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
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, 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)
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)
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
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
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
- - 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
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.
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
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
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)
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)
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.
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