Localized Bose-Einstein Condensation in Liquid 4He in Disorder

1. Localized Bose-Einstein Condensationin 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 • Bulk liquid 4He. Measurements of : - superfluidity (historically first) - phonon-roton modes - BEC BEC, P-R modes, superflow coincide. • 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. (TC < T < TC ) 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 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

7. Phase Diagram of Bulk Helium

8. Phase Diagram Bulk helium

9. SUPERFLUIDITY 1908 – 4He first liquified in Leiden by Kamerlingh Onnes 1925 – Specific heat anomaly observed at Tλ= 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 vS = 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 vS = grad φ (r)

11. SUPERFLUID: Bulk Liquid SF Fraction s(T) Critical Temperature Tλ = 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 ← Δ Donnelly et al., J. Low Temp. Phys. (1981)  Glyde et al., Euro Phys. Lett. (1998)

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 Condensate wave function: ψ(r) = √n0 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

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

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

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

22. Phase Diagram Bulk helium

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

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

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

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

27. 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

28. 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, <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

30. 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

31. 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

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 ← Δ  Donnelly et al.,J. Low Temp. Phys. (1981)  Glyde et al.,Euro Phys. Lett. (1998)

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

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 • 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. • 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. • 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 4He in MCM-41 Diallo, Azuah, Glyde et al. (2014)

47. 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