BoseEinstein Condensation Superfluidity and Elementary Excitations in Quantum
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 4 He, 3 He-4 He mixtures, 3 D, 2 D. -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 (IN 5, IN 6). 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 4 He. - modes vs pressure - modes in the solid: are there liquid like modes in solid He that superflow? 2. Measurements: BEC, n(k) -bulk liquid 4 He, to solidification. -2 D helium -Solid helium -Porous media, now and in future.
Phase Diagram of Bulk Helium
Phase Diagram Bulk helium
Phase Diagram Bulk helium
SUPERFLUIDITY 1908 – 4 He 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 v. S = grad φ (r)
Kamerlingh Onnes
SUPERFLUID: Bulk Liquid SF Fraction s(T) Critical Temperature Tλ = 2. 17 K
Landau Theory of 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, n 0 = N 0/N = 100 % T = 0 K Condensate wave function: ψ(r) = √n 0 e iφ(r)
Bose-Einstein Condensation: Gases in Traps
SUPERFLUIDITY 1908 – 4 He 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 v. S = grad φ (r)
London
Bose-Einstein Condensation: Gases in Traps
Bose-Einstein Condensation, Bulk Liquid 4 He 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 =k. Q= 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 B 83, 100507 (2011)
BEC: Bulk Liquid 4 He vs pressure PR B 83, 100507 (R)(2011)
Bose-Einstein Condensate Fraction Liquid Helium versus Pressure Glyde et al. PR B 83, 100507 (R)(2011)
Bose-Einstein Condensate Fraction Liquid Helium versus Density PR B 83, 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 4 He Talbot et al. , PRB, 38, 11229 (1988)
Maxon in bulk liquid 4 He Talbot et al. , PRB, 38, 11229 (1988)
Beyond the Roton in Bulk 4 He Data: Pearce et al. J. Phys Conds Matter (2001)
BEC, Excitations and Superfluidity Bulk Liquid 4 He 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> = √n 0 eιφ ; 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 4 He. 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 B 11 isotope GELSIL (Geltech, 4 F) 25 Å pores 44 Å pores 34 Å pores 50% porous MCM-41 47 Å pores 30% porous 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 4 He 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 4 He 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 AF Mott Insulator Metal 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 4 He 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 4 He 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, n 0 ≤ 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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