1 / 70

冷却原子気体，並びに固体物質における L OFF 超流動研究の現状

07.5.10. 東大. 冷却原子気体，並びに固体物質における L OFF 超流動研究の現状. 岡山大学自然科学研究科 町田一成. 共同研究者　　　市岡優典，水島健，高橋雅裕. Outline. 1) General introduction to cold atom gases: BEC, BCS, and crossover 2) Resonace Fermionic superfluid with mismatched FS’s

lisbet
Download Presentation

冷却原子気体，並びに固体物質における L OFF 超流動研究の現状

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 07.5.10. 東大 冷却原子気体，並びに固体物質におけるLOFF超流動研究の現状 岡山大学自然科学研究科 町田一成 共同研究者　　　市岡優典，水島健，高橋雅裕

  2. Outline 1) General introduction to cold atom gases: BEC, BCS, and crossover 2) Resonace Fermionic superfluid with mismatched FS’s Possible realization of Fulde-Ferrell-Larkin-Ovchinnikov state (FFLO) 3) Microscopic calculation;Bogoliubov-de Gennes (BdG) equation 4) Topological structure of vortex in FFLO; physics of p shift 5) Condensed matter systems; superconductivity in CeCoIn5-- a heavy Fermion material; Quasi-classical Eilenberger formalism 6) Conclusions

  3. Trapping potential Magnetic confinement ⇒3-dimensional harmonic trap Typically, Axial symmetry Inter-atomic interaction a: s-wave scattering length (e.g., a = 2.75nm in 23Na) “Laser cooling” ⇒By using Feshbach resonance, a → ±∞ Trapped atomic gases Neutral atoms: Li, Na, K, Rb, Cs, Cr, Yb, H, He* ⇒ Hyperfine spin F (e.g., 6Li atoms, F = 9/2, 7/2)

  4. trapping cooling imaging

  5. What are statistics of Alkali atoms? Nuclear physics: Odd # neutrons + Odd # protons= Unstable Alkali’s tend to be Bosons: odd p,e even n Why Alkali’s? • Strong transitions in optical/near IR: • Easily manipulated with lasers Composite Bosons: Made of even number of fermions Composite Fermions: odd number of fermions Only Fermionic Isotopes: Alkali Atoms

  6. Observing statistics Hulet et al., Science (2001) Bosons Fermions in situ image Condensation in real & momentum space! Fermi degeneracy

  7. Recent Progress BEC: Li, Na, Rb, Yb, K, Cs, Cr, He, H Fermionic SF: Li, K • Settings • Low Dimension • Rotation • Optical lattices • Ring trap • Chips • States • Vortices (multiply-quantized & coreless vortices) • Soliton • Dipolar BEC • SF-Insulator Transition • Tonks-Girardeau gas & BKT phase • BCS-BEC crossover • Imbalanced Fermionic Superfluid • Controls • Interactions • Population • New Probes • in situ & TOF image (Density) • RF Spectroscopy (Tunneling current, density of states) • Noise Correlations

  8. Spin triplet channel Bound state energy is shifted relative to continuum Energy Bound state (spin singlet) Magnetic field: B B0 Controlling Interaction “Feshbach resonance” between two lowest hf states Scattering is dominated by bound state closest to threshold

  9. Zwierlein et al., Nature (2005) Strong interactions Universality? Fraction of molecules? s-wave scattering length vs Magnetic field: 6Li ← Molecular BEC BCS → Scattering length a bound state Atoms form stable molecules Magnetic Field: B [G]

  10. Dance Analogy (Figures: Markus Greiner) E Fast Dance Slow Dance Every boy is dancing with every girl: distance between pairs greater than distance between people Tightly bound pairs

  11. Ultra cold atoms by laser cooling Atomic Bose-Einsteincondensate (sodium) Molecular Bose-Einsteincondensate (lithium 6Li2) Pairs of fermionicatoms (lithium-6)

