Bose-Einstein Condensation, Superfluidity and Elementary Excitations in Quantum Liquids Henry R. GlydeDepartment of Physics & AstronomyUniversity of Delaware

ISIS Facility Rutherford Appleton LaboratoryHarwell, Oxford17 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 partof historical superflow measurements.

BEC, Superfluidity and NeutronsScientific Goals: Observe and document BEC and atomic momentum distribution in liquid 4He, 3He-4He mixtures, 3D, 2D .-single particle excitations, S(Q,) at high Q, -SNS (ARCS), ISIS (MARI) Observe Phonon-roton, layer modes (porous media)-collective modes, S(Q,) at low Q, -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, USASouleymane Omar Diallo - Spallation Neutron source, ORNL, Oak Ridge, TNNorbert Mulders - University of Delaware

Douglas Abernathy- Spallation Neutron source, ORNL, Oak Ridge, TNJon V. Taylor - ISIS Facility, UK

Oleg Kirichek - ISIS Facility, UK

Collective (Phonon-roton) Modes, Structure Collaborators:(ILL)

JACQUES BOSSY Institut Nel, CNRS-UJF, Grenoble, France

Helmut SchoberInstitut Laue-LangevinGrenoble, France

Jacques OllivierInstitut Laue-LangevinGrenoble, France

Norbert Mulders University of Delaware

BEC, Superfluidity and SuperfluidityOrganization 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

SUPERFLUIDITY1908 4He first liquified in Leiden by Kamerlingh Onnes

1925 Specific heat anomaly observed at T = 2.17 K by Keesom.Denoted the 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 (r)

Kamerlingh Onnes

SUPERFLUID: Bulk Liquid SF Fraction s(T) Critical Temperature T = 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 Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)

BOSE-EINSTEIN CONDENSATION 1924

Bose gas : k = exp[ik.r] , Nk

k = 0 state is condensate state for uniform fluids. Condensate fraction, n0 = N0/N = 100 % T = 0 KCondensate wave function: (r) = n0 e i(r)

Bose-Einstein Condensation: Gases in Traps

SUPERFLUIDITY1908 4He first liquified in Leiden by Kamerlingh Onnes

1925 Specific heat anomaly observed at T = 2.17 K by Keesom.Denoted the 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 (r)

London

Bose-Einstein Condensation: Gases in Traps

Bose-Einstein Condensation, Bulk Liquid 4HeGlyde, Azuah, and StirlingPhys. Rev., 62, 14337 (2000)

Bose-Einstein Condensation: Bulk LiquidExpt: Glyde et al. PRB (2000)

Bose-Einstein CondensationModel One Body density matrix:Model momentum distribution:y =kQ= k.Q

Full Dynamic Structure Factor

Model One Body Density Matrix: Bulk Helium

Bose-Einstein Condensate FractionLiquid Helium versus DensityPR B83, 100507 (2011)

BEC: Bulk Liquid 4He vs pressurePR B83, 100507 (R)(2011)

Bose-Einstein Condensate FractionLiquid Helium versus PressureGlyde et al. PR B83, 100507 (R)(2011)

Bose-Einstein Condensate FractionLiquid Helium versus DensityPR B83, 100507 (2011)

J(Q,y) and BEC in Liquid Helium at 24 barDiallo et al. PRB 85, 140505 (R) (2012)

Bose-Einstein Condensate FractionLiquid Helium versus PressureDiallo et al. PRB 85, 140505 (R) (2012)

PHONON-ROTON MODE: Dispersion Curve Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)

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

Maxon in bulk liquid 4He Talbot et al., PRB, 38, 11229 (1988)

Beyond the Roton in Bulk 4HeData: Pearce et al. J. Phys Conds Matter (2001)

BEC, Excitations and SuperfluidityBulk Liquid 4He

1. Bose-Einstein Condensation,

2. Well-defined phonon-roton modes, at Q > 0.8 -1

3. Superfluidity All co-exist in same p and T range. They have same critical temperature,

T = 2.17 K SVP

T = 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, = n0e ; vs ~ grad

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 MEDIAAEROGEL*95% porousOpen87% porousA87% porousB- 95 % sample grown by John Beamish at U of A entirely with deuterated materials

VYCOR (Corning)30% porous pore Dia.-- grown with B11 isotope

GELSIL (Geltech, 4F) 50% porous25 pores44 pores34 poresMCM-4130% porous47 poresNANOTUBES (Nanotechnologies Inc.) Inter-tube spacing in bundles 1.4 nm 2.7 gm sample

* University of Delaware, University of Alberta

Bosons in DisorderLiquid 4He in Porous Media

Flux Lines in High Tc Superconductors

Josephson Junction Arrays

Granular Metal Films

Cooper Pairs in High Tc Superconductors

Models of Disorderexcitation changesnew excitations at low energy

Helium in Porous Media

Tc in Porous Media

Phonon-Roton Dispersion Curve 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 KGlyde 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

Tc ~ 1.3 K

Liquid 4He in gelsil 25 A pore diameter

Conclusions:

Localization of Bose-Einstein Condensation in disorderObserve phonon-roton modes up to T ~ T = 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

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,) of Helium in MCM-41 powder

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

Schematic Phase Diagram High Tc Superconductors

Alvarez et al. PRB (2005)

Patches of Antiferromagnetic and Superconducting regionsAlvarez et al. PRB (2005)

Helium in MCM-41 (45 A) and in gelsil (25 A)Bossy et al. PRB 84,1084507 (R) (2010)

Conclusions:

Liquid 4He in Disorder and Boson LocalizationBelow 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 T have no BEC at all.

Conclusions: BECLiquid 4He and Solid HeliumNeutrons 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.

**