1. Localized Bose-Einstein Condensation in Liquid 4He in Disorder Henry R. Glyde Department of Physics & Astronomy University of Delaware APS March Meeting Denver, Co 3-7 March, 2014

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, Phonon-roton modes and Superfluidity Scientific Goals : Observe BEC and Phonon-roton modes in bulk liquid helium and in helium in porous media (also layer modes in porous media) Explore the interdependence of BEC, well defined phonon- roton modes and superflow. BEC is the origin superflow. Well defined p-r modes exist because there is BEC.

4. BEC, Superfluidity and Superfluidity Organization of Talk 1.Bulk liquid 4He. Measurements of : - superfluidity (historically first) - phonon-roton modes - BEC BEC, P-R modes, superflow coincide. 2.Measurements in Porous Media (Bosons in disorder) -P-R modes -BEC (just starting) P-R modes and BEC exist at temperatures above superfluid phase in PM. (T C < T < T C ) P-R modes exist where there is BEC.

5. 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

6. 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

7. Phase Diagram of Bulk Helium

8. Phase Diagram Bulk helium Phase Diagram Bulk helium

9. 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)

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

12. 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  ).

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

14. 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)

15. Bose-Einstein Condensation: Gases in Traps

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

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

18. Phase Diagram Bulk helium Phase Diagram Bulk helium

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

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

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

22. Phase Diagram Bulk helium Phase Diagram Bulk helium

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

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

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

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

27. 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

28. Phase Diagram Bulk helium Phase Diagram Bulk helium

29. 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 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. 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

30. 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

31. 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

32. Helium in Porous Media: Superfluidity

33. Superfluid Density in Porous Media Chan et al. (1988)

34. - Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phase Diagram in gelsil: 25 A pore diameter

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

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

37. S(Q,ω) of Helium in MCM-41 powder

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

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

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

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

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

43. Normal Liquid He Response vs Pressure

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

45. P-R modes and BEC: Conclusions 1.At 34 bar P-R modes exist up a specific temperature only, T = 1.5 K, a temperature that is identified as Tc (BEC), critical temperature for BEC. 2.The intensity in the mode decreases with increasing T without mode broadening and vanishes at Tc (BEC), because Tc (BEC) is so low at 34 bars. 3. At 34 bar the response of normal liquid is like that of a classical fluid (the intensity peaks near ω = 0) 3. Phonon-roton modes at higher wave vector exist at temperatures and pressures where there is BEC.

46. BEC: Liquid 4 He in MCM-41 Diallo, Azuah, Glyde et al. (2014)

47. Conclusions: Localization of Bose-Einstein Condensation in disorder Observe phonon-roton modes and BEC up to T ~ T λ 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

51. Localized Bose-Einstein Condensation in Films of Liquid 4He in Disorder Henry R. Glyde Department of Physics & Astronomy University of Delaware APS March Meeting Denver, Co 3-7 March, 2014

52. - Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phase Diagram in gelsil: 25 A pore diameter

53. Phase Diagram in gelsil Films in gelsil

54. Phase diagram of 4He films in gelsil: 25 A

55. Adsorption Isotherm of 4He in gelsil 25 A pore diameter

56. Phonon-Roton Dispersion Curve (in gelsil F = 86 %) Bossy et al. (in preparation) ← Δ

57. Phonon-Roton Dispersion Curve (in gelsil F = 97 %) Bossy et al. (in preparation) ← Δ

58. Phonon-roton and layer mode versus Filling

59. Phonon-roton and layer mode vs temperature

60. Phonon-roton mode at Filling F = 86 %

61. Phonon-roton and layer mode at Filling F = 86 %

62. Modes vs Filling F = 86-97 %

64. Temperature Dependence of modes of modes

65. Mode Intensities vs Temperature

66. Phase diagram of 4He films in gelsil: 25 A

67. Conclusions: Liquid 4He in Disorder and Boson Localization At partial fillings, we observe P-R modes (BEC) at temperatures above T c at temperatures above the superfluid phase. Above T c we have apparently localized BEC, islands of BEC, as at full filling. It is not clear if we have 2D or 3D liquid close to full filling.Above T c we have apparently localized BEC, islands of BEC, as at full filling. It is not clear if we have 2D or 3D liquid close to full filling. P-R modes and superflow start at about the same filling, 20-25 μmol/m**2.P-R modes and superflow start at about the same filling, 20-25 μmol/m**2.

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

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

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

71. Kamerlingh Onnes Kamerlingh Onnes

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

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

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

75. Phase Diagram High Tc Superconductor Phase Diagram High Tc Superconductor Gomes et al. Nature (2007)

76. Patches of Energy gap, T C = 65K Patches of Energy gap, T C = 65K Gomes et al. Nature (2005)

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

78. Conclusions: Liquid 4He in Disorder and Boson Localization T c for superfow is supressed below T BEC in porous media. T c < T BEC in confinement and disorder. T BEC ~ T λ. In the temperature range T c < T < T BEC the BEC is localized to patches, denoted the localized BEC region. The localized BEC region lies between the superfluid and normal phase. Superfluid – non superfluid liquid transition is associated with an extended BEC to localized BEC cross over. Well defined Phonon-roton modes (Q > 0.8 A-1) exist because there is BEC.