Phonon-roton excitations and quantum phase transitions in liquid 4He in nanoporus mediaHenry R. GlydeDepartment of Physics & AstronomyUniversity of Delaware

Recent Progress in Many Body TheoriesBarcelona, 16-20 July, 2007

Excitations, BEC, and SuperfluidityCollaborators:

Jonathan PearceUniversity of Delaware, ILLNational Physical LaboratoryTeddington, UK

Jacques Bossy Centre de Recherche sur LesTrs Basses TemperatureCNRS, Grenoble, France

Francesco Albergamo -ESRF, Grenoble, France

Bjorn Fk - Commissariat lEnergie Atomique, Grenoble, France

Norbert Mulders -University of DelawareRichard T. Azuah -NIST Center for Neutron Research, Gaithersburg, Maryland, USA

Helmut Schober Institut Laue-LangevinGrenoble, France

Excitations, BEC, and SuperfluidityCollaborators (Cont):

Oliver Plantevin -Universit de Paris Sud

Helmut Schober -Institut Laue Langevin, Grenoble, France

Excitations, BEC, and SuperfluidityGoals:

Explore the interdependence of Bose-Einstein Condensation (BEC), phonon-roton excitations, and superfluidity.

Reveal origin of superfluidity in disorder and confinement. -BEC or well defined excitations.

Neutron scattering studies of excitations of liquid 4He in confinement and disorder. Compare with measurements of superfluid density.

Excitations, BEC, and SuperfluidityLandau Theory: Superfluidity follows from existence of well defined phonon-roton modes. The P-R mode is the only mode in superfluid 4He.

Bose-Einstein Condensation: Superfluidity follows from BEC. An extended condensate has a well defined magnitude and phase, = n0e ;

vs ~ grad

Bose-Einstein Condensation (BEC): Well defined phonon-roton modes follow from BEC. Single particle and P-R modes have the same energy when there is BEC. No low energy single particle modes.

Bosons in DisorderLiquid 4He in aerogel, Vycor, gelsil (Geltech)

Bose gases in traps with disordered potentials

Josephson Junction Arrays

Granular Metal Films

Cooper Pairs in High Tc Superconductors

Flux Lines in High Tc Superconductors

Specific Present Goals:

Impact of finite size (confinement) and disorder on excitations and Bose-Einstein condensation.

Localization of Bose-Einstein Condensation by disorder

Search for a Quantum Phase Transition

Explore liquid helium at higher pressure

Helium at negative pressure and on nanotubes (1D)

Excitations, BEC, and SuperfluidityOrganization of Talk

Bulk liquid 4He --review Superfluid density, S BEC condensate fraction, n0 Phonon-roton excitations.

2. Porous media p ~ 0, T dependence Review S , TC Present phonon-roton data. Evidence for localized BEC at temperatures above TC

3. Porous media high pressures, low TPhonon-roton modes disappear at 37 bars and T ~ 0 K, evidence for a superfluid-normal transition at T ~ 0 K, a quantum phase transiton? Or just solidification.

BULK HELIUM: Phase Diagram

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

London

Superfluid Density s(T)

Superfluid Density S (T) = 0 at T = TBulk Liquid 4He

Phase Diagram of Bulk Helium

BOSE-EINSTEIN CONDENSATION Atoms in Traps

Bose-Einstein Condensation: Atoms in Traps

Bose-Einstein CondensationGlyde, Azuah, and StirlingPhys. Rev. B62, 14337 (2000)

Bose-Einstein Condensation

Expt: Glyde et al. PRB (2000)

Condensate fraction bulk 4He

L. Vranjes and J. Boronat et al. PRL (2005)

Condensate fraction bulk 4He

Moroni and Boninsegni JLTP (2004)50 bars

Bose-Einstein CondensationSolid Helium p = 41 barsDiallo et al. PRL 98, 205301 (2007)

PHONONS AND ROTONS Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)

Roton Energy versus PressureRoton energy at Q ~ 2.1 -1 as a function of pressure.Vranjes et al. PRL (2005)

Liquid 4He at Negative Pressure

Liquid 4He at Negative Pressure Dispersion curve at SVP and - 5 bar

Liquid 4He at Negative Pressure MCM-41 Adsorption isotherm

Pores are full with 4He at negative pressure at fillings C to H. C = -5.5 bar.

