CAP Annual Congress
Charlottetown
June 2003

4
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
CAP Annual Congress
Charlottetown
June 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

Goals
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), phononroton excitations, and superfluidity.
Compare bulk liquid 4 He and 4 He in porous media (confinement and disorder).

Bosons in Disorder
Liquid 4 He in Aerogel, Vycor, Geltech
Flux Lines in High T c
Superconductors
Josephson Junction Arrays
Granular Metal Films
Cooper Pairs in High T c
Superconductors
Models of Disorder excitation changes new excitations at low energy
Localization of Bose-Einstein Condensation by Disorder

Superfluid Properties in
Confinement/Disorder
Confinement reduces T c
Porous media is a “laboratory” to investigate the relation between superfluidity, excitations, and BEC.
Measure corresponding excitations and condensate fraction, n o (T). (new, 1995)

BEC, Excitations, and Superfluidity

Excitations, BEC, and Superfluidity
Collaborators:
Francesco Albergamo Institut Laue Langevin
Grenoble, France
Richard T. Azuah NIST
Center for Neutron Research
Gaithersburg, Maryland, USA
Jacques Bossy Centre de Recherche sur Les
Très Basses Temperature
CNRS
Grenoble, France
Bjorn Fåk ISIS Facility
Rutherford Appleton Lab
United Kingdom and
Commissariat à l’Energie
Atomique
Grenoble, France

Excitations, BEC, and Superfluidity
Collaborators (Con’t):
Oliver Plantevin European Synchrotron
Radiation Facility, Grenoble
Gerrit Coddens Laboratoire des solides irradiés
Ecole Polytechnique
Palaiseau, France
Reinhard Scherm Physikalisch-Technische
Bundesanstalt, Braunschweig
Norbert Mulders University of Delaware
Newark, Delaware USA
John Beamish University of Alberta
Edmonton, Canada
Helmut Schober Institut Laue Langevin
Grenoble, France

Neutron 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.

Superfluid Density
 s
(T)
Bulk Liquid 4 He
Superfluid Density  s
( t )  0 at T


2 .
17 K

London

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

Bose-Einstein Condensation
Glyde, Azuah, and Sterling
Phys. Rev., 62, 14337 (2001)

Bose-Einstein Condensation:
Atoms in Traps

Bose-Einstein Condensation:
Atoms in Traps

Bose-Einstein Condensation

( r )
 n o
( r )
1 / 2 e i

( r )
Condensate Fraction n o
( t )  0 at T


2 .
17 K

Bose-Einstein Condensation
Liquid 4 He in Vycor
T c
(Superfluidity) = 1.95-2.05 K
Azuah et al., JLTP (2003)

Bose-Einstein Condensation
Liquid 4 He in Vycor
T c
(Superfluidity) = 1.95-2.05 K
Azuah et al., JLTP (2003)

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 Condensation
Bogoliubov (1947) showed:
Bose gas with BEC -- quasiparticles have energy:

Q
 cQ - phonon (sound) form
Quasiparticle mode coincides with sound mode.
Only one excitation when have BEC.

Phonons and Rotons Arise From
Bose-Einstein Condensation
Gavoret and Nozi ères (1964) showed:
Dense liquid with BEC – only one excitation: density and quasiparticle modes have the same energy, 
Q
 cQ
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

Superfluidity
Landau 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, Ø (r)
Superfluidity follows directly from BEC, phase conherence .
s
 

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

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

Beyond the Roton in Bulk Liquid 4 He

Excitations, BEC, and Superfluidity
Bulk Liquid 4 He
BEC, well-defined excitations and superfluidity coincide e.g., all have some critical temperature, T

T

= 2.17 K SVP
T

= 1.92 K 20 bar

BEC, Excitations, and Superfluidity

Excitations in a Bose Fluid

Superfluid Properties in
Confinement/Disorder
Confinement reduces T c
Porous media is a “laboratory” to investigate the relation between superfluidity, excitations, and BEC.
Measure corresponding excitations and condensate fraction, n o (T). (new, 1995)

Porous Media
AEROGEL 95% porous
87% porous A
87% porous B
-- grown with deuterated materials or flushed with D
2
VYCOR 30% porous

