Bose-Einstein Condensation,
Superfluidity and Elementary Excitations
in Quantum Liquids
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
ISIS Facility
Rutherford Appleton Laboratory
Harwell, Oxford
17 September, 2013
BEC, Excitations, Superfluidity
Bose Einstein Condensation
(neutrons)
1968Collective Phonon-Roton modes (neutrons)
1958Superfluidity
(torsional oscillators)
`
1938He in porous media integral part
of historical superflow measurements.
BEC, Superfluidity and Neutrons
Scientific Goals:
•Observe and document BEC and atomic momentum
distribution in liquid 4He, 3He-4He mixtures, 3D, 2D .
-single particle excitations, S(Q,ω) at high Q, ω
-SNS (ARCS), ISIS (MARI)
•Observe Phonon-roton, layer modes (porous media)
-collective modes, S(Q,ω) at low Q, ω
-ISIS (ORIRIS,IRIS), ILL (IN5,IN6)
.Explain Superflow: BEC is the origin superflow
BEC and n (k) (single particle excitations)
Collaborators: SNS and ISIS
Richard T. Azuah
Souleymane Omar Diallo
Norbert Mulders
Douglas Abernathy
- NIST Center for Neutron
Research, Gaithersburg, USA
- Spallation Neutron source,
ORNL, Oak Ridge, TN
- University of Delaware
Jon V. Taylor
- Spallation Neutron source,
ORNL, Oak Ridge, TN
- ISIS Facility, UK
Oleg Kirichek
- ISIS Facility, UK
Collective (Phonon-roton) Modes, Structure
Collaborators: (ILL)
JACQUES BOSSY Institut Néel, CNRS- UJF,
Grenoble, France
Helmut Schober
Institut Laue-Langevin
Grenoble, France
Jacques Ollivier
Institut Laue-Langevin
Grenoble, France
Norbert Mulders
University of Delaware
BEC, Superfluidity and Superfluidity
Organization of Talk
1. Phase diagrams: liquid, solid, superfluidity.
2. P-R Modes in liquid 4He.
- modes vs pressure
- modes in the solid: are there liquid
like modes in solid He that superflow?
2. Measurements: BEC, n(k)
-bulk liquid 4He, to solidification.
-2D helium
-Solid helium
-Porous media, now and in future.
Phase Diagram of Bulk Helium
Phase Diagram Bulk helium
Phase Diagram Bulk helium
SUPERFLUIDITY
1908 – 4He first liquified in Leiden by
Kamerlingh Onnes
1925 – Specific heat anomaly observed at
Tλ = 2.17 K by Keesom.
Denoted the λ transiton to He II.
1938 – Superfluidity observed in He II by
Kaptiza and by Allen and Misener.
1938 – Superfluidity interpreted as
manifestation of BEC by London
vS = grad φ (r)
Kamerlingh Onnes
SUPERFLUID: Bulk Liquid SF Fraction s(T)
Critical Temperature Tλ = 2.17 K
Landau Theory of Superfluidity
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 ).
PHONON-ROTON MODE: Dispersion Curve
←Δ
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
BOSE-EINSTEIN CONDENSATION
1924
Bose gas : Φk = exp[ik.r] , Nk
k = 0 state is condensate state for uniform fluids.
Condensate fraction, n0 = N0/N = 100 % T = 0 K
Condensate wave function: ψ(r) = √n0 e iφ(r)
Bose-Einstein Condensation: Gases in Traps
SUPERFLUIDITY
1908 – 4He first liquified in Leiden by
Kamerlingh Onnes
1925 – Specific heat anomaly observed at
Tλ = 2.17 K by Keesom.
Denoted the λ transiton to He II.
1938 – Superfluidity observed in He II by
Kaptiza and by Allen and Misener.
1938 – Superfluidity interpreted as
manifestation of BEC by London
vS = grad φ (r)
London
Bose-Einstein Condensation: Gases in Traps
Bose-Einstein Condensation, Bulk Liquid 4He
Glyde, Azuah, and Stirling
Phys. Rev., 62, 14337 (2000)
Bose-Einstein Condensation: Bulk Liquid
Expt: Glyde et al. PRB (2000)
Bose-Einstein Condensation
Model momentum distribution:
y =kQ= k.Q
Model One Body density matrix:
Full Dynamic Structure Factor
Model One Body Density Matrix: Bulk Helium
Bose-Einstein Condensate Fraction
Liquid Helium versus Density
PR B83, 100507 (2011)
BEC: Bulk Liquid
4He vs pressure
PR B83, 100507 (R)(2011)
Bose-Einstein Condensate Fraction
Liquid Helium versus Pressure
Glyde et al. PR B83, 100507 (R)(2011)
Bose-Einstein Condensate Fraction
Liquid Helium versus Density
PR B83, 100507 (2011)
J(Q,y) and BEC in Liquid Helium at 24 bar
Diallo et al. PRB 85, 140505 (R) (2012)
Bose-Einstein Condensate Fraction
Liquid Helium versus Pressure
Diallo et al. PRB 85, 140505 (R) (2012)
PHONON-ROTON MODE: Dispersion Curve
←Δ
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
Roton in Bulk Liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
Maxon in bulk liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
Beyond the Roton
in Bulk 4He
Data: Pearce et al.