Maxon Energy versus PressureMaxon energy at Q = 1.1 -1 as a function of pressure.

Phonon-roton mode of 4He under pressure, 24.7 bars

Phonon-roton mode of 4He under pressure, 31.2 bars

Temperature dependence of mode intensity: Maxon, bulk liquid 4He Talbot et al., PRB, 38, 11229 (1988)

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

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

Phonons and Rotons (sharply defined modes) arise From Bose-Einstein CondensationBogoliubov (1947) showed: Bose gas with BEC -- quasiparticles have energy:

- phonon (sound) form

Quasiparticle mode coincides with sound mode.Only one excitation when have BEC.

Phonons and Rotons Arise From Bose-Einstein CondensationGavoret and Nozires (1964) showed: Dense liquid with BEC only one excitation: density and quasiparticle modes have the same energy, 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.

Excitations in a Bose Fluid+

Excitations, BEC, and SuperfluidityBulk Liquid 4He

BEC, well-defined phonon-roton modes at Q > 0.8 -1 and superfluidity coincide.

e.g., all have some critical temperature,

T = 2.17 K SVP

T = 1.76 K 25 bar

Phase Diagram of Bulk Helium

SuperfluidityLandau 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, (r)

Superfluidity follows directly from BEC, phase conherence .

Landau

POROUS MEDIAAEROGEL95% porousOpen87% porousA87% porousB-- grown with deuterated materials or flushed with D2

VYCOR30% porous pore Diameter -- grown with B11 isotope

GELSIL (GELTECH) 50% porous44 pore Diameter34 pore Diameter25 pore Diameter

MCM-4130% porous47 pores

Superfluid Properties in Confinement/DisorderConfinement reduces Tc 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, no(T). (new, 1995)

Tc in Porous Media

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

- Yamamoto et al. Phys. Rev. Lett. 93, 075302 (2004)Superfluid Density in gelsil (Geltech) 25 A diameter

Schematic Phase Diagram of Helium Confined to Nanoscales

e.g. 2 - 4 nm

- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Phase Diagram of gelsil: 25 pore diameter

Bose-Einstein CondensationLiquid 4He in VycorAzuah et al., JLTP (2003)

Tc (Superfluidity) = 2.05 K

Bose-Einstein Condensation Vycor

Azuah et al., JLTP (2003)

Phonons, Rotons, and Layer Modes in Vycor and Aerogel

Temperature Dependenceof Roton EnergyFk et al., PRL, 85 (2000)

Liquid helium in porous media supports well defined phonon-roton excitations up to wave vectors Q 2.8 .

Energies and widths (within precision) are the same as in bulk 4He at all T.

Liquid also supports layer modes at roton wave vectors.

At partial fillings, can also see ripplons on 4He liquid surfaces. (Lauter et al. Appl. Phys. A 74, S1547 (2002))

Conclusions:

Excitations of Liquid 4He in Confinement

Intensity in P-R Mode vs. TGlyde et al., PRL, 84 (2000)

Mode Intensity in Vycor:T = 1.95 K

Mode Intensity in Vycor T = 2.05 K

Mode Intensity in Vycor:T = 2.15 K

Mode Intensity in Vycor:T = 2.25 K

Fraction, fs(T), of Total Intensity in Phonon-Roton Mode Vycor Tc = 2.05 KAlbergamo et al. Phys. Rev. B69, 014514 (2004)

Mode Intensity in 44A Gelsil:versus T. Tc = 1.92 KAlbergamo et al. PRB (2007)

Fraction, fs(T), of total scattering intensity in Phonon-Roton Mode- gelsil 44 A pore diameter

Liquid 4He in 25 A gelsil (Geltech)Tc (Superfluidity) ~ 1.3 K

Observe phonon-roton modes up toT = 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.Vycor Tc = 2.05 Kgelsil (44 ) Tc = 1.92 Kgelsil (25 ) Tc = 1.3 K

At temperatures Tc < T < T - BEC is localized by disorder- No extended phase coherence across the sample- No superflow

Conclusions:

Localization of Bose-Einstein Condensation in disorder

Extended BEC at temperature below Tc in superfluid phase.