  12. Universality Only length-scale near resonance is density: No microscopic parameters enter equation of state Hypothesis:b is Universal parameter -- independent of system Nuclear matter is near resonance!! Binding energy: 2 MeV << proton mass (GeV) pion mass (140 MeV) Implications: Heavy Ion collisions, Neutron stars Tune quark masses: drive QCD to resonance Braaten and Hammer, Phys. Rev. Lett. 91, 102002 (2003) Implications: Lattice QCD calculations Bertsch: Challenge problem in many-body physics (1998): ground state of resonant gas

  13. Calculations Fixed Node Diffusion Monte Carlo G. E. Astrakharchik, J. Boroonat, J. Casulleras, and S. Giorgini, Phys. Rev. Lett. 93, 200404 (2004) Fixed Node Greens Function Monte Carlo J. Carlson, S.-Y Chang, V. R. Pandharipande, and K. E. Schmidt Phys. Rev, Lett. 91, 050401 (2003) Lowest Order Constrained Variational Method H. Heiselberg, J. Phys. B: At. Mol. Opt. Phys. 37, 1 (2004) Linked Cluster Expansion G. A. Baker, Phys. Rev. C 60, 054311 (1999) Ladder (Galitskii) approximation H. Heiselberg, Phys. Rev. A 63, 043606 (2003) Resumation using an effective field theory Steele, nucl-th/0010066 Mean field theory Engelbrecht, Randeria, and Sa de Melo, Phys. Rev. B 55, 15153 (1997) No systematic expansion Experiments: Duke: -0.26(7) Innsbruck: -0.68(1) JILA: -0.4 ENS: -0.3

  14. Superfluidity near resonance E Superfluidity: Needs bosons which condense B Molecules: Atoms: Fermions with attractive interactions -- pair (cf BCS) form superfluid Bosons -- condense, form superfluid Theory: continuously deform one into other; BCS-BEC crossover Leggett, J. Phys. (Paris) C7, 19 (1980) P. Nozieres and S. Schmitt-Rink, J. Low Temp Phys. 59, 195 (1985)

  15. Superfluidity near resonance E All properties smooth across resonance B Pairs shrink BEC BCS B

  16. Fermionic Superfluidity withImbalanced Spin Populations

  17. 350nK 260nK 190nK 70nK SF or Normal ? 50nK 70nK 100nK 50-50% BCS ? Bimodal structure in minority component ⇒the dense in the central area marks the onset of the condensation! Experiments • Zwierlein et al., Science (2006); Nature (2006) TOF images (after expansion) Dashed lines: normal fermions (TF approximation)

  18. Reconstructed 3D profiles from the integrated 2D distributions ⇒Only assuming the axial symmetry Empty core! (P < Pc ~ 0.8)　⇒　locally 50-50% BCS pairing Absorption images In situ & reconstructed 3D images Columnar densities Cross section

  19. Observation of quantum phase transition Critical difference in “Fermi energies” Critical population imbalance Pc

  20. Question Is the density in the superfluid always 50-50%? ⇒ SF-N phase separation or other exotic pairing? Summary of MIT experiments 1. Density profile (integrated & cross-section profiles) Bimodal structure ⇒ Observation of fermionic superfluidity with mismatched spin population Phase separation like profile 2. Direct observation of quantum phase transition Critical population imbalance ~ pairing gap

  21. Universal Physics On resonancea diverges Only remaining energy scales are EF1 and EF2 Condition for breakdown Dm = universal constant ·D will relate EF1 to EF2 and thus pick out a universal number mismatch for breakdown in a harmonic trap: d = 70(3) % The critical imbalance is a measure of the unitary interaction strength!

