Excitations, Bose-Einstein Condensation and Superfluidity in Liquid 4 He Henry R. Glyde Department of Physics & Astronomy University of Delaware

Phase Diagram of Helium

Goals Neutron scattering studies of excitations of quantum liquids in disorder. phonons and rotons in disorder new excitations in disorder Reveal the interdependence of Bose- Einstein Condensation (BEC), phonon- roton excitations, and superfluidity. Compare bulk liquid 4 He and 4 He in porous media (confinement and disorder).

Phonon-Roton Dispersion Curve  Donnelly et al., J. Low Temp. Phys. (1981)  Glyde et al., Euro Phys. Lett. (1998)

Bosons in Disorder Liquid 4 He in Aerogel, Vycor, Geltech Flux Lines in High T c Superconductors Josephson Junction Arrays Granular Metal Films Cooper Pairs in High T c Superconductors Models of Disorder excitation changes new excitations at low energy Localization of Bose-Einstein Condensation by Disorder

Superfluid Properties in Confinement/Disorder Confinement reduces T c below. Confinement modifies (T dependence). Confinement reduces (magnitude). Porous media is a “laboratory” to investigate the relation between superfluidity, excitations, and BEC. Measure corresponding excitations and condensate fraction, n o (T). (new, 1995)

Graduate Students Jonathan DuBois Bose-Einstein Condensation of Bosons in Traps, Variational Monte Carlo, Diffusion MC Asaad Sakhel Models of excitations in liquid 4 He BEC in traps Ali Shams Souleymane Omar Diallo

Excitations, BEC, and Superfluidity Collaborators: Francesco Albergamo -Institut Laue Langevin Grenoble, France Richard T. Azuah -NIST Center for Neutron Research Gaithersburg, Maryland, USA Jacques Bossy -Centre de Recherche sur Les Très Basses Temperature CNRS Grenoble, France Bjorn Fåk -ISIS Facility Rutherford Appleton Lab United Kingdom and Commissariat à l’Energie Atomique Grenoble, France

Excitations, BEC, and Superfluidity Collaborators (Con’t): Oliver Plantevin -European Synchrotron Radiation Facility, Grenoble Gerrit Coddens -Laboratoire des solides irradiés Ecole Polytechnique Palaiseau, France Reinhard Scherm -Physikalisch-Technische Bundesanstalt, Braunschweig Norbert Mulders -University of Delaware Newark, Delaware USA John Beamish -University of Alberta Edmonton, Canada Helmut Schober -Institut Laue Langevin Grenoble, France

Neutron Scattering Laboratories Institute Laue Langevin Grenoble, France ISIS Rutherford Appleton Laboratories Oxfordshire, England NIST Center for Neutron Research National Institute of Standards and Technology Gaithersburg, Maryland

Neutron Scattering: ILL

Excitations and Bose-Einstein Condensation in Quantum Liquids in Disorder Henry R. Glyde, University of Delaware, DMR Figure 1. Top: The Insitiut Laue Langevin (just behind the ESRF synchrotron ring) in Grenoble. Bottom: Left to right, Jacques Bossy, Henry Glyde, Francesco Albergamo and Olivier Plantevin in front of the IN6 neutron spectrometer of ILL.

Bose-Einstein Condensation: Atoms in Traps

Bose-Einstein Condensation Glyde, Azuah, and Sterling Phys. Rev., 62, (2001)

Bose-Einstein Condensation Condensate Fraction

T c in Porous Media

Superfluid Density  s (T) Superfluid Density Bulk Liquid 4 He

London

BEC, Excitations, and Superfluidity

Landau

Phonon-Roton Dispersion Curve  Donnelly et al., J. Low Temp. Phys. (1981)  Glyde et al., Euro Phys. Lett. (1998)

Superfluidity Landau Theory 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  ). Via P-R excitations, superflow arises from BEC. BEC and Phase Coherence, Ø (r) Superfluidity follows directly from BEC, phase conherence.

Phonons and Rotons Arise From Bose-Einstein Condensation Gavoret and Nozières (1964) showed: Dense liquid with BEC – only one excitation: density and quasiparticle modes have the same energy, At low Q, as in Bose gas. No other excitations at low energy (could have vortices). Ma and Woo (1967), Griffin and Cheung (1973), and others showed: Only a single mode at all Q with BEC -- the phonon-roton mode.

Maxon in Bulk Liquid 4 He Talbot et al., PRB, 38, (1988)

Roton in Bulk Liquid 4 He Talbot et al., PRB, 38, (1988)

Beyond the Roton in Bulk Liquid 4 He

BEC, Excitations, and Superfluidity

Excitations, BEC, and Superfluidity Bulk Liquid 4 He BEC, well-defined excitations and superfluidity coincide e.g., all have some critical temperature, = 2.17 K SVP = 1.92 K 20 bar

Porous Media AEROGEL95% porous 87% porousA 87% porousB -- grown with deuterated materials or flushed with D 2 VYCOR30% porous 70 diameter pores -- grown with B 11 isotope GELTECH SILICA50% porous 25 diameter pores -- flushed with D 2

T c in Porous Media

Geltech (25 Å pores) Superfluid Density in Porous Media Chan et al. (1988) Miyamoto and Takeno (1996)

