Bose einstein condensation superfluidity and elementary excitations in quantum liquids
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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.

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Bose einstein condensation superfluidity and elementary excitations in quantum liquids

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

BEC, Excitations, Superfluidity

Bose Einstein Condensation (neutrons)

1968-

Collective Phonon-Roton modes (neutrons)

1958-

Superfluidity (torsional oscillators)

`1938-

He in porous media integral part

of historical superflow measurements.


Bec superfluidity and neutrons

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

BEC and n (k) (single particle excitations)

Collaborators: SNS and ISIS

Richard T. Azuah - NIST Center for Neutron Research, Gaithersburg, USA

Souleymane Omar Diallo - Spallation Neutron source, ORNL, Oak Ridge, TN

Norbert Mulders - University of Delaware

Douglas Abernathy- Spallation Neutron source, ORNL, Oak Ridge, TN

Jon V. Taylor - ISIS Facility, UK

Oleg Kirichek - ISIS Facility, UK


Collective phonon roton modes structure

Collective (Phonon-roton) Modes, Structure

Collaborators:(ILL)

JACQUES BOSSY Institut Néel, CNRS-UJF,

Grenoble, France

Helmut SchoberInstitut Laue-Langevin

Grenoble, France

Jacques OllivierInstitut Laue-Langevin

Grenoble, France

Norbert Mulders University of Delaware


Bec superfluidity and superfluidity

BEC, Superfluidity and Superfluidity

Organization of Talk

  • Phase diagrams: liquid, solid, superfluidity.

  • 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 of Bulk Helium


Phase diagram bulk helium

Phase Diagram Bulk helium


Phase diagram bulk helium1

Phase Diagram Bulk helium


Superfluidity

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

Kamerlingh Onnes


Superfluid bulk liquid sf fraction s t

SUPERFLUID: Bulk Liquid SF Fraction s(T)

Critical Temperature Tλ = 2.17 K


Landau theory of superfluidity

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

PHONON-ROTON MODE: Dispersion Curve

← Δ

Donnelly et al., J. Low Temp. Phys. (1981)

 Glyde et al., Euro Phys. Lett. (1998)


Bose einstein condensation

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

Bose-Einstein Condensation: Gases in Traps


Superfluidity1

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

London


Bose einstein condensation gases in traps1

Bose-Einstein Condensation: Gases in Traps


Bose einstein condensation bulk liquid 4he

Bose-Einstein Condensation, Bulk Liquid 4He

Glyde, Azuah, and Stirling

Phys. Rev., 62, 14337 (2000)


Bose einstein condensation bulk liquid

Bose-Einstein Condensation: Bulk Liquid

Expt: Glyde et al. PRB (2000)


Bose einstein condensation1

Bose-Einstein Condensation

Model momentum distribution:

y =kQ= k.Q

Model One Body density matrix:


Full dynamic structure factor

Full Dynamic Structure Factor


Model one body density matrix bulk helium

Model One Body Density Matrix: Bulk Helium


Bose einstein condensate fraction liquid helium versus density

Bose-Einstein Condensate FractionLiquid Helium versus Density

PR B83, 100507 (2011)


Bec bulk liquid 4he vs pressure

BEC: Bulk Liquid 4He vs pressure

PR B83, 100507 (R)(2011)


Bose einstein condensate fraction liquid helium versus pressure

Bose-Einstein Condensate FractionLiquid Helium versus Pressure

Glyde et al. PR B83, 100507 (R)(2011)


Bose einstein condensate fraction liquid helium versus density1

Bose-Einstein Condensate FractionLiquid Helium versus Density

PR B83, 100507 (2011)


J q y and bec in liquid helium at 24 bar

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 pressure1

Bose-Einstein Condensate FractionLiquid Helium versus Pressure

Diallo et al. PRB 85, 140505 (R) (2012)


Phonon roton mode dispersion curve1

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 4 he

Roton in Bulk Liquid 4He

Talbot et al., PRB, 38, 11229 (1988)


Maxon in bulk liquid 4 he

Maxon in bulk liquid 4He

Talbot et al., PRB, 38, 11229 (1988)


Beyond the roton in bulk 4 he

Beyond the Rotonin Bulk 4He

Data: Pearce et al.

J. Phys Conds Matter (2001)


Bec excitations and superfluidity

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

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

B. HELIUM IN POROUS MEDIA

AEROGEL*95% porous

Open87% porousA

87% porousB

- 95 % sample grown by John Beamish at U of A entirely with deuterated materials

VYCOR (Corning)30% porous

  • Å pore Dia.-- grown with B11 isotope

    GELSIL (Geltech, 4F) 50% porous

    25 Å pores

    44 Å pores

    34 Å pores

    MCM-4130% 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

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

Helium in Porous Media


T c in porous media

Tc in Porous Media


Phonon roton dispersion curve

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

Phonons, Rotons, and Layer Modes in Vycor and Aerogel


Intensity in single excitation vs t t c 2 05 k

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

P-R Mode in Vycor, T = 1.95 K

Tc = 2.05 K


P r mode in vycor t 2 05 k

P- R Mode in Vycor: T = 2.05 K

Tc = 2.05 K


Fraction f s t of total scattering intensity in phonon roton mode vycor 70 a pores

Fraction, fs(T), of Total Scattering Intensityin Phonon-Roton Mode- Vycor 70 A pores

Tc = 2.05 K


Fraction f s t of total scattering intensity in phonon roton mode gelsil 44 a pore

Fraction, fs(T), of total scattering intensity in Phonon-Roton Mode- gelsil 44 A pore

Tc = 1.92 K


Bose einstein condensation superfluidity and elementary excitations in quantum liquids

Liquid 4He in gelsil

25 A pore diameter

Tc ~ 1.3 K


Bose einstein condensation superfluidity and elementary excitations in quantum liquids

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 Tcin porous media, in the temperature range Tc< T <Tλ= 2.17 K

    VycorTc = 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 media1

Helium in Porous Media


Helium in mcm 41 45 a and in gelsil 25 a

Helium in MCM-41 (45 A) and in gelsil (25 A)

Bossy et al. PRB 84,1084507 (R) (2010)


S q of helium in mcm 41 powder

S(Q,ω) of Helium in MCM-41 powder


Pressure dependence of s q at the roton q 2 1 1 mcm 41

Pressure dependence of S(Q,ω) at the roton (Q=2.1Å-1): MCM-41


Net liquid he at 34 bar in 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

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 a1

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

Schematic Phase Diagram He in Nanoporous media

Bossy et al., PRL 100, 025301 (2008)


Schematic phase diagram he in nanoporous media1

Schematic Phase Diagram: He in Nanoporous media


Kamerlingh onnes1

Kamerlingh Onnes


Bose einstein condensation superfluidity and elementary excitations in quantum liquids

Cuprates Superconductors

Insulator

T

Pseudo-gap Metal

Metal

AF Mott Insulator

Superconductor

Doping Level


Schematic phase diagram high tc superconductors

Schematic Phase Diagram High Tc Superconductors

Alvarez et al. PRB (2005)


Patches of antiferromagnetic and superconducting regions

Patches of Antiferromagnetic and Superconducting regions

Alvarez et al. PRB (2005)


Helium in mcm 41 45 a and in gelsil 25 a2

Helium in MCM-41 (45 A) and in gelsil (25 A)

Bossy et al. PRB 84,1084507 (R) (2010)


Bose einstein condensation superfluidity and elementary excitations in quantum liquids

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.


Bose einstein condensation superfluidity and elementary excitations in quantum liquids

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.


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