1. Bose-Einstein Condensation, Superfluidity and Elementary Excitations in Quantum Liquids Henry R. Glyde Department of Physics & Astronomy University of Delaware ISIS Facility Rutherford Appleton Laboratory Harwell, Oxford 17 September, 2013

2. BEC, Excitations, Superfluidity Bose Einstein Condensation (neutrons) 1968- Collective Phonon-Roton modes (neutrons) 1958- Superfluidity (torsional oscillators) `1938- He in porous media integral part of historical superflow measurements.

3. BEC, Superfluidity and Neutrons Scientific Goals : Observe and document BEC and atomic momentum distribution in liquid 4He, 3He-4He mixtures, 3D, 2D. -single particle excitations, S(Q,ω) at high Q, ω -SNS (ARCS), ISIS (MARI) Observe Phonon-roton, layer modes (porous media) -collective modes, S(Q,ω) at low Q, ω -ISIS (ORIRIS,IRIS), ILL (IN5,IN6).Explain Superflow: BEC is the origin superflow

4. BEC and n (k) (single particle excitations) Collaborators: SNS and ISIS Richard T. Azuah - NIST Center for Neutron Research, Gaithersburg, USA Souleymane Omar Diallo - Spallation Neutron source, ORNL, Oak Ridge, TN Norbert Mulders - University of Delaware Douglas Abernathy- Spallation Neutron source, ORNL, Oak Ridge, TN Jon V. Taylor - ISIS Facility, UK Oleg Kirichek - ISIS Facility, UK

5. Collective (Phonon-roton) Modes, Structure Collective (Phonon-roton) Modes, Structure Collaborators:(ILL) JACQUES BOSSY Institut Néel, CNRS-UJF, Grenoble, France Helmut SchoberInstitut Laue-Langevin Grenoble, France Jacques OllivierInstitut Laue-Langevin Grenoble, France Norbert Mulders University of Delaware

6. BEC, Superfluidity and Superfluidity Organization of Talk 1.Phase diagrams: liquid, solid, superfluidity. 2.P-R Modes in liquid 4He. - modes vs pressure - modes in the solid: are there liquid like modes in solid He that superflow? 2. Measurements: BEC, n(k) -bulk liquid 4He, to solidification. -2D helium -Solid helium -Porous media, now and in future.

7. Phase Diagram of Bulk Helium

8. Phase Diagram Bulk helium Phase Diagram Bulk helium

9. Phase Diagram Bulk helium

10. SUPERFLUIDITY SUPERFLUIDITY 1908 – 4 He first liquified in Leiden by Kamerlingh Onnes 1925 – Specific heat anomaly observed at T λ = 2.17 K by Keesom. Denoted the λ transiton to He II. 1938 – Superfluidity observed in He II by Kaptiza and by Allen and Misener. 1938 – Superfluidity interpreted as manifestation of BEC by London v S = grad φ (r)

11. Kamerlingh Onnes Kamerlingh Onnes

12. SUPERFLUID: Bulk Liquid SF Fraction  s (T) Critical Temperature T λ = 2.17 K

13. Landau Theory of Superfluidity Superfluidity follows from the nature of the excitations: - that there are phonon-roton excitations only and no other low energy excitations to which superfluid can decay. - have a critical velocity and an energy gap (roton gap  ).

14. PHONON-ROTON MODE: Dispersion Curve  Donnelly et al., J. Low Temp. Phys. (1981)  Glyde et al., Euro Phys. Lett. (1998) ← Δ

15. BOSE-EINSTEIN CONDENSATION 1924 Bose gas : Φ k = exp[ik.r], N k k = 0 state is condensate state for uniform fluids. Condensate fraction, n 0 = N 0 /N = 100 % T = 0 K Condensate wave function: ψ(r) = √n 0 e iφ(r)

16. Bose-Einstein Condensation: Gases in Traps

17. SUPERFLUIDITY SUPERFLUIDITY 1908 – 4 He first liquified in Leiden by Kamerlingh Onnes 1925 – Specific heat anomaly observed at T λ = 2.17 K by Keesom. Denoted the λ transiton to He II. 1938 – Superfluidity observed in He II by Kaptiza and by Allen and Misener. 1938 – Superfluidity interpreted as manifestation of BEC by London v S = grad φ (r)

