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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

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.

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

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

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

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.

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)

Critical Temperature Tλ = 2.17 K

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 ).

← Δ

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

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

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)

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)

Glyde, Azuah, and Stirling

Phys. Rev., 62, 14337 (2000)

Expt: Glyde et al. PRB (2000)

Model momentum distribution:

y =kQ= k.Q

Model One Body density matrix:

PR B83, 100507 (2011)

PR B83, 100507 (R)(2011)

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

PR B83, 100507 (2011)

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

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

← Δ

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

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

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

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

Data: Pearce et al.

J. Phys Conds Matter (2001)

- 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

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.

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

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

← Δ

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

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

Glyde et al., PRL, 84 (2000)

Tc = 2.05 K

Tc = 2.05 K

Tc = 2.05 K

Tc = 2.05 K

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

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

Bossy et al. EPL 88, 56005 (2012)

Bossy et al. EPL 88, 56005 (2012)

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

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

Cuprates Superconductors

Insulator

T

Pseudo-gap Metal

Metal

AF Mott Insulator

Superconductor

Doping Level

Alvarez et al. PRB (2005)

Alvarez et al. PRB (2005)

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.