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Excitations, Bose-EinsteinExcitations, Bose-EinsteinCondensation and Condensation and
Superfluidity in Liquid Superfluidity in Liquid 44HeHe
Henry R. GlydeDepartment of Physics & Astronomy
University of Delaware
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Phase Diagram of HeliumPhase Diagram of Helium
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GoalsGoals
Neutron scattering studies of excitations of quantum liquids in disorder.
• phonons and rotons in disorder
• new excitations in disorder
Reveal the interdependence of Bose-Einstein Condensation (BEC), phonon-roton excitations, and superfluidity.
Compare bulk liquid 4He and 4He in porous media (confinement and disorder).
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Phonon-Roton Dispersion CurvePhonon-Roton Dispersion Curve
Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)
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Bosons in DisorderBosons in Disorder
Liquid 4He in Aerogel, Vycor, Geltech
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
Localization of Bose-Einstein Condensation by Disorder
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Superfluid Properties in Superfluid Properties in Confinement/DisorderConfinement/Disorder
Confinement reduces Tc below .
Confinement modifies (T dependence).
Confinement reduces (magnitude).
Porous media is a “laboratory” to investigate the relation between superfluidity, excitations, and BEC.
Measure corresponding excitations and condensate fraction, no(T). (new, 1995)
KT 172
)(Ts
)(Ts
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Graduate StudentsGraduate Students
Jonathan DuBois
Bose-Einstein Condensation of Bosons in Traps, Variational Monte Carlo, Diffusion MC
Asaad Sakhel
Models of excitations in liquid 4HeBEC in traps
Ali Shams
Souleymane Omar Diallo
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Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Collaborators:
Francesco Albergamo - Institut Laue LangevinGrenoble, France
Richard T. Azuah - NISTCenter for Neutron ResearchGaithersburg, Maryland,
USA
Jacques Bossy - Centre de Recherche sur LesTrès Basses TemperatureCNRSGrenoble, France
Bjorn Fåk - ISIS FacilityRutherford Appleton LabUnited Kingdom andCommissariat à l’Energie AtomiqueGrenoble, France
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Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Collaborators (Con’t):
Oliver Plantevin - European SynchrotronRadiation Facility, Grenoble
Gerrit Coddens - Laboratoire des solides irradiés Ecole PolytechniquePalaiseau, France
Reinhard Scherm - Physikalisch-TechnischeBundesanstalt, Braunschweig
Norbert Mulders - University of DelawareNewark, Delaware USA
John Beamish - University of AlbertaEdmonton, Canada
Helmut Schober - Institut Laue LangevinGrenoble, France
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Neutron Scattering LaboratoriesNeutron Scattering Laboratories
Institute Laue Langevin
Grenoble, France
ISIS Rutherford Appleton Laboratories
Oxfordshire, England
NIST Center for Neutron Research
National Institute of Standards and TechnologyGaithersburg, Maryland
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Neutron Scattering: ILLNeutron Scattering: ILL
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Excitations and Bose-Einstein Condensation in Quantum Liquids in Disorder
Henry R. Glyde, University of Delaware, DMR-9972011
Figure 1. Top: The Insitiut Laue Langevin (just behind the ESRF synchrotron ring) in Grenoble. Bottom: Left to right, Jacques Bossy, Henry Glyde, Francesco Albergamo and Olivier Plantevin in front of the IN6 neutron spectrometer of ILL.
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Bose-Einstein Condensation: Bose-Einstein Condensation: Atoms in TrapsAtoms in Traps
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Bose-Einstein Condensation: Bose-Einstein Condensation: Atoms in TrapsAtoms in Traps
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Bose-Einstein CondensationBose-Einstein Condensation
Glyde, Azuah, and SterlingPhys. Rev., 62, 14337 (2001)
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Bose-Einstein CondensationBose-Einstein Condensation
Condensate Fraction
)(2/1)()( ri
oernr
KTtno
17.2at 0)(
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TTcc in Porous Media in Porous Media
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Superfluid Density Superfluid Density ss(T)(T)
Superfluid Density KTts
17.2at 0)(
Bulk Liquid 4He
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LondonLondon
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BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity
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LandauLandau
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Phonon-Roton Dispersion CurvePhonon-Roton Dispersion Curve
Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)
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SuperfluiditySuperfluidity
Landau TheoryLandau Theory
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 ).
Via P-R excitations, superflow arises from BEC.
BEC and Phase Coherence, BEC and Phase Coherence, Ø (r)Ø (r)
Superfluidity follows directly from BEC, phase conherence .)(r
s
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Phonons and Rotons Arise From Phonons and Rotons Arise From Bose-Einstein CondensationBose-Einstein Condensation
Gavoret and NoziGavoret and Nozièreères (1964) showed:s (1964) showed:
Dense liquid with BEC – only one excitation: density and quasiparticle modes have the same energy, At low Q, as in Bose gas.