18. London

19. Bose-Einstein Condensation: Gases in Traps

20. Bose-Einstein Condensation, Bulk Liquid 4He Glyde, Azuah, and Stirling Phys. Rev., 62, 14337 (2000)

21. Bose-Einstein Condensation: Bulk Liquid Expt: Glyde et al. PRB (2000)

22. Bose-Einstein Condensation Model One Body density matrix: Model momentum distribution: y =k Q = k.Q

23. Full Dynamic Structure Factor Full Dynamic Structure Factor

24. Model One Body Density Matrix: Bulk Helium

25. Bose-Einstein Condensate Fraction Liquid Helium versus Density PR B83, 100507 (2011)

26. BEC: Bulk Liquid 4He vs pressure PR B83, 100507 (R)(2011)

27. Bose-Einstein Condensate Fraction Liquid Helium versus Pressure Glyde et al. PR B83, 100507 (R)(2011)

28. Bose-Einstein Condensate Fraction Liquid Helium versus Density PR B83, 100507 (2011)

29. J(Q,y) and BEC in Liquid Helium at 24 bar Diallo et al. PRB 85, 140505 (R) (2012)

30. Bose-Einstein Condensate Fraction Liquid Helium versus Pressure Diallo et al. PRB 85, 140505 (R) (2012)

31. PHONON-ROTON MODE: Dispersion Curve  Donnelly et al., J. Low Temp. Phys. (1981)  Glyde et al., Euro Phys. Lett. (1998) ← Δ

32. Roton in Bulk Liquid 4 He Talbot et al., PRB, 38, 11229 (1988)

33. Maxon in bulk liquid 4 He Talbot et al., PRB, 38, 11229 (1988)

34. Beyond the Roton in Bulk 4 He Data: Pearce et al. J. Phys Conds Matter (2001 )

35. BEC, Excitations and Superfluidity Bulk Liquid 4 He 1. Bose-Einstein Condensation, 2. Well-defined phonon-roton modes, at Q > 0.8 Å -1 3. Superfluidity All co-exist in same p and T range. They have same “critical” temperature, T λ = 2.17 K SVP T λ = 1.76 K 25 bar

36. Excitations, BEC, and Superfluidity Bose-Einstein Condensation: Superfluidity follows from BEC. An extended condensate has a well defined magnitude and phase, = √n 0 e ιφ ; v s ~ grad φ Landau Theory: Superfluidity follows from existence of well defined phonon-roton modes. The P-R mode is the only mode in superfluid 4He. Energy gap Bose-Einstein Condensation : Well defined phonon-roton modes follow from BEC. Single particle and P-R modes have the same energy when there is BEC. When there is BEC there are no low energy single particle modes.

37. B. HELIUM IN POROUS MEDIA B. HELIUM IN POROUS MEDIA AEROGEL*95% porous Open87% porousA 87% porousB - 95 % sample grown by John Beamish at U of A entirely with deuterated materials VYCOR (Corning)30% porous 70Å pore Dia.-- grown with B 11 isotope GELSIL (Geltech, 4F) 50% porous 25 Å pores 44 Å pores 34 Å pores MCM-4130% porous 47 Å pores NANOTUBES (Nanotechnologies Inc.) Inter-tube spacing in bundles 1.4 nm 2.7 gm sample * University of Delaware, University of Alberta

38. Bosons in Disorder Liquid 4 He in Porous Media Flux Lines in High T c Superconductors Josephson Junction Arrays Granular Metal Films Cooper Pairs in High T c Superconductors Models of Disorder excitation changes new excitations at low energy

