Excitations, Bose-EinsteinExcitations, Bose-EinsteinCondensation and Condensation and

Superfluidity in Liquid Superfluidity in Liquid 44HeHe

Henry R. GlydeDepartment of Physics & Astronomy

University of Delaware

Phase Diagram of HeliumPhase Diagram of Helium

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).

Phonon-Roton Dispersion CurvePhonon-Roton Dispersion Curve

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

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

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

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

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

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

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

Neutron Scattering: ILLNeutron Scattering: ILL

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.

Bose-Einstein Condensation: Bose-Einstein Condensation: Atoms in TrapsAtoms in Traps

Bose-Einstein Condensation: Bose-Einstein Condensation: Atoms in TrapsAtoms in Traps

Bose-Einstein CondensationBose-Einstein Condensation

Glyde, Azuah, and SterlingPhys. Rev., 62, 14337 (2001)

Bose-Einstein CondensationBose-Einstein Condensation

Condensate Fraction

)(2/1)()( ri

oernr

KTtno

17.2at 0)(

TTcc in Porous Media in Porous Media

Superfluid Density Superfluid Density ss(T)(T)

Superfluid Density KTts

17.2at 0)(

Bulk Liquid 4He

LondonLondon

BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity

LandauLandau

Phonon-Roton Dispersion CurvePhonon-Roton Dispersion Curve

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

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

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.

Maxon in Bulk Liquid Maxon in Bulk Liquid 44HeHe

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 in Bulk Liquid Beyond the Roton in Bulk Liquid 44HeHe

BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity

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

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

TTcc in Porous Media in Porous Media

Geltech (25 Å pores)

Superfluid Density in Porous MediaSuperfluid Density in Porous Media

Chan et al. (1988)

Miyamoto and Takeno (1996)

Bose-Einstein CondensationBose-Einstein CondensationLiquid Liquid 44He in VycorHe in Vycor

Azuah et al., JLTP (2003)

Tc (Superfluidity) = 1.95-2.05 K

Phonons, Rotons, and Layer Modes Phonons, Rotons, and Layer Modes in Vycor and Aerogelin Vycor and Aerogel

Layer Mode in Vycor and AerogelLayer Mode in Vycor and Aerogel

Temperature DependenceTemperature Dependenceof Roton Energyof Roton Energy

Fåk et al., PRL, 85 (2000)

Intensity in Single Excitation vs. Intensity in Single Excitation vs. TT

Glyde et al., PRL, 84 (2000)

Phonon-Roton Mode in Vycor:Phonon-Roton Mode in Vycor:T = 2.05 KT = 2.05 K

Roton in Geltech Silica: Partial Roton in Geltech Silica: Partial FillingFilling

Plantevin et al., PRB, 65 (2002)

Liquid Liquid 44He in Geltech SilicaHe in Geltech Silica

Tc (Superfluidity) = 0.725 K

Fraction, Fraction, ffss(T)(T), of Total Scattering , of Total Scattering

Intensity in Phonon-Roton ModeIntensity in Phonon-Roton Mode

BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity

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

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

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

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

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)

Bose-Einstein CondensationBose-Einstein CondensationLiquid Liquid 44He in VycorHe in Vycor

Azuah et al., JLTP (2003)

Tc (Superfluidity) = 1.95-2.05 K

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

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 ,

Excitations in a Bose FluidExcitations in a Bose Fluid

Filling Dependence Filling Dependence of Roton and Layer Modesof Roton and Layer Modes

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

)(

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

ooo Naa

oo Na

aaQ kQkk

)(

)(QNa oQ

aaNa kQkkoQ

'

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

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.