No other excitations at low energy (could have vortices).
cQQ
Ma and Woo (1967), Griffin and Ma and Woo (1967), Griffin and Cheung (1973), and others showed:Cheung (1973), and others showed:
Only a single mode at all Q with BEC -- the phonon-roton mode.
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Maxon in Bulk Liquid Maxon in Bulk Liquid 44HeHe
Talbot et al., PRB, 38, 11229 (1988)
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Roton in Bulk Liquid Roton in Bulk Liquid 44HeHe
Talbot et al., PRB, 38, 11229 (1988)
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Beyond the Roton in Bulk Liquid Beyond the Roton in Bulk Liquid 44HeHe
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BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity
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Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Bulk Liquid Bulk Liquid 44HeHe
BEC, well-defined excitations and superfluidity coincide
e.g., all have some critical temperature,
= 2.17 K SVP
= 1.92 K 20 bar
T
T
T
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Porous MediaPorous Media
AEROGEL 95% porous87% porous A87% porous B
-- grown with deuterated materials or flushed
with D2
VYCOR 30% porous70 diameter pores
-- grown with B11 isotope
GELTECH SILICA 50% porous25 diameter pores
-- flushed with D2
A
A
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TTcc in Porous Media in Porous Media
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Geltech (25 Å pores)
Superfluid Density in Porous MediaSuperfluid Density in Porous Media
Chan et al. (1988)
Miyamoto and Takeno (1996)
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Bose-Einstein CondensationBose-Einstein CondensationLiquid Liquid 44He in VycorHe in Vycor
Azuah et al., JLTP (2003)
Tc (Superfluidity) = 1.95-2.05 K
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Phonons, Rotons, and Layer Modes Phonons, Rotons, and Layer Modes in Vycor and Aerogelin Vycor and Aerogel
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Layer Mode in Vycor and AerogelLayer Mode in Vycor and Aerogel
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Temperature DependenceTemperature Dependenceof Roton Energyof Roton Energy
Fåk et al., PRL, 85 (2000)
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Intensity in Single Excitation vs. Intensity in Single Excitation vs. TT
Glyde et al., PRL, 84 (2000)
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Phonon-Roton Mode in Vycor:Phonon-Roton Mode in Vycor:T = 2.05 KT = 2.05 K
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Roton in Geltech Silica: Partial Roton in Geltech Silica: Partial FillingFilling
Plantevin et al., PRB, 65 (2002)
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Liquid Liquid 44He in Geltech SilicaHe in Geltech Silica
Tc (Superfluidity) = 0.725 K
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Fraction, Fraction, ffss(T)(T), of Total Scattering , of Total Scattering
Intensity in Phonon-Roton ModeIntensity in Phonon-Roton Mode
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BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity
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Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Liquid Liquid 44He in disorderHe in disorder
BEC, well-defined excitations and separated from superfluidity in disorder
e.g., Tc - superfluidity
Tc (BEC) - Bose-Einstein condensation
Tc (BEC) > Tc
Disorder localizes the condensate.
New HereNew Here
Measurements of phonon-roton excitations and BEC in disorder
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BEC in DisorderBEC in Disorder
Both no and reduced by static disorder (homogeneous).
Huang & Meng, PR 1992dilute gas limit, analytic
Astraljparehik, et al., preprint (2002)fluid densities, Monte Carlo
reduced more than no
Could have localized BEC. As T is reduced, BEC forms first in favorable regions, in pockets. Superflow occurs at a lower T when regions grow and connect to have phase coherence across the entire sample.
s
s
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ConclusionsConclusions
Have Bose-Einstein Condensation in liquid 4He.
The well defined phonon-roton excitations in superfluid 4He (the sharp dispersion curve) is a consequence of BEC. Well defined phonon-roton excitations do not exist above in the normal phase where no = 0 (no phase coherence).
Landau theory and BEC theories of superfluidity have common dependence on BEC.
In liquid 4He in disorder, observe phonons and rotons as in bulk liquid 4He. In addition, observe 2D layer modes. Also observe excitations above Tc – in the normal phase.
Disorder can localize BEC and superfluidity. In disorder, have phase coherence over short length scales above Tc for macroscopic superfluidity. Can “see” this localized BEC in excitations but not in Torsional Oscillator measurements.
Future: Use confinement/disorder to “tune” and investigate BEC, excitations and superfluidity. Explore reduced dimensions.
