Excitations, BoseEinstein Condensation and Superfluidity in Liquid 4He

1
Excitations, Bose-EinsteinCondensation and
Superfluidity in Liquid 4He

• Henry R. Glyde
• Department of Physics Astronomy
• University of Delaware

2
Phase Diagram of Helium
3
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), phonon-roton excitations, and
  superfluidity.
• Compare bulk liquid 4He and 4He in porous media
  (confinement and disorder).

4
Phonon-Roton Dispersion Curve
? Donnelly et al., J. Low Temp. Phys. (1981) ?
Glyde et al., Euro Phys. Lett. (1998)
5
Bosons 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
Disorder excitation changes new excitations at
low energy Localization of Bose-Einstein
Condensation by Disorder
6
Superfluid Properties in Confinement/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)
7
Graduate Students
Jonathan DuBois Bose-Einstein Condensation of
Bosons in Traps, Variational Monte Carlo,
Diffusion MC Asaad Sakhel Models of
excitations in liquid 4He BEC in traps Ali
Shams Souleymane Omar Diallo
8
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 lEnergie
Atomique Grenoble, France
9
Excitations, BEC, and Superfluidity
Collaborators (Cont) Oliver Plantevin
- European Synchrotron Radiation Facility,
Grenoble Gerrit Coddens
- Laboratoire des solides irradiés Ecole
Polytechnique Palaiseau, France Reinhard
Scherm - Physikalisch-Technische Bunde
sanstalt, Braunschweig Norbert Mulders
- University of Delaware Newark, Delaware
USA John Beamish - University of
Alberta Edmonton, Canada Helmut Schober
- Institut Laue Langevin Grenoble,
France
10
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
11
Neutron Scattering ILL
12
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.
13
Bose-Einstein Condensation Atoms in Traps
14
Bose-Einstein Condensation Atoms in Traps
15
Bose-Einstein Condensation
Glyde, Azuah, and Sterling Phys. Rev., 62, 14337
(2001)
16
Bose-Einstein Condensation
Condensate Fraction
17
Tc in Porous Media
18
Superfluid Density ?s(T)
Bulk Liquid 4He
Superfluid Density
19
London
20
BEC, Excitations, and Superfluidity
21
Landau
22
Phonon-Roton Dispersion Curve
? Donnelly et al., J. Low Temp. Phys. (1981) ?
Glyde et al., Euro Phys. Lett. (1998)
23
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 .
24
Phonons and Rotons Arise From Bose-Einstein
Condensation
Gavoret and Nozières (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.
25
Maxon in Bulk Liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
26
Roton in Bulk Liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
27
Beyond the Roton in Bulk Liquid 4He
28
BEC, Excitations, and Superfluidity
29
Excitations, BEC, and Superfluidity
Bulk 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
30
Porous Media
AEROGEL 95 porous 87 porous A 87
porous B -- grown with deuterated
materials or flushed with D2 VYCOR 30
porous 70 diameter pores --
grown with B11 isotope GELTECH SILICA 50
porous 25 diameter pores --
flushed with D2
31
Tc in Porous Media
32
Superfluid Density in Porous Media
Chan et al. (1988)
Miyamoto and Takeno (1996)
Geltech (25 Å pores)
33
Bose-Einstein CondensationLiquid 4He in Vycor
Tc (Superfluidity) 1.95-2.05 K
Azuah et al., JLTP (2003)
34
Phonons, Rotons, and Layer Modes in Vycor and
Aerogel
35
Layer Mode in Vycor and Aerogel
36
Temperature Dependenceof Roton Energy
Fåk et al., PRL, 85 (2000)
37
Intensity in Single Excitation vs. T
Glyde et al., PRL, 84 (2000)
38
Phonon-Roton Mode in VycorT 2.05 K
39
Roton in Geltech Silica Partial Filling
Plantevin et al., PRB, 65 (2002)
40
Liquid 4He in Geltech Silica
Tc (Superfluidity) 0.725 K
41
Fraction, fs(T), of Total Scattering Intensity in
Phonon-Roton Mode
42
BEC, Excitations, and Superfluidity
43
Excitations, BEC, and Superfluidity
Liquid 4He in disorder BEC, well-defined
excitations and separated from superfluidity in
disorder e.g., Tc - superfluidity
Tc (BEC) - Bose-Einstein condensation
Tc (BEC) gt Tc Disorder localizes the
condensate. New Here Measurements of
phonon-roton excitations and BEC in disorder
44
BEC in Disorder
Both no and reduced by static disorder
(homogeneous). Huang Meng, PR 1992 dilute
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.
45
Conclusions
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.
46
(No Transcript)
47
(No Transcript)
48
Focused Research Group NSF 2001
Oscar Vilches University of Washington John
Larese University of Tennessee Henry Glyde
(PI) University of Delaware
49
Goals
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 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)
50
Bose-Einstein CondensationLiquid 4He in Vycor
Tc (Superfluidity) 1.95-2.05 K
Azuah et al., JLTP (2003)
51
Phonons and Rotons Arise From Bose-Einstein
Condensation
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.
52
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.
53
Excitations in a Bose Fluid
54
Filling Dependence of Roton and Layer Modes
55
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.
56
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.
57
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.
58
(No Transcript)
59
Localization of Bose-Einstein Condensation by
DisorderHenry 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.