Bose-Einstein Condensation, Superfluidity and Elementary Excitations in Quantum Liquids

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 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

6. BEC, Superfluidity and Superfluidity Organization of Talk • Phase diagrams: liquid, solid, superfluidity. • 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

9. Phase Diagram Bulk helium

10. 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)

11. Kamerlingh Onnes

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

15. 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)

16. Bose-Einstein Condensation: Gases in Traps

17. 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)

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 momentum distribution: y =kQ= k.Q Model One Body density matrix:

23. Full Dynamic Structure Factor

24. Model One Body Density Matrix: Bulk Helium

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

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

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

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

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

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

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

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

35. 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

36. 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 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 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

38. 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

39. Helium in Porous Media

40. Tc in Porous Media

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

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

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

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

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

46. Fraction, fs(T), of Total Scattering Intensityin Phonon-Roton Mode- Vycor 70 A pores Tc = 2.05 K

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

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

49. Localization of Bose-Einstein Condensation in disorder Conclusions: • Observe phonon-roton modes up to T ~ Tλ= 2.17 K 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

50. Helium in Porous Media