Reminiscences of Jurgen Frank

Alberta and DelawareCAP Annual CongressCharlottetownJune 2003

Excitations, Bose-EinsteinCondensation and Superfluidity in Liquid 4HeHenry R. GlydeDepartment of Physics & AstronomyUniversity of DelawareCAP Annual CongressCharlottetownJune 2003

Jurgen Franck

Jurgen Franck

Phase Diagram of Helium

Lab Notes: JPF at Delaware

Quantum Fluids and Solids Conference 1986

Quantum Fluids and Solids Conference 1986

Jurgen Franck

GoalsNeutron 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).

Bosons in DisorderLiquid 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 Confinement/DisorderConfinement 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)

BEC, Excitations, and Superfluidity

Excitations, BEC, and SuperfluidityCollaborators:

Francesco Albergamo -Institut Laue LangevinGrenoble, France

Richard T. Azuah -NISTCenter for Neutron ResearchGaithersburg, Maryland, USA

Jacques Bossy -Centre de Recherche sur LesTrs Basses TemperatureCNRSGrenoble, France

Bjorn Fk -ISIS FacilityRutherford Appleton LabUnited Kingdom andCommissariat lEnergie AtomiqueGrenoble, France

Excitations, BEC, and SuperfluidityCollaborators (Cont):

Oliver Plantevin -European SynchrotronRadiation Facility, Grenoble

Gerrit Coddens -Laboratoire des solides irradis 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: ILL

Excitations and Bose-Einstein Condensation in Quantum Liquids in DisorderHenry R. Glyde, University of Delaware, DMR-9972011Figure 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.

Superfluid Density s(T)

Superfluid DensityBulk Liquid 4He

London

Superfluid Density in Porous MediaGeltech (25 pores)Chan et al. (1988)Miyamoto and Takeno (1996)

Bose-Einstein CondensationGlyde, Azuah, and SterlingPhys. Rev., 62, 14337 (2001)

Bose-Einstein Condensation: Atoms in Traps

Bose-Einstein Condensation: Atoms in Traps

Bose-Einstein Condensation

Condensate Fraction

Bose-Einstein CondensationLiquid 4He in VycorAzuah et al., JLTP (2003)

Tc (Superfluidity) = 1.95-2.05 K

Bose-Einstein CondensationLiquid 4He in VycorAzuah et al., JLTP (2003)

Tc (Superfluidity) = 1.95-2.05 K

Phonon-Roton Dispersion Curve Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)

Phonons and Rotons Arise From Bose-Einstein CondensationBogoliubov (1947) showed: Bose gas with BEC -- quasiparticles have energy:

- phonon (sound) form

Quasiparticle mode coincides with sound mode.

Only one excitation when have BEC.

Phonons and Rotons Arise From Bose-Einstein CondensationGavoret and Nozires (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).Ma and Woo (1967), Griffin and Cheung (1973), and others showed: Only a single mode at all Q with BEC -- the phonon-roton mode.

Landau

SuperfluidityLandau 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, (r)

Superfluidity follows directly from BEC, phase conherence .

Maxon in Bulk Liquid 4HeTalbot et al., PRB, 38, 11229 (1988)

Roton in Bulk Liquid 4HeTalbot et al., PRB, 38, 11229 (1988)

Beyond the Roton in Bulk Liquid 4He

Excitations, BEC, and SuperfluidityBulk Liquid 4He

BEC, well-defined excitations and superfluidity coincide

e.g., all have some critical temperature,

= 2.17 K SVP

= 1.92 K 20 bar

BEC, Excitations, and Superfluidity

Excitations in a Bose Fluid

Superfluid Properties in Confinement/DisorderConfinement 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)

Porous MediaAEROGEL95% porous87% porousA87% porousB

-- grown with deuterated materials or flushed with D2

VYCOR30% porous70 diameter pores-- grown with B11 isotope

GELTECH SILICA50% porous25 diameter pores-- flushed with D2

Tc in Porous Media

Phonons, Rotons, and Layer Modes in Vycor and Aerogel

Temperature Dependenceof Roton EnergyFk et al., PRL, 85 (2000)

Layer Mode in Vycor and Aerogel

Intensity in Single Excitation vs. TGlyde et al., PRL, 84 (2000)

Phonon-Roton Mode in Vycor:T = 2.05 K

Fraction, fs(T), of Total Scattering Intensity in Phonon-Roton Mode

Roton in Geltech Silica: Partial FillingPlantevin et al., PRB, 65 (2002)

Liquid 4He in Geltech SilicaTc (Superfluidity) = 0.725 K

Excitations, BEC, and SuperfluidityLiquid 4He 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 Here

Measurements of phonon-roton excitations and BEC in disorder

BEC in DisorderBoth 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.

ConclusionsHave 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.

BEC, Excitations, and Superfluidity

Excitations,Bose-EinsteinCondensation and Superfluidity in Liquid 4HeHenry R. GlydeDepartment of Physics & AstronomyUniversity of DelawareUniversity of DelawareFebruary 20, 2002

Excitations,Bose-EinsteinCondensation and Superfluidity in Liquid 4HeHenry R. GlydeDepartment of Physics & AstronomyUniversity of DelawareUniversity of WashingtonFebruary 25, 2002

Neutron Scattering LaboratoriesInstitute Laue Langevin

Grenoble, France

ISIS Rutherford Appleton Laboratories Oxfordshire, England

NIST Center for Neutron Research

National Institute of Standards and TechnologyGaithersburg, Maryland

Graduate StudentsJonathan 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

GoalsPrecision 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 BECdo 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)

Density and Quasiparticle Excitations (BEC)Bogoliubov (1947), Gavoret and Nozieres (1964), Griffin (1993), and 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.

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.

BEC (continued)Density and quasiparticle become one and the same excitation. They have the same energy.

Composite densityquasiparticle 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.

Future ResearchMeasure no(T) in 50 porous media.

Tc well below .

no(T) in 2D films

is it there?2D to 3D crossover.

Measure excitations near Tc

Explore new disordered media.

Superfluid Properties in Confinement/DisorderConfinement 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)

RotonLiquid 4He in Geltech Silica: Tc = 0.725 K

Bulk Liquid 4He: Tc = 2.17 K

Plantevin et al., PRB, 65 (2002)

Roton in Bulk Liquid 4He Multiexcitation ResponseTalbot et al., PRB, 38, 11229 (1988)

Phonon-Roton Energy

Beyond the Roton in Bulk Liquid 4He

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 DisorderHenry R. Glyde, University of Delaware, DMR-9972011