Superfluid - Normal liquid transition associated with an extended to localized BEC cross over at SVP.

Conclusions:

Liquid 4He in Disorder and Boson Localization

Schematic Phase Diagram of BEC in Nanoporous media

gelsil 44 mean pore diameter,Pearce et al. PRL (2004)

gelsil 34 mean pore diameter - Pearce et al. Preprint (2006)

gelsil 25 mean pore diameter - being analysed (2006)

Compare with Yamamoto et al. PRL (2004) , superfluid density in 25 gelsil. PRESSURE DEPENDENCE Phonon-Roton modes, Low TLiquid 4He up 57 bars in gelsil

- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Quantum Phase Transition in 25 A pore diameter gelsil ?

Phonon-roton mode of 4He under pressure, 31.2 bars

Pressure dependence: 44 gelsil

phonon (Q = 0.7 -1) roton (Q=2.1-1)

Pressure dependence of S(Q,) at the roton (Q=2.1-1)34 A gelsil

Pressure dependence of S(Q,) at the roton (Q=2.1-1)25 A gelsil

Roton energy and intensity in roton peak vs pressuregelsil 34 Pearce et al. (2006)

Phase diagram of modes of liquid 4He in 34 pore diameter gelsil

4He remains liquid in 34 A gelsil up to what pressure?

p = pL pS = 2 / RcpS = 25.3 bars Rc = 14

(a) = 0.17 erg/cm2 -- constant

pL = 50 bars

= -increases with pressure (Maris and Caupin, JLTP 131, 145 (2003))

pL = 70 bars

Vycor, pL = 45 bars Rc = 35

- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Quantum Phase Transition in 25 A pore diameter gelsil ?

Schematic Phase Diagram QPT in Nanoporous media

Net Scattering intensity gelsil 34 Pearce et al. PRL ( rejected 2006-7) Compare with L. Vranjes, J. Boronat et al. PRL,95, 145302 (2005)

Net Scattering intensity, gelsil 34 and bulk liquid simulation compared. Pearce et al. (in progress) 60 barsBulk liquid

Scattering intensity, gelsil 70 and p = 70 bars Wallacher et al. JLTP 138, 1013 (2005)

Schematic Phase Diagram QPT in Nanoporous media

Extended BEC at temperature below Tc in superfluid phase at SVP.

Superfluid - Normal liquid transition associated with an extended to localized BEC cross over at SVP.

Quantum Phase Transition at p ~ 35 bars Only localized BEC at p > 35 bars.

Conclusions:

Liquid 4He in Disorder and Boson Localization

At T ~ 0 K and higher pressure, ( p > 25 bars) BEC condensate fraction is small.(n0 ~ 1 % at p = 70 bars, bulk 4He)

. Speculation:At T ~ 0 K and pressures p > pc - BEC is localized by disorder- No extended phase coherence across the sample- No superflow Quantum Phase Transition at 35 bars . Phonon roton modes disappear, p ~ 38 barsHave liquid up to 38 bars and liquid-solid co-existence above 38 bars, probably up to 45-50 bars.

Conclusions (QPT):

Liquid 4He in Disorder and Boson Localization

Excitations of superfluid 4He at pressures up to 40 bars

Phase diagran and excitations of superfluid 4He in 44 gelsilPearce et al., PRL (2004)

Bose-Einstein Condensation

PHONONS AND ROTONS Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)

Superfluid Properties in Confinement/DisorderConfinement reduces Tc 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, no(T). (new, 1995)

Excitations of liquid 4He in 34 pore diameter gelsilPearce et al.,(2006) (in progress)

BEC, Excitations, and Superfluidity

BEC in 2DBoninsegni et al. PRL 96, 070601 (2006)

Condensate fraction bulk 4He

L. Vranjes and J. Boronat et al. PRL (2005)

Condensate fraction bulk 4He

Moroni and Boninsegni JLTP (2004)50 bars

Sum rule for condensate component of S(Q,) HRG, PRL (1995)

Topic of Talk:

Well defined p-r excitations (Q > 0.8 ) exist because there is Bose-Einstein condensation (BEC).

