localized bose-einstein condensation in liquid 4he in disorder
DESCRIPTION
Localized Bose-Einstein Condensation in Liquid 4He in Disorder. Henry R. Glyde Department of Physics & Astronomy University of Delaware. APS March Meeting Denver, Co 3-7 March, 2014. BEC, Excitations, Superfluidity. Bose Einstein Condensation (neutrons) 1968- - PowerPoint PPT PresentationTRANSCRIPT
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.