Localized Bose-Einstein Condensation in Localized Bose-Einstein Condensation in Liquid 4He in DisorderLiquid 4He in Disorder

Henry R. GlydeDepartment of Physics & Astronomy

University of Delaware

APS March Meeting Denver, Co3-7 March, 2014

BEC, Excitations, SuperfluidityBEC, Excitations, Superfluidity

Bose Einstein Condensation (neutrons)1968-

Collective Phonon-Roton modes (neutrons)1958-

Superfluidity (torsional oscillators)` 1938-

He in porous media integral partof historical superflow measurements.

BEC, Phonon-roton modes and SuperfluidityBEC, 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.

BEC, Superfluidity and SuperfluidityBEC, Superfluidity and Superfluidity

Organization of Talk

1. Bulk liquid 4He. Measurements of : - superfluidity (historically first) - phonon-roton modes - BEC BEC, P-R modes, superflow coincide.

2. 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.

BEC and n (k) (single particle excitations)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 Collective (Phonon-roton) Modes, Structure

Collaborators: (ILL)

JACQUES BOSSY Institut Néel, CNRS- UJF, Grenoble, France

Helmut Schober Institut Laue-LangevinGrenoble, France

Jacques Ollivier Institut Laue-LangevinGrenoble, France

Norbert Mulders University of Delaware

Phase Diagram of Bulk HeliumPhase Diagram of Bulk Helium

Phase Diagram Bulk heliumPhase Diagram Bulk helium

SUPERFLUIDITYSUPERFLUIDITY1908 – 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)

LondonLondon

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 SUPERFLUID: Bulk Liquid SF Fraction ss(T) (T)

Critical Temperature Tλ = 2.17 K

Landau Theory of SuperfluidityLandau 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 CurvePHONON-ROTON MODE: Dispersion Curve

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

← Δ

BOSE-EINSTEIN CONDENSATIONBOSE-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 KCondensate wave function: ψ(r) = √n0 e iφ(r)

Bose-Einstein Condensation: Gases in TrapsBose-Einstein Condensation: Gases in Traps

Bose-Einstein Condensation, Bulk Liquid 4HeBose-Einstein Condensation, Bulk Liquid 4He

Glyde, Azuah, and StirlingPhys. Rev., 62, 14337 (2000)

Bose-Einstein Condensation: Bulk LiquidBose-Einstein Condensation: Bulk Liquid

Expt: Glyde et al. PRB (2000)

Phase Diagram Bulk heliumPhase Diagram Bulk helium

BEC: Bulk Liquid BEC: Bulk Liquid 4He vs pressure4He vs pressure

PR B83, 100507 (R)(2011)

Bose-Einstein Condensate FractionBose-Einstein Condensate FractionLiquid Helium versus PressureLiquid Helium versus Pressure

Glyde et al. PR B83, 100507 (R)(2011)

Bose-Einstein Condensate FractionBose-Einstein Condensate FractionLiquid Helium versus PressureLiquid Helium versus Pressure

Diallo et al. PRB 85, 140505 (R) (2012)

Phase Diagram Bulk heliumPhase Diagram Bulk helium

PHONON-ROTON MODE: Dispersion CurvePHONON-ROTON MODE: Dispersion Curve

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

← Δ

Maxon in bulk liquid Maxon in bulk liquid 44He He

Talbot et al., PRB, 38, 11229 (1988)

Roton in Bulk Liquid Roton in Bulk Liquid 44HeHe

Talbot et al., PRB, 38, 11229 (1988)

Beyond the Roton Beyond the Roton in Bulk in Bulk 44HeHe

Data: Pearce et al. J. Phys Conds Matter (2001)

BEC, Excitations and SuperfluidityBEC, Excitations and Superfluidity

Bulk Liquid Bulk Liquid 44HeHe

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 heliumPhase Diagram Bulk helium

Excitations, BEC, and SuperfluidityExcitations, 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 MEDIAB. HELIUM IN POROUS MEDIA

AEROGEL* 95% porousOpen 87% porous A

87% porous B- 95 % sample grown by John Beamish at U of A entirely with deuterated

materials

VYCOR (Corning) 30% porous70 Å pore Dia. -- grown with B11 isotope

GELSIL (Geltech, 4F) 50% porous25 Å pores44 Å pores34 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 DisorderBosons 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 Disorderexcitation changesnew excitations at low energy

Helium in Porous Media: SuperfluidityHelium in Porous Media: Superfluidity

Superfluid Density in Porous MediaSuperfluid Density in Porous Media

Chan et al. (1988)

- - Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)

Phase Diagram in gelsil: 25 A pore diameterPhase Diagram in gelsil: 25 A pore diameter