  22. A condensate emerges from the Fermi sea Increase atom number of smaller cloud: Critical Imbalance dc= 71(3)%

  23. FFLO and -shift physics

  24. magnetization D(z) Fulde & Ferrell, PR 135, A550 (1964) Larkin & Ovchinnikov, JETP 20, 762 (1965) Introduction to FFLO • Superfluid phase in unequal mixture of two species with mismatched FS’s Cooper pairing(k,-k) Cooper pairing(k,-k+q) Cooper pairing has a non-vanishing center-of-mass momentumq (k↑,-k+q↓): spatially inhomogeneous pairing field D(z) ~ exp(iqz) FF state D(z) ~ sin(qz) LO state

  25. K. Machida and H. Nakanishi, PRB30,122 (1984). Physics of p-shift Doubly degenerate ground state Order parameter changes sign When connecting two ground states Midgap state

  26. THEORETICAL FRAMEWORK: Mean-field theory Bogoliubov-de Genns (BdG) equation • Self-consistent condition: Pairing field & particle density

  27. up-spin down-spin +(r) FFLO nodal plane -shift Zeeman splitting 2dm = 1.0 -(r) FFLO State in Uniform System Pairing field |D(r,z)| Local magnetization: r↑ - r↓ -phase shift ① ① Local Density of States (LDOS): Ns(z, E) p-phase shift　→　“mid-gap states” with zero-energy

  28. FFLO nodal plane Ground state at T=0 g=-1.5　⇒　(0)/EF(0) =0.35 and Pc = 0.62 Pairing field (r) P= 0.34 N SF BCS FFLO Density (r) Shell structure!

  29. 0(0)/EF(0) = 0.32 Spatial Profiles of Ground State in finite P Pairing field Local “magnetization” FFLO modulated pairing ⇒ SF is still robust! Pc Condensation radii Locally equal population　⇒　BCS pairing • Ground state in nonzero P at T = 0　⇒　Spatially modulated “FFLO-like” pairing state • With increasing P, the area of suppressed polarization shrinks toward the trap center. • i.e., the stable region of “BCS” pairing shrinks, • BUT, the FFLO oscillation emerges outside region, which allows • the coexistence with excess atoms　⇒　NOT simple BCS-Normal Phase separated state!

  30. Difference Profiles on Resonance Zwierlein et al., Science (2006); Nature (2006) Depletion throughcondensate! ~ Pc = 0.7

  31. Phase diagram at T = 0 “FFLO” ⇒ Pairing state which changes sign “BCS” ⇒ Pairing state having a definite sign BdG in trapped system Critical population imbalance & pair potential ⇒Linear relation in WC limit  Zwierlein et al., Science ‘06 On resonance?

  32. Phase diagram (0)/EF(0) =0.32 Critical temperature at P = 0 c0/ ~ 5.8 Lifshitz (Leung) point TL ~ 0.6Tc0 Tc curve for BCS-Normal phase transition obtained from the gap equation Generic phase diagram e.g., CDW, SDW, and stripe phase etc. ⇒ Transition from C (BCS) to IC (FFLO) phases Critical population imbalance at T = 0 Pc = 0.57

  33. Conclusions Superfluidity of a two-component Fermi gas with asymmetric spin densities based on the microscopic theory approaching from the WC towards SC limits. 1. Superfluid state of unequal mixture at T = 0 • The stable region of “BCS” pairing shrinks • toward the trap center, with increasing P, • while the “FFLO” pairing emerges in the outer region. • The strong suppression of the local “magnetization” • ⇒direct evidence of “superfluidity”. 2. Stable superfluid state in finite T’s and phase diagram • “FFLO” pairing is favored in large P and low T’s • The T-dependence of Pc(T) is observable in the experiment! • Especially, enhancement of Pc in low T region • Generic phase diagram • e.g., (i) Double-phase transition (BCS ⇒ FFLO ⇒ Normal), • (ii) Two second-order phase transition lines • merge in the L point with TL ~ 0.6 Tc0. 50-50% BCS core+FFLO pairing + surrounded by fully polarized normal cloud For the details, Machida, Mizushima, Ichioka, PRL (2006)

  34. Vortex lattices in rotating Fermionic superflid Top imaging Side imaging

  35. Quantized vortices in imbalanced superfluid Direct observation of “superfluidity” in unequal mixture ⇒Quantized vortices induced by external rotation Zwierlein et al., Science 311, 492 (2006) 0.32 P = 1 0.74 0.58 0.48 0.16 0.07 0