Bose-Einstein Condensation Liquid 4 He in Vycor Azuah et al., JLTP (2003) T c (Superfluidity) = K

Phonons, Rotons, and Layer Modes in Vycor and Aerogel

Layer Mode in Vycor and Aerogel

Temperature Dependence of Roton Energy Fåk et al., PRL, 85 (2000)

Intensity in Single Excitation vs. T Glyde et al., PRL, 84 (2000)

Phonon-Roton Mode in Vycor: T = 2.05 K

Roton in Geltech Silica: Partial Filling Plantevin et al., PRB, 65 (2002)

Liquid 4 He in Geltech Silica T c (Superfluidity) = K

Fraction, f s (T), of Total Scattering Intensity in Phonon-Roton Mode

BEC, Excitations, and Superfluidity

Excitations, BEC, and Superfluidity Liquid 4 He in disorder BEC, well-defined excitations and separated from superfluidity in disorder e.g., T c - superfluidity T c (BEC) - Bose-Einstein condensation T c (BEC) > T c Disorder localizes the condensate. New Here Measurements of phonon-roton excitations and BEC in disorder

BEC in Disorder Both n o and reduced by static disorder (homogeneous). Huang & Meng, PR 1992 dilute gas limit, analytic Astraljparehik, et al., preprint (2002) fluid densities, Monte Carlo reduced more than n o Could have localized BEC. As T is reduced, BEC forms first in favorable regions, in pockets. Superflow occurs at a lower T when regions grow and connect to have phase coherence across the entire sample.

Conclusions Have Bose-Einstein Condensation in liquid 4 He. The well defined phonon-roton excitations in superfluid 4 He (the sharp dispersion curve) is a consequence of BEC. Well defined phonon-roton excitations do not exist above in the normal phase where n o = 0 (no phase coherence). Landau theory and BEC theories of superfluidity have common dependence on BEC. In liquid 4 He in disorder, observe phonons and rotons as in bulk liquid 4 He. In addition, observe 2D layer modes. Also observe excitations above T c – in the normal phase. Disorder can localize BEC and superfluidity. In disorder, have phase coherence over short length scales above T c for macroscopic superfluidity. Can “see” this localized BEC in excitations but not in Torsional Oscillator measurements. Future: Use confinement/disorder to “tune” and investigate BEC, excitations and superfluidity. Explore reduced dimensions.

Focused Research Group: NSF 2001 Oscar Vilches University of Washington John Larese University of Tennessee Henry Glyde (PI) University of Delaware

Goals Precision Measurement of excitations in liquid 4 He (and 3 He) by inelastic neutron scattering. Measurement of condensation fraction and momentum distribution n(k) by high energy transfer inelastic neutron scattering. Reveal relation between excitations and BEC—do well defined phonon-roton excitations exist because there is BEC? Reconcile theories of superfluidity. e.g.,Landau theory ( ) - phonons-rotons (no BEC) London (1938) - BEC (no phonons-rotons)

Bose-Einstein Condensation Liquid 4 He in Vycor Azuah et al., JLTP (2003) T c (Superfluidity) = K

Phonons and Rotons Arise From Bose-Einstein Condensation Bogoliubov (1947) showed: Bose gas with BEC -- quasiparticles have energy: - phonon (sound) form Quasiparticle mode coincides with sound mode. Only one excitation when have BEC.

BEC (continued) Density and quasiparticle become one and the same excitation. They have the same energy. Composite “density—quasiparticle” excitation has the phonon energy. At low. Independent of strength of interaction. No “quasiparticle” excitations lying under the phonon- roton dispersion curve to which the phonon-roton excitations can decay.

Excitations in a Bose Fluid

Filling Dependence of Roton and Layer Modes

Density and Quasiparticle Excitations (BEC) Bogoliubov (1947), Gavoret and Nozieres (1964), Griffin (1993), and Glyde (1994) Density Operator First quantization: Second quantization: -- density operator -- creates a particle at r -- creates particle with momentum k -- density operator Density operator is a two particle operator.

Density and Quasiparticle Excitations (BEC) A macroscopic number of particles N o in k = 0 state. -- number in state k -- large (10 22 ) -- a number Density Operator Density operator includes quasiparticle excitation.

Figure 2. Discussing analsis of neutron scattering data at Delaware are (left to right): Zhicheng Yan, Richard Azuah, Assad Sakhel, Jonathan DuBois, and Henry Glyde. Excitations and Bose-Einstein Condensation in Quantum Liquids in Disorder Henry R. Glyde, University of Delaware, DMR

Localization of Bose-Einstein Condensation by Disorder Henry Glyde, University of Delaware, Oscar Vilches, University of Washington, John Larese, University of Tennessee Focused Research Group, DMR Our neutron scattering studies of liquid 4 He in porous media show evidence of Bose-Einstein Condensation localized by disorder. In bulk, pure systems the origin of superfluidity (and superconductivity) is BEC. Once there is BEC, there are simultaneously phonon-roton excitations and superfluidity. In contrast, in disorder the BEC can be localized so that there are P-R excitations but no macroscopic superfluidity. Superfluidity follows at a lower temperature when the BEC becomes extended across the sample. The “localized BEC” state in liquid 4 He is similar to the “pseudo gap” state observed in high T c superconductors.