Helium in MCM-41 (45 A) and in gelsil (25 A)Helium in MCM-41 (45 A) and in gelsil (25 A)

Bossy et al. PRB 84,1084507 (R) (2010)

Phonon-Roton Dispersion CurvePhonon-Roton Dispersion Curve

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

← Δ

S(Q,ω) of Helium in MCM-41 powder

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

Net Liquid He at 34 bar in MCM-41

Bossy et al. EPL 88, 56005 (2012)

Tc ~ 1.3 K

Liquid Liquid 44He in gelsil He in gelsil 25 A pore diameter 25 A pore diameter

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)Helium in MCM-41 (45 A) and in gelsil (25 A)

Bossy et al. PRB 84,1084507 (R) (2010)

P-R modes and BEC: ConclusionsP-R modes and BEC: Conclusions

1. At 34 bar P-R modes exist up a specific temperature only, T = 1.5 K, a temperature that isidentified as Tc (BEC), critical temperature for BEC.

2. 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.

3. 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.

BEC: Liquid BEC: Liquid 44He in MCM-41He in MCM-41

Diallo, Azuah, Glyde et al. (2014)

Conclusions:Conclusions:

Localization of Bose-Einstein Condensation in disorderLocalization of Bose-Einstein Condensation in disorder

• 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

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

Henry R. GlydeDepartment of Physics & Astronomy

University of Delaware

APS March Meeting Denver, Co3-7 March, 2014

- - Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)

Phase Diagram in gelsil: 25 A pore diameterPhase Diagram in gelsil: 25 A pore diameter

Phase Diagram Phase Diagram in gelsil in gelsil

Films in gelsilFilms in gelsil

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

Adsorption Isotherm of 4He in gelsil Adsorption Isotherm of 4He in gelsil 25 A pore diameter25 A pore diameter

Phonon-Roton Dispersion Curve (in gelsil F = 86 %)Phonon-Roton Dispersion Curve (in gelsil F = 86 %)

Bossy et al. (in preparation)

← Δ

Phonon-Roton Dispersion Curve (in gelsil F = 97 %)Phonon-Roton Dispersion Curve (in gelsil F = 97 %)

Bossy et al. (in preparation)

← Δ

Phonon-roton and layer mode versus FillingPhonon-roton and layer mode versus Filling

Phonon-roton and layer mode vs temperaturePhonon-roton and layer mode vs temperature

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

Phonon-roton and layer 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 %

Modes vs Filling F = 86-97 %Modes vs Filling F = 86-97 %

Temperature DependenceTemperature Dependence of modesof modes

Mode Intensities vs TemperatureMode Intensities vs Temperature

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

Conclusions:Conclusions:

Liquid 4He in Disorder and Boson LocalizationLiquid 4He in Disorder and Boson Localization

• At partial fillings, we observe P-R modes (BEC) at temperatures above Tc at temperatures above the superfluid phase.

• Above TAbove Tcc we have apparently localized BEC, we have apparently localized BEC, islands of BEC, as at full filling. It is not clear if islands of BEC, as at full filling. It is not clear if we have 2D or 3D liquid close to full filling. we have 2D or 3D liquid close to full filling.

• P-R modes and superflow start at about the P-R modes and superflow start at about the same filling, 20-25 same filling, 20-25 μμmol/m**2.mol/m**2.

Helium in MCM-41 (45 A) and in gelsil (25 A)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 mediaSchematic Phase Diagram He in Nanoporous media

Bossy et al., PRL 100, 025301 (2008)

Schematic Phase Diagram: He in Schematic Phase Diagram: He in Nanoporous mediaNanoporous media

Kamerlingh OnnesKamerlingh Onnes

Cuprates Superconductors

AF Mott Insulator

Insulator

Metal

T

Doping Level

Superconductor

Pseudo-gap Metal

Schematic Phase Diagram High Tc Schematic Phase Diagram High Tc

SuperconductorsSuperconductors

Alvarez et al. PRB (2005)

Patches of Antiferromagnetic and Patches of Antiferromagnetic and Superconducting regionsSuperconducting regions

Alvarez et al. PRB (2005)

Phase Diagram High Tc Phase Diagram High Tc

SuperconductorSuperconductor

Gomes et al. Nature (2007)

Patches of Energy gap, TPatches of Energy gap, TCC= 65K= 65K

Gomes et al. Nature (2005)

Helium in MCM-41 (45 A) and in gelsil (25 A)Helium in MCM-41 (45 A) and in gelsil (25 A)

Bossy et al. PRB 84,1084507 (R) (2010)

Conclusions:Conclusions:

Liquid 4He in Disorder and Boson LocalizationLiquid 4He in Disorder and Boson Localization

• 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.