  36. Vortex core structure in population imbalance -----why vortex is visible in balance case ? -----why vortex is invisible in imbalance case ? BEC ------ OP----- n (r) BCS ----- OP -----  (r) vortex visibility or invisibility M. Takahashi, et al, PRL (2006)

  37. Local density of states(LDOS) Fermi level: EF P = 0 Vortex center Lowest CdGM state (A) with finite amplitude at core ⇒ Positive shift Caroli-de Gennes-Matricon state & Quantum depletion Hayashi et al., PRL 80, 2921 (1998); JPSJ 67, 3368 (1998) Continuous 2p phase change around the singularity p-phase shift Quasiparticles passing through vortex experience the p-phase shift ↓ Appearance of core-bound state “Caroli-de Gennes-Matricon (CdGM) state”

  38. Caroli-de Gennes-Matricon state & Quantum depletion Hayashi et al., PRL 80, 2921 (1998); JPSJ 67, 3368 (1998) Lowest CdGM state ⇒ Discretization & Positive shift ⇒ Unoccupied at low T vortex core “Quantum depletion” Total density with vortex at T = 0 (solid line) cf Majorana zero mode when chiral p wave px+ipy Vortex center

  39. Reduced quantum depletion inside core in imbalance case Vortex core structure at P = 0.3 and 0/EF= 0.32 Pairing field Densities vortex with imbalance vortex with balance vortex free Local “polarization”: m(r) = n↑(r)-n↓(r) ⇒ Peak at core

  40. Reduced quantum depletion inside core in imbalance case Total density WC “Core filling factor” SC F = n(0)/nmax

  41. Majority@P=0.3 Minority@P=0.3 Total@balanced case Total@P=0.3 It is difficult to see the quantum depletion in imbalanced case But minority component core is still visible in density profile experiment.

  42. Majority@P=0.3 Minority@P=0.3 Total@balanced case Total@P=0.3 It is difficult to see the quantum depletion in imbalanced case But minority component core is still visible in density profile experiment.

  43. Summary Vortex core structure under population imbalance • Core is filled in by majority component ⇒ difficult to see • But minority component core is visible in density profile experiment • This can be checked by in situ imaging (Zweirlein et al. 2006) • Local polarization shows a peak at vortex core • Splitting of CdGM states due to the resonance with mid-gap states at FFLO node Ref: Takahashi, Mizushima, Ichioka, Machida, PRL(2006)

  44. Topological structure of a vortex in FFLO superfluid TM, Ichioka, Machida, PRL 95, 117003 (2005) Ichioka, Adachi, TM, Machida, preprint (2006) What happens in quasiparticle structure if there exists FFLO nodal plane crossing vortex line ? • FFLO modulation vector // Vortex line Vortex line +(r) FFLO nodal plane “-phase shift” -(r) Splitting of CdGM states due to resonance with mid-gap (surface) states

  45. Vortex line 2p phase winding FFLO nodal plane p phase shift Topological structure of a vortex in FFLO superfluid Mizushima, Ichioka, Machida, PRL 95, 117003 (2005) • FFLO state (2D localization): 2-dimensional (planar) defects • ⇒2D localization of excess atoms at nodal plane • Vortex state with BCS-pairing: 1-dimensional (line) defects • ⇒1D accumulation of excess atoms at vortex line • Vortex state with FFLO modulated pairing • →? Paramagnetic moment　⇄　Electronic state (local density of states) Topological structure of the pair potential in the FFLO state

  46. FFLO States With a Vortex Line Neglecting the background potential: V = 0 Local Polarization: m = r↑ - r↓ Pairing field: D0/EF = 0.1, dm = 0.5 FFLO Vortex Missing of local magnetization at the intersection point ? p-shift p+p-shift p-shift Quasiparticles crossing the intersection point cannot experience p phase shift

  47. + p 0 - 0 p Topology of FFLO vortex vortex line: magnetization accumulation due to p shift---line defect m-rod Two dimensional nodal plane: magnetization accumulation due to p shift---planar defect m-sheet • Intersection point of node and vortex: • ＋ p shiftnon-singular No bound state Localized magnetization absent

More Related