemical reactions KRb +KRb K 2 +Rb 2 New trends in ultracold chemistry Suppress instability induce intermolecular repulsion For example, 2D geometry with dipoles perpendicular to the plane d V(r) 1/r 3 r Reduction of the decay rate by 2 orders of magnitude at JILA Select non-reactive molecules, like NaK, KCs, RbCs Creation of ground-state NaK fermionic molecules (MIT, now also Munich) What are prospects for novel physics? p. 6

7 Theoretical studies Collisional physics Julienne (Gaithersburg), Krems (Vancouver), Greene (Purdue) Bohn (Boulder), Dulieu (Orsay), Hutson (Durham) Many-body physics Santos (Hannover), Pupillo (Strassbourg), Demler (Harvard) Zoller/Baranov (Innsbruck), Gorshkov (Maryland) Lewenstein (Barcelona), Carr (Colorado), G.S. Many other works p. 7

8 Are there novel many-body states? Does the dipole-dipole interaction lead to the emergence of novel phases for identical fermions? p. 8

9 Why single-component fermions are interesting? Topological aspects of p x +ip y state in 2D Vortices. Zero-energy mode related to two vortices. (Read/Green, 2000) ε The number of zero-energy states exponentially grows with the number of vortices 2 (N v/2 1) Non-abelian statistics Exchanging vortices creates a different state! Non-local character of the state. Local perturbation does not cause decoherence Topologically protected state for quantum information processing p. 9

10 p-wave resonance for fermionic atoms p-wave resonance Experiments at JILA, ENS, Melbourne, Tokyo, elsewhere ( BCS T c exp 1 ) (k F b) 2 practically zero Molecular and strongly interacting regimes rather high T c, but collisional instability Gurarie/Radzihovsky; Gurarie/Cooper; Castin/Jona-Lazinio g p wave molecules unstable SIR unstable BCS stable B p. 10

11 RF-dressed polar molecules in 2D (Gorshkov et al, 2007) E dc E ac 2B J=1 J=0 σ + polarized RF + constant 0 E dc E ac Dressed states α = A A 2 +Ω 2 ; β = + = α 0,0 +β 1,1 ;, = β 0,0 α 1,1 Ω A 2 +Ω 2 ; A = 1 2 (δ + δ 2 +4Ω 2 ) Two RFD molecules in 2D. The dipole moment is rotating with RF frequency 1/2 d =2 α c β d V eff r d c r d c Large r V eff = (1 3cos 2 φ) d2 c r 3 = d2 c 2r 3; r = md 2 c/2 2 p. 11

12 Fermionic RFD molecules. Superfluid transition Fermionic RFD molecules in a single quantum state in 2D J. Levinsen, N.R. Cooper, G.S. ( ) Attractive interaction for the p-wave scattering (l = ±1) Ĥ = d 2 r ˆΨ (r){ ( 2 /2m) + d 2 r ˆΨ (r )V eff (r r )ˆΨ(r ) µ}ˆψ(r) (r r ) = V eff (r r )ˆΨ(r)ˆΨ(r ) Gap equation (k) = d 2 k (2π) V 2 eff (k k ) (k ) tanh(ǫ(k )/T) 2ǫ(k ) ǫ(k) = ( 2 k 2 /2m µ) 2 + (k) 2 ; µ E F T c E F exp( 3π/4k F r ) (k) = exp(iφ k ) p x +ip y state (l = ±1) p. 12

13 Superfluid transition. Role of anomalous scattering For short-range potentials should be V eff k 2 and T c exp( 1/(k F b) 2 ) This is the case for the atoms Anomalous scattering in 1/r 3 potential Contribution from r 1/k V eff (k) = 8 2 3m (kr ); k = k ( ) 1 T c exp ν(k F ) V eff (k F ) ; ν = m 2π 2 T C exp ( ) 3π 4k F r p. 13

14 Transition temperature Do better than simple BCS. Reveal the role of short-range physics (k ) = Renormalized gap equation { tanh[ǫ(k)/2t] f(k,k) (k) 2ǫ(k) 1 (E k E k i0) } d 2 k (2π) 2 (k) = (k)exp(iφ k );f(k,k)=f(k,k)exp[i(φ k φ k )] scattering amplitude (k) = (k F )f(k,k F )/f(k F,k F ) (k) k F k p. 14