A
-- grown with B 11 isotope
GELTECH SILICA 50% porous

25 A diameter pores
-- flushed with D
2

T c in Porous Media

Phonons, Rotons, and Layer Modes in Vycor and Aerogel

Temperature Dependence of Roton Energy
Fåk et al., PRL, 85 (2000)

Layer Mode in Vycor and Aerogel

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

Phonon-Roton Mode in Vycor:
T = 2.05 K

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

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

Liquid 4 He in Geltech Silica
T c
(Superfluidity) = 0.725 K

Excitations, BEC, and Superfluidity
Liquid 4 He in disorder
BEC, well-defined excitations and separated from superfluidity in disorder e.g., T c
- superfluidity
T c
(BEC)
- Bose-Einstein condensation
T c
(BEC)
> T c
Disorder localizes the condensate.
New Here
Measurements of phonon-roton excitations and BEC in disorder

BEC in Disorder
Both n o

(homogeneous).
Huang & Meng, PR 1992 dilute gas limit, analytic
Astraljparehik, et al., preprint (2002) fluid densities, Monte Carlo
 s reduced more than n o
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.

Conclusions
Have Bose-Einstein Condensation in liquid 4 He.
The well defined phonon-roton excitations in superfluid
4 He (the sharp dispersion curve) is a consequence of
BEC. Well defined phonon-roton excitations do not exist
T o = 0 (no phase coherence).
Landau theory and BEC theories of superfluidity have common dependence on BEC.
In liquid 4 He in disorder, observe phonons and rotons as in bulk liquid 4 He. In addition, observe 2D layer modes.
Also observe excitations above T c
– in the normal phase.
Disorder can localize BEC and superfluidity. In disorder, have phase coherence over short length scales above T c for macroscopic superfluidity. Can “see” this localized BEC in excitations but not in Torsional
Oscillator measurements.
Future: Use confinement/disorder to “tune” T c
,
 s
( T ) and investigate BEC, excitations and superfluidity.
Explore reduced dimensions.

BEC, Excitations, and Superfluidity

4
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
University of Delaware
February 20, 2002

4
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
University of Washington
February 25, 2002

Neutron Scattering Laboratories
Institute Laue Langevin
Grenoble, France
ISIS
Rutherford Appleton Laboratories
Oxfordshire, England
NIST Center for Neutron Research
National Institute of Standards and Technology
Gaithersburg, Maryland

Graduate Students
Jonathan DuBois
Bose-Einstein Condensation of Bosons in Traps,
Variational Monte Carlo, Diffusion MC
Asaad Sakhel
Models of excitations in liquid 4 He
BEC in traps
Ali Shams
Souleymane Omar Diallo

Goals
Precision Measurement of excitations in liquid 4 He (and
3 He) 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)

Density and Quasiparticle Excitations (BEC)
Bogoliubov (1947), Gavoret and Nozieres (1964), Griffin (1993), and Glyde (1994)
Density Operator
First quantization:

( Q )
  k a
 k

Q a k

( r )
  
( r )

( r )
Second quantization:
 ˆ
( r )
  ˆ 
( r )
 ˆ
( r )
 
( r )
 
( r )

 k a k
 e  ik
 r
 a k
-- 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 N o in k = 0 state.
a
 k a k

N k -- number in state k a
 o a o

N o -- large (10 22 ) a o

N o -- a number
Density Operator

( Q )
  a k


Q a k k
 a

Q
N o
  ' k a
 k

Q a k
 a

Q
N o
  
( Q )
Density operator includes quasiparticle excitation.

BEC (continued)
Density and quasiparticle become one and the same excitation. They have the same energy.
Composite “density—quasiparticle” excitation has the

Independent of strength of interaction.
No “quasiparticle” excitations lying under the phononroton dispersion curve to which the phonon-roton excitations can decay.

Future Research

Measure n o A
T c n o (T) in 2D films is it there?
2D to 3D crossover.
Measure excitations near T c
Explore new disordered media.

Superfluid Properties in
Confinement/Disorder
Confinement reduces T c
Porous media is a “laboratory” to investigate the relation between superfluidity, excitations, and BEC.
Measure corresponding excitations and condensate fraction, n o (T). (new, 1995)

Roton
Liquid 4 He in Geltech Silica: T c
= 0.725 K
Bulk Liquid 4 He: T c
= 2.17 K
Plantevin et al., PRB, 65 (2002)

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

Phonon-Roton Energy

Beyond the Roton in Bulk Liquid 4 He

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