T
)(, TT sc
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Focused Research Group: NSF 2001Focused Research Group: NSF 2001
Oscar Vilches University of Washington
John Larese University of Tennessee
Henry Glyde (PI) University of Delaware
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GoalsGoals
Precision Measurement of excitations in liquid 4He (and 3He) by inelastic neutron scattering.
Measurement of condensation fraction and momentum distribution n(k) by high energy transfer inelastic neutron scattering.
Reveal relation between excitations and BEC—do well defined phonon-roton excitations exist because there is BEC?
Reconcile theories of superfluidity.
e.g., Landau theory (1941-1947) - phonons-rotons (no BEC)
London (1938) - BEC (no phonons-rotons)
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Bose-Einstein CondensationBose-Einstein CondensationLiquid Liquid 44He in VycorHe in Vycor
Azuah et al., JLTP (2003)
Tc (Superfluidity) = 1.95-2.05 K
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Phonons and Rotons Arise From Phonons and Rotons Arise From Bose-Einstein CondensationBose-Einstein Condensation
Bogoliubov (1947) showed:Bogoliubov (1947) showed:
Bose gas with BEC -- quasiparticles have energy:
- phonon (sound) form
Quasiparticle mode coincides with sound mode.
Only one excitation when have BEC.
cQQ
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BECBEC (continued)(continued)
Density and quasiparticle become one and the same excitation. They have the same energy.
Composite “density—quasiparticle” excitation has the phonon energy. At low .
Independent of strength of interaction.
No “quasiparticle” excitations lying under the phonon-roton dispersion curve to which the phonon-roton excitations can decay.
QCQ Q ,
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Excitations in a Bose FluidExcitations in a Bose Fluid
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Filling Dependence Filling Dependence of Roton and Layer Modesof Roton and Layer Modes
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Density and Quasiparticle Excitations (BEC)Density and Quasiparticle Excitations (BEC)Bogoliubov (1947), Gavoret and Nozieres (1964), Griffin (1993), and Bogoliubov (1947), Gavoret and Nozieres (1964), Griffin (1993), and Glyde (1994)Glyde (1994)
Density Operator
First quantization:
Second quantization:
-- density operator
-- creates a particle at r
-- creates particle with
momentum k
-- density operator
Density operator is a two particle operator.
)()()( rrr
)(ˆ)(ˆ)(ˆ rrr
)(r
ear rikk k
)(
ak
aaQ kQkk
)(
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Density and Quasiparticle Excitations (BEC)Density and Quasiparticle Excitations (BEC)
A macroscopic number of particles No in k = 0 state.
-- number in state k
-- large (1022)
-- a number
Density Operator
Density operator includes quasiparticle excitation.
Naa kkk
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![Page 57: Excitations, Bose-Einstein Condensation and Superfluidity in Liquid 4 He Henry R. Glyde Department of Physics & Astronomy University of Delaware.](https://reader038.fdocuments.net/reader038/viewer/2022110207/56649d7e5503460f94a6108e/html5/thumbnails/57.jpg)
Figure 2. Discussing analsis of neutron scattering data at Delaware are (left to right): Zhicheng Yan, Richard Azuah, Assad Sakhel, Jonathan DuBois, and Henry Glyde.
Excitations and Bose-Einstein Condensation in Quantum Liquids in Disorder
Henry R. Glyde, University of Delaware, DMR-9972011
![Page 58: Excitations, Bose-Einstein Condensation and Superfluidity in Liquid 4 He Henry R. Glyde Department of Physics & Astronomy University of Delaware.](https://reader038.fdocuments.net/reader038/viewer/2022110207/56649d7e5503460f94a6108e/html5/thumbnails/58.jpg)
![Page 59: Excitations, Bose-Einstein Condensation and Superfluidity in Liquid 4 He Henry R. Glyde Department of Physics & Astronomy University of Delaware.](https://reader038.fdocuments.net/reader038/viewer/2022110207/56649d7e5503460f94a6108e/html5/thumbnails/59.jpg)
Localization of Bose-Einstein Condensation by Disorder
Henry Glyde, University of Delaware, Oscar Vilches, University of Washington,
John Larese, University of Tennessee Focused Research Group, DMR-0115663
Our neutron scattering studies of liquid 4He in porous media show evidence of Bose-Einstein Condensation localized by disorder. In bulk, pure systems the origin of superfluidity (and superconductivity) is BEC. Once there is BEC, there are simultaneously phonon-roton excitations and superfluidity. In contrast, in disorder the BEC can be localized so that there are P-R excitations but no macroscopic superfluidity. Superfluidity follows at a lower temperature when the BEC becomes extended across the sample. The “localized BEC” state in liquid 4He is similar to the “pseudo gap” state observed in high Tc
superconductors.