J. Phys Conds Matter (2001)
BEC, Excitations and Superfluidity
Bulk Liquid 4He
1. Bose-Einstein Condensation,
2. Well-defined phonon-roton modes, at Q > 0.8 Å-1
3. Superfluidity
All co-exist in same p and T range.
They have same “critical” temperature,
Tλ = 2.17 K
SVP
Tλ = 1.76 K
25 bar
Excitations, BEC, and Superfluidity
Bose-Einstein Condensation:
Superfluidity follows from BEC. An extended condensate
has a well defined magnitude and phase, <ψ> = √n0eιφ ;
vs ~ grad φ
Landau Theory:
Superfluidity follows from existence of well defined
phonon-roton modes. The P-R mode is the only mode in
superfluid 4He. Energy gap
Bose-Einstein Condensation :
Well defined phonon-roton modes follow from BEC.
Single particle and P-R modes have the same energy when there
is BEC. When there is BEC there are no low energy single
particle modes.
B.
HELIUM IN POROUS MEDIA
AEROGEL*
Open
95% porous
87% porous
A
87% porous
B
- 95 % sample grown by John Beamish at U of A entirely with deuterated
materials
VYCOR (Corning)
70 Å pore Dia.
30% porous
-- grown with B11 isotope
GELSIL (Geltech, 4F)
25 Å pores
44 Å pores
34 Å pores
50% porous
MCM-41
30% porous
47 Å pores
NANOTUBES (Nanotechnologies Inc.)
Inter-tube spacing in bundles 1.4 nm
2.7 gm sample
* University of Delaware, University of Alberta
Bosons in Disorder
Liquid 4He in Porous Media
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
Helium in Porous Media
Tc in Porous Media
Phonon-Roton Dispersion Curve
←Δ
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
Phonons, Rotons, and Layer Modes in Vycor and Aerogel
Intensity in Single Excitation vs. T
Tc = 2.05 K
Glyde et al., PRL, 84
(2000)
Tc = 2.05 K
P-R Mode in Vycor, T = 1.95 K
Tc = 2.05 K
P- R Mode in Vycor: T = 2.05 K
Tc = 2.05 K
Fraction, fs(T), of Total Scattering Intensity
in Phonon-Roton Mode- Vycor 70 A pores
Tc = 2.05 K
Fraction, fs(T), of total scattering intensity in
Phonon-Roton Mode- gelsil 44 A pore
Tc = 1.92 K
Liquid 4He in gelsil
25 A pore diameter
Tc ~ 1.3 K
Localization of Bose-Einstein Condensation in disorder
Conclusions:
• Observe phonon-roton modes up to T ~ Tλ = 2.17 K
in porous media, i.e. above Tc for superfluidity.
• Well defined phonon-roton modes exist because there is
a condensate. Thus have BEC above Tc in porous media,
in the temperature range Tc < T <Tλ = 2.17 K
Vycor
Tc = 2.05 K
gelsil (44 Å)
Tc = 1.92 K
gelsil (25 Å)
Tc = 1.3 K
• At temperatures above Tc
- BEC is localized by disorder
- No superflow
Helium in Porous Media
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
S(Q,ω) of Helium in MCM-41 powder
Pressure dependence of S(Q,ω) at the roton
(Q=2.1Å-1): MCM-41
Net Liquid He at 34 bar in MCM-41
Bossy et al. EPL 88, 56005 (2012)
Net Liquid He in MCM-41
Temperature dependence
Bossy et al. EPL 88, 56005 (2012)
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
Schematic Phase Diagram He in Nanoporous media
Bossy et al., PRL 100, 025301 (2008)
Schematic Phase Diagram: He in
Nanoporous media
Kamerlingh Onnes
Cuprates Superconductors
Insulator
T
Pseudo-gap
Metal
Metal
AF Mott
Insulator
Superconductor
Doping Level
Schematic Phase Diagram High Tc
Superconductors
Alvarez et al. PRB (2005)
Patches of Antiferromagnetic and
Superconducting regions
Alvarez et al. PRB (2005)
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
Liquid 4He in Disorder and Boson Localization
Conclusions:
• Below Tc in the superfluid phase, have
extended BEC.
• Superfluid – non superfluid liquid transition is
associated with an extended to localized BEC
cross over.
• Above Tc have only localized BEC (separated
islands of BEC).
• Close to and above Tλ have no BEC at all.
Liquid 4He and Solid Helium
Conclusions: BEC
• Neutrons play a unique role in measuring BEC and
momentum distributions in liquid and solid helium bulk
and in porous media.
• Condensate fraction in the liquid decreases from 7 % at
SVP to 3 % in liquid at solidification pressure.
• In the solid, n0 ≤ 0.3 %. Need to correlate measurement
with defects in solid (e.g. amorphous solid).
• Can measure BEC in porous media. Opens direct
measurement of BEC phases (e.g. localized BEC,
amorphous solid) in porous media, in Bosons in
disorder.