1. Department of Physics & Astronomy
Localized Bose-Einstein Condensation in Films of Liquid 4He in Disorder
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
ACNS Meeting
Knoxville, TN
1- 5 June, 2014

2. BEC, Excitations, Superfluidity
Scientific Goals:
Observe Bose Einstein Condensation (BEC), phonon-roton (P-R) modes and superfluidity in liquid helium in porous media (in disorder).
Determine interdependence of BEC, P-R modes and superfluidity
Can have BEC and no superflow in disorder, a localized BEC region (like pseudogap region?)

3. 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.

4. BEC, Superfluidity and Superfluidity
Organization of Talk
Bulk liquid 4He. Measurements of :
- superfluidity (historically first)
- phonon-roton modes
- BEC
BEC, P-R modes, superflow coincide.
Liquid 4He porous media (Bosons in disorder). Superfluidity measured extensively
-P-R modes measured
-BEC (just starting)
P-R modes and BEC exist at temperatures above superfluid phase in PM. P-R modes exist where there is BEC.

5. BEC, Superfluidity and Superfluidity
Organization of Talk (Cont’d)
3. Films in Porous Media (2D Bosons in disorder?). Superfluidity measured extensively
- we measure P-R modes
Do P-R modes and BEC exist at temperatures above superfluid phase in disordered films. Are films more 2D or 3D like?

6. 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

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

8. Phase Diagram of Bulk Helium

9. Phase Diagram Bulk helium

10. BEC, Excitations and Superfluidity
Bulk Liquid 4He
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,
Tλ = 2.17 K SVP
Tλ = 1.76 K bar

11. SUPERFLUIDITY
1938 – Superfluidity observed in He II by Kaptiza and by Allen and Misener.
1938 – Superfluidity interpreted as manifestation of BEC by London
vS = grad φ (r)

12. London
1938 – Superfluidity observed in He II by Kaptiza and by Allen and Misener.
1938 – Superfluidity interpreted as manifestation of BEC by London
vS = grad φ (r)

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

14. BOSE-EINSTEIN CONDENSATION
1924
Bose gas : Φk = exp[ik.r] , Nk
k = 0 state is condensate state for uniform fluids.
Condensate fraction, n0 = N0/N = 100 % T = 0 K

15. Bose-Einstein Condensation: Gases in Traps

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

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

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

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

20. 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 ).

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

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

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

24. BEC, Excitations and Superfluidity
Bulk Liquid 4He
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,
Tλ = 2.17 K SVP
Tλ = 1.76 K bar

25. Phase Diagram Bulk helium

26. Excitations, BEC, and Superfluidity
Bose-Einstein Condensation:
Superfluidity follows from BEC. An extended condensate has a well defined magnitude and phase, <ψ> = √n0eιφ ;
vs ~ 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

27. B. HELIUM IN POROUS MEDIA
AEROGEL* 95% porous
Open 87% porous A
87% porous B
- 95 % sample grown by John Beamish at U of A entirely with deuterated materials
VYCOR (Corning) 30% porous
Å pore Dia. -- grown with B11 isotope
GELSIL (Geltech, 4F) 50% porous
25 Å pores
44 Å pores
34 Å pores
MCM % 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

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

29. Helium in Porous Media: Superfluidity

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

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

32. Liquid 4He in gelsil
25 A pore diameter
Tc ~ 1.3 K

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

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

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

36. S(Q,ω) of Helium in MCM-41 powder

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

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

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

40. Normal Liquid He Response vs Pressure

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

42. P-R modes and BEC: Conclusions
At 34 bar P-R modes exist up to T = 1.5 K, a temperature that is identified with the critical temperature for BEC, TBEC
At 34 bar the response of normal liquid is like that of a classical fluid (the intensity peaks near ω = 0)
Phonon-roton modes at higher wave vector exist at temperatures and pressures where there is BEC.

43. Localization of Bose-Einstein Condensation in disorder
Conclusions:
Observe phonon-roton modes and BEC up to T ~ Tλ
in porous media, i.e. above Tc for superfluidity.
Thus have BEC above Tc in porous media. The temperature range Tc < T <Tλ , is a region of localized BEC.
At temperatures above Tc
- BEC is localized by disorder
- No superflow

44. Phase Diagram in gelsil
Films in gelsil

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

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

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

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

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

50. Phonon-roton and layer mode versus Filling

51. Phonon-roton and layer mode vs temperature

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

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

54. Modes vs Filling F = %

55. Modes vs Filling F = %

56. Temperature Dependence
of modes

57. Modes vs Temperature F = 97 %

58. Mode Intensities vs Temperature

59. Mode Intensities vs Temperature

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

61. Liquid 4He in Disorder and Boson Localization
Conclusions:
At partial fillings, we observe P-R modes (BEC) at temperatures above Tc at temperatures above the superfluid phase.
Above Tc 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, μmol/m**2.

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

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

64. Schematic Phase Diagram: He in Nanoporous media

65. Kamerlingh Onnes

66. Cuprates Superconductors
AF Mott Insulator
Insulator
Metal T
Doping Level
Superconductor
Pseudo-gap Metal 66 66

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

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

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

70. Patches of Energy gap, TC= 65K
Gomes et al. Nature (2005)

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

72. Liquid 4He in Disorder and Boson Localization
Conclusions:
Tc for superfow is supressed below TBEC in porous media. Tc < TBEC in confinement and disorder.
TBEC ~ Tλ .
In the temperature range Tc < T < TBEC 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.

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

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

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

83. Department of Physics & Astronomy
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

84. 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.
Show that there is a temperature range in porous
media (in disorder) where there is BEC but no superflow
in films as in fully filled porous media. This is a Localized BEC region like the pseudogap phase in cuprate superconductors.