Measure superfluid density s (T) and determine the normal to superfluid transition temperature Tc in Vycor (same sample). Find:

Tc = 2.05 K Tc, up to T = T = 2.17 K

Thus BEC in Vycor above Tc , at temperatures Tc < T < T . - localized BEC.

Momentum distribution solid 4He

Layer Mode in Porous Media

Layer Mode in Vycor and Aerogel

Observe phonon-roton modes up toT = 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.Vycor Tc = 2.05 KGeltech (44 ) Tc = 1.92 KGeltech (25 ) Tc = 1.0 K

At temperatures Tc < Tc < T - BEC is localized by disorder- No extended phase coherence across the sample- No superflow

Conclusions:

Liquid 4He in Disorder and Boson Localization

Quantum Liquids in ConfinementLopatin and Vinokur (2002):

Same model as Huang & Meng -- disorder arising from random impurities

Reduction of critical temperature for BEC by disorder

Reduction of critical temperature for superfluidity by disorder.

Quantum Liquids in ConfinementGiorgini et al. (1994):

Same model as Huang & Meng -- disorder arising from random impurities

Sound velocity

Half width of phonons

Quantum Liquids in ConfinementHuang and Meng (1992):

Dilute Bose gas in disorder (T = OK). Disorder potential arises from hard sphere impurities placed at random.

Condensate fraction

Superfluid density

where

Astrakharchik et al (2002) -- Monte Carlo extension to Bose fluid.

Beyond the Roton in Bulk Liquid 4He

- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Phase Diagram of gelsil: 25 A pore diameter

Bose-Einstein CondensationLiquid 4He in VycorAzuah et al., JLTP (2003)

Tc (Superfluidity) = 1.95-2.05 K

Phonon in Bulk Liquid 4He

Q= 0.4 -1Stirling and Glyde, PRB, 41, 4224 (1990)

Excitations, BEC, and SuperfluidityLiquid 4He in confinement, disorder

BEC and well-defined phonon-roton modes are separated from superfluidity.

Below Tc have superfluidity, BEC and well-defined phonon-roton modes. BEC is extended. Have extended phase coherence.

Above Tc - have phonon-roton modes and BEC but no superflow. BEC is localized by disorder. No extended phase coherence.

Localized BEC at Tc < T < T .Localized BEC at p > pc

New Here

Measurements of phonon-roton excitations and BEC in disorder

- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)Quantum Phase Transition in 25 A pore diameter gelsil ?

Superfluid and Normal 4HeJ(Q,s) = r1(s) R(Q,s)J(Q,s) - Fourier transform of J(Q,y)Shows difference arising from the condensatePhysics & Astronomy

Excitations, BEC, and SuperfluidityNeutron scattering studies of excitations of liquid 4He in confinement and disorder.

phonons and rotons in helium at nanoscale size, in disorder, near surfaces. identify new excitations. temperature and pressure dependence.

Explore the interdependence of Bose-Einstein Condensation (BEC), phonon-roton excitations, and superfluidity.

Reveal origin of superfluidity, BEC or well defined excitations.

Phonon-roton mode of liquid 4He in 34 pore diameter gelsilPearce et al. (2006)

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

Excitations, BEC, and SuperfluidityConclusions -- porous media

At SVP and lower p, have localized BEC in normal liquid phase, i.e. for temperatures Tc < T < T . Have order in the normal phase up to T

At SVP, superfluid-normal transition in porous media is associated with an extended to localized BEC cross over.

At pressures, p > 35 bars, liquid 4He no longer supports well- defined P-R modes. No roton for p > 35 bars.

Loss of P-R modes coincides with a superfluid normal Quantum Phase Transition at pc ~ 35 bars

Localized BEC at Tc < T < T .No phonon - roton mode at p > pc

Excitations, BEC, and SuperfluidityFuture program:

* Observe BEC in solid helium.

* Observe P-R modes in 25 gelsil (same sample as used by Yamamoto et al). Compare directly with S (p, T), pc , Tc .

* Observe OBDM in 2D. (peak in n(k) in 2D).

1D 4He on nanotubes, observe vibrational density of states.

Carl Weyman and Eric Cornell