15 2D scattering in the potential with a 1/r 3 tail Scattering amplitude. No transparent exact solution for a finite k Asymptotic method for slow scattering (kr 1) Divide the range of distances into two parts, r < r 0 and r > r 0 The distance r 0 is such that r 0 r, but kr 0 1 V(r) r r 0 * r r < r 0 Match exact zero-energy with free finite-k solution at r = r 0 : f (π/2)d 2 r k 2 lnk r > r 0 interaction as perturbation: f = (8π/3)d 2 k +(π/2)d 2 r k 2 lnk Related results for the off-shell scattering amplitude p. 15

16 f(k,k) = πd 2 kf Manipulate T c? ( 1 2, 1 k2,2, 2 k 2 ) ; k k ; kr 1 Include k 2 -term f = 1 2 πd2 r k 2 ln[kr u] { T c = 2eC π E F exp 3π } 9π2 4k F r 64 ln[k Fr u] Take into account second-order Gor kov-melik-barkhudarov processes p p p (k) = d 2 k (2π) 2 f(k,k ) p δv 2nd order { tanh(ǫ(k )/T) 2ǫ(k ) 1 2(E k E k ) d 2 k (2π) 2 δv(k,k ) tanh(ǫ(k )/T) T c = κe 0.3 F E 0.7 exp { 3π 4k F r 2ǫ(k ) (k ) } ; E = 2 2mr 2 } (k ) E F κ depends on short-range physics and can be varied within 2 orders of magnitude p. 16

17 Collisional stability andt c p-wave atomic superfluids: BCS T c 0 Resonance collisional instability Polar molecules sufficiently large T c and collisional stability V(r) r α in = A m (kr ) 2 ; A α in ( ) cm 2 /s NaK molecules d 2.7 D r 3200a 0 n = cm 2 E F = 2π 2 n/m 100 nk T c 10 nk; τ 2s p. 17

18 Bilayered dipolar fermionic systems d V(ρ) d λ 2 λ ρ { V(ρ) = d 2 1 (ρ 2 +λ 2 ) 3λ 2 } 3/2 (ρ 2 +λ 2 ) 5/2 Dipole-dipole length r = md 2 / 2 V min = 2d2 λ 3 ; Dipole-dipole strength β = r /λ. 0 V(r)rdr = 0 Always a bound state of and dipoles B. Simon, 1974 β 1 ǫ b 2 mλ 2 exp[ 8/β2 +8/β (5+2C 2ln2)] p. 18

19 BCS-BEC crossover ǫ b E F (r b n 1/2 ) f < 0 s-wave BCS pairing ǫ b E F Molecules of and dipoles (interlayer dimers). Molecular BEC New BCS-BEC crossover (Pikovski, Klawunn, Santos, GS), 2010 Baranov et al, 2011, Zinner et al, 2011 p. 19

20 Kosterlitz-Thouless transition Transition temperature ǫ b E F T KT is close to T BCS k F r r 2 /λ 2 Short-range contribution f = 4π 2 /mln(e F /ǫ b ) E F T KT eγ π 2EF ǫ b k F r r /λ 2 2 (λ r ) Anomalous scattering wins { } f(k) = 2 8kr πr2 m 2λ 2 +4πk2 r λ+3π(kr ) 2 lnξkλ ; kλ 1 ξ 6 ( ) 0.46 E0 T KT 0.1 exp{ π } G(k F λ,r /λ) 4k F r E 0 = 2 /mλ 2 ; G(x,y) = (1 πx/2+πy/16x) 1 E F ǫ b Formation of bound pairs by fermions of different layers T KT of a weakly interacting Bose gas p. 20

21 Transition temperature T / E F T c T KT β λk F =0.5 NaK molecules λ 250 nm, n cm 2, k F λ 2, E F 230 nk T KT up to 10 nk p. 21

22 Concluding slide Many possibilities to generate novel many-body states in dipolar Fermi gases Thank you for attention p. 22