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Localized Bose-Einstein Condensation in Films of Liquid 4He in Disorder

This talk discusses the observation of Bose-Einstein condensation (BEC), phonon-roton (P-R) modes, and superfluidity in liquid helium in porous media (in disorder). The interdependence of BEC, P-R modes, and superfluidity is explored, along with the existence of localized BEC regions. The talk also delves into the measurement of superfluidity, P-R modes, and BEC in bulk liquid 4He, as well as in films and porous media.

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Localized Bose-Einstein Condensation in Films of Liquid 4He in Disorder

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  1. Localized Bose-Einstein Condensationin 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 Grenoble, France Jacques Ollivier Institut Laue-Langevin Grenoble, France 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 25 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, 14337 (2000)

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

  18. Bose-Einstein Condensate FractionLiquid Helium versus Pressure Diallo et al. PRB 85, 140505 (R) (2012)

  19. Bose-Einstein Condensate FractionLiquid Helium versus Pressure Glyde et al. PR B83, 100507 (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, 11229 (1988)

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

  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

  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 Tcin porous media, in the temperature range Tc< T <Tλ= 2.17 K VycorTc = 2.05 K gelsil (44 Å) Tc = 1.92 K gelsil (25 Å) Tc = 1.3 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, 56005 (2012)

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

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

  40. Normal Liquid He Response vs Pressure

  41. Helium in MCM-41 (45 A) and in gelsil (25 A) Bossy et al. PRB 84,1084507 (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) 3. 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 Tcin 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 84,1084507 (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

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