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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

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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

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

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 - 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

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

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 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 FractionLiquid Helium versus Density

PR B83, 100507 (2011)


BEC: Bulk Liquid 4He vs pressure

PR B83, 100507 (R)(2011)


Bose-Einstein Condensate FractionLiquid Helium versus Pressure

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


Bose-Einstein Condensate FractionLiquid 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 FractionLiquid 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 Rotonin 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*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

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 Intensityin 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 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 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.


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