39. Helium in Porous Media

40. T c in Porous Media

41. Phonon-Roton Dispersion Curve  Donnelly et al., J. Low Temp. Phys. (1981)  Glyde et al., Euro Phys. Lett. (1998) ← Δ

42. Phonons, Rotons, and Layer Modes in Vycor and Aerogel

43. Intensity in Single Excitation vs. T T c = 2.05 K Glyde et al., PRL, 84 (2000) T c = 2.05 K

44. P-R Mode in Vycor, T = 1.95 K T c = 2.05 K

45. P- R Mode in Vycor: T = 2.05 K T c = 2.05 K

46. Fraction, f s (T), of Total Scattering Intensity in Phonon-Roton Mode- Vycor 70 A pores T c = 2.05 K

47. Fraction, f s (T), of total scattering intensity in Phonon-Roton Mode- gelsil 44 A pore T c = 1.92 K

48. T c ~ 1.3 K Liquid 4 He in gelsil 25 A pore diameter

49. Conclusions: Localization of Bose-Einstein Condensation in disorder Observe phonon-roton modes up to T ~ T λ = 2.17 K in porous media, i.e. above T c for superfluidity. Well defined phonon-roton modes exist because there is a condensate. Thus have BEC above T c in porous media, in the temperature range T c < T <T λ = 2.17 K Vycor T c = 2.05 K gelsil (44 Å) T c = 1.92 K gelsil (25 Å) T c = 1.3 K At temperatures above T c - BEC is localized by disorder - No superflow

50. Helium in Porous Media

51. Helium in MCM-41 (45 A) and in gelsil (25 A) Bossy et al. PRB 84,1084507 (R) (2010)

52. S(Q,ω) of Helium in MCM-41 powder

53. Pressure dependence of S(Q,ω) at the roton (Q=2.1Å -1 ): MCM-41

54. Net Liquid He at 34 bar in MCM-41 Bossy et al. EPL 88, 56005 (2012)

55. Net Liquid He in MCM-41 Temperature dependence Bossy et al. EPL 88, 56005 (2012)

56. Helium in MCM-41 (45 A) and in gelsil (25 A) Bossy et al. PRB 84,1084507 (R) (2010)

57. Schematic Phase Diagram He in Nanoporous media Schematic Phase Diagram He in Nanoporous media Bossy et al., PRL 100, 025301 (2008)

58. Schematic Phase Diagram: He in Nanoporous media Schematic Phase Diagram: He in Nanoporous media

59. Kamerlingh Onnes Kamerlingh Onnes

60. Cuprates Superconductors AF Mott Insulator Insulator Metal T Doping Level Superconductor Pseudo-gap Metal

61. Schematic Phase Diagram High Tc Superconductors Schematic Phase Diagram High Tc Superconductors Alvarez et al. PRB (2005)

62. Patches of Antiferromagnetic and Superconducting regions Patches of Antiferromagnetic and Superconducting regions Alvarez et al. PRB (2005)

63. Helium in MCM-41 (45 A) and in gelsil (25 A) Bossy et al. PRB 84,1084507 (R) (2010)

64. Conclusions: Liquid 4He in Disorder and Boson Localization Below T c in the superfluid phase, have extended BEC. Superfluid – non superfluid liquid transition is associated with an extended to localized BEC cross over. Above T c have only localized BEC (separated islands of BEC).Above T c have only localized BEC (separated islands of BEC). Close to and above T λ have no BEC at all.Close to and above T λ have no BEC at all.

65. Conclusions: BEC Liquid 4He and Solid Helium Neutrons play a unique role in measuring BEC and momentum distributions in liquid and solid helium bulk and in porous media. Condensate fraction in the liquid decreases from 7 % at SVP to 3 % in liquid at solidification pressure. In the solid, n 0 ≤ 0.3 %. Need to correlate measurement with defects in solid (e.g. amorphous solid).In the solid, n 0 ≤ 0.3 %. Need to correlate measurement with defects in solid (e.g. amorphous solid). Can measure BEC in porous media. Opens direct measurement of BEC phases (e.g. localized BEC, amorphous solid) in porous media, in Bosons in disorder.Can measure BEC in porous media. Opens direct measurement of BEC phases (e.g. localized BEC, amorphous solid) in porous media, in Bosons in disorder.