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

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?)

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.

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.

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?

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

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

Phase Diagram of Bulk Helium

Phase Diagram Bulk helium

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

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)

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)

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

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

Bose-Einstein Condensation: Gases in Traps

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

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

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

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

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 ).

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

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

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

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

Phase Diagram Bulk helium

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

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-41 30% 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

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

Helium in Porous Media: Superfluidity

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

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

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

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

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 = 1.3 K At temperatures above Tc - BEC is localized by disorder - No superflow

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

S(Q,ω) of Helium in MCM-41 powder

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

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

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

Normal Liquid He Response vs Pressure

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

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.

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

Phase Diagram in gelsil Films in gelsil

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

Phase diagram of 4He films in gelsil: 25 A

Adsorption Isotherm of 4He in gelsil 25 A pore diameter

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

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

Phonon-roton and layer mode versus Filling

Phonon-roton and layer mode vs temperature

Phonon-roton mode at Filling F = 86 %

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

Modes vs Filling F = 86-97 %

Modes vs Filling F = 86-97 %

Temperature Dependence of modes

Modes vs Temperature F = 97 %

Mode Intensities vs Temperature

Mode Intensities vs Temperature

Phase diagram of 4He films in gelsil: 25 A

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, 20-25 μmol/m**2.

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

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

Schematic Phase Diagram: He in Nanoporous media

Kamerlingh Onnes

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

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

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

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

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

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

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.

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

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

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

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

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.