Signatures of Superfluidity in Dilute Fermi Gases near a Feshbach Resonance

Transcription

1 Signatures of Superfluidity in Dilute ermi Gases near a eshbach Resonance A. Bulgac (Seattle), Y. Yu (Seattle Lund) P.. Bedaque (Berkeley), G.. Bertsch (Seattle), R.A. Broglia (Milan), A.C. onseca (Lisbon) These slides will be posted shortly at

2 Topics Brief/incomplete survey of theory and experiment Superfluid LDA (SLDA) Vortex structure Collective oscillations Atom Molecule mixtures

3 Bertsch Many-Body X challenge, Seattle, 1999 What are the ground state properties of the many-body system composed of spin ½ fermions interacting via a zero-range, range, infinite scattering-length contact interaction. In 1999 it was not yet clear, either theoretically or experimentally, whether such fermion matter is stable or not. - systems of bosons are unstable (Efimov effect) - systems of three or more fermion species are unstable (Efimov effect) Baker (winner of the MBX challenge) concluded that the system is stable. See also Heiselberg (entry to the same competition) Carlson et al (003) ixed-node Green unction Monte Carlo and Astrakharchik et al. (004) N-DMC provided best the theoretical estimates for the ground state energy of such systems. Thomas Duke group (00) demonstrated experimentally that such systems are (meta)stable.

4 Expected phases of a two species dilute ermi system BCS-BEC crossover High T, normal atomic (plus a few molecules) phase T Strong interaction weak interactions weak interaction BCS Superfluid a<0 no -body bound state Molecular BEC and Atomic+Molecular Superfluids a>0 shallow -body bound state halo dimers 1/a

5 Density unctional Theory (DT) Hohenberg and Kohn, 1964 E gs rε[ ρ( r )] 3 = d particle density Local Density Approximation (LDA) Kohn and Sham, Egs = drερr τr i= 1 i= 1 [ ( ), ( )] N ρ( r) = ψ ( r) N τ( r) = ψ ( r) i i Normal ermi systems only!

6 number and kinetic densities anomalous density Cutoff and position running coupling constant! Superfluid LDA (SLDA) nr ( ) v ( r), ( r) v ( r) = k τ = k 0< E < E 0< E < E ν ( r) = v ( r)u ( r) 0< E < E k k c k c c * k k Divergent! 3 5/3 * E = dr τ( rnr ) ( ) + β[ xr ( )] nr ( ) [ xr ( )] ν ( r) m m γ eff [ xr ( )] 1 [ xr ( )] = ν ( r), xr ( ) = 1/3 m n( r) k ( r) a T + U( r) µ ( r ) u() k r u() k r E * = i ( r) ( T + U( r) µ ) v() k r v() k r Bogoliubov-de Gennes like equations. Correlations are however included by default!

7 Chang, Pandharipande, Carlson and Schmidt physics/ r 1 n 0 1/3 a E 3 ς 5ι = ε[ n] ε ξ, ξ 0.44, ς 1, ι 1 N GMC 5 k a 3( k a) 7/3 3 π k k GMC ε n ε 3π 1 exp, =, =, x = e k a m k a ε SLDA [ nn ] = ε n+ kin 5/3 ν β[ x] n + γ[ x] + Renormalization 1/3 m m n Dimensionless coupling constants

8 Chang et al. physics/ Astrakharchik et al, cond-mat/

9 Vortex in fermion matter r i n ikz u α kn ( ) u α( ρ)exp[ ( + 1/ ) φ ] =, n - half-integer v α kn ( r) v α( ρ)exp[ i( n 1/) φ ikz] ( r) = ( ρ)exp( iφ), r = ( ρ, φ, z) [cyllindrical coordinates] Oz - vortex symmetry axis Ideal vortex, Onsager's quantization (one per Cooper pair) 1 V ( ) ( ) v r ( y, x,0) V r dr m = v mρ π = C

10 How can one put in evidence a vortex in a ermi superfluid? Hard to see, since density changes are not expected, unlike the case of a Bose superfluid. However, if the gap is not small, one can expect a noticeable density depletion along the vortex core, and the bigger the gap the bigger the depletion, due to an extremely fast vortical motion. vs T < v T ε NB T c unknown in the strong coupling limit! c

11 The depletion along the vortex core is reminiscent of the corresponding density depletion in the case of a vortex in a Bose superfluid, when the density vanishes exactly along the axis for 100% BEC. rom Ketterle s group ermions with 1/k a = 0.3, 0.1, 0, -0.1, -0.5 Bosons with na 3 = 10-3 and 10-5 Extremely fast quantum vortical motion! Number density and pairing field profiles Local vortical speed as fraction of ermi speed

12 Sound in infinite fermionic matter ω = v s k Local shape of ermi surface Sound velocity Collisional Regime - high T! Compressional mode Spherical v s v 3 irst sound Superfluid collisionless- low T! Compressional mode Normal ermi fluid collisionless - low T! Incompressional mode Spherical Elongated along propagation direction v v s s s > 1 v 3 = sv Anderson-Bogoliubov sound Landau s zero sound

13 Diabatic (approximate) frequency Landau s zero sound regime Grimm s group experiment Thomas group experiment Transition region from Anderson-Bogoliubov sound to Landau zero sound Adiabatic frequency Anderson-Bogoliubov sound

14 requency shifts in these modes might carry information about possible atom-halo dimer mixture 3 k ς 5ι 1 ε( n) = ξ + O 5 m ka ka ka ξ 0.44, ς 1, ι 1 U = δω ω ( + + λ ) mω x y z 0 ς = ξ k 1 K (0) a ( ) ( ) 3 Adiabatic regime Spherical ermi surface Perturbation theory result using GMC equation of state in a trap

15 Consider now a dilute mixture of fermionic atoms and (bosonic) dimers at temperatures smaller than the dimer binding energy (a>0 and a r 0 ) E V = 3 5 k m n f π a + m n f 3.537π + m a n f n b 0.6π + m a n b + ε n b + corrections 3 k n f =, ε = - 3π ma Even though atoms repel there is BCS pairing! fbf bb (, ω ) = U q U U fb n ε ω ε ( ε + nu ) bb, εq b mb in coordinate representation at ω = 0 U fbf 4π a = = m U () r = exp U fb 1 r bb 4πξb r ξb b q q q b bb q One can show that pairing is typically weak in dilute systems! Induced fermion-fermion interaction Bardeen et al. (1967), Heiselberg et al. (000), Bijlsma et al. (000) Viverit (000), Viverit and Giorgini (000) coherence/healing length

16 The atom-dimer mixture can potentially be a system where relatively strong coupling pairing can occur. ( ) 1 7/3 k ln 1 4kξ + b = exp e m πka 4kξ b /ε 0.1 n b a 3 = (solid line) n b a 3 =0.037(dashed line) p-wave pairing (dots) n /n f b

17 How this atomic-molecular cloud really looks like in a trap? Core: Molecular BEC Crust: normal ermi fluid Mantle: Molecular BEC + Atomic ermi Superfluid Everything s made of one kind of atoms only, in two different hyperfine states.

18 Main conclusions Theory: easy easy hard hard easy ermion superfluidity, more specificaly superflow, has not yet been demonstrated unambiguously experimentally. There is lots of circumstantial evidence and facts in agreement with theoretical models assuming its existence. Vortices!? Theory is able to make very precise predictions in this regime and the agreement with experiment can be check quantitatively.