Phonon-roton excitations Phonon-roton excitations and quantum phase and quantum phase
transitions in liquid transitions in liquid 44He in He in nanoporus mediananoporus media
Henry R. GlydeDepartment of Physics & Astronomy
University of Delaware
Recent Progress in Many Body Theories
Barcelona, 16-20 July, 2007
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Collaborators:
Jonathan Pearce University of Delaware, ILLNational Physical Laboratory
Teddington, UK
Jacques Bossy Centre de Recherche sur LesTrès Basses TemperatureCNRS, Grenoble, France
Francesco Albergamo -ESRF, Grenoble, France
Bjorn Fåk - Commissariat à l’Energie Atomique, Grenoble, France
Norbert Mulders -University of Delaware
Richard T. Azuah - NIST Center for Neutron Research, Gaithersburg, Maryland, USA
Helmut Schober Institut Laue-Langevin
Grenoble, France
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Collaborators (Con’t):
Oliver Plantevin - Université de Paris Sud
Helmut Schober - Institut Laue Langevin, Grenoble, France
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Goals:
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 SuperfluidityExcitations, BEC, and Superfluidity
Landau 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, <ψ> = √n0eιφ ;
vs ~ grad φ
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 DisorderBosons in Disorder
Liquid 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: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 SuperfluidityExcitations, BEC, and Superfluidity
Organization of Talk
1. Bulk liquid 4He --review Superfluid density, ρS
BEC condensate fraction, n0 Phonon-roton excitations.
2. Porous media – p ~ 0, T dependence Review ρS , 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 DiagramBULK HELIUM: Phase Diagram
SUPERFLUIDITYSUPERFLUIDITY
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)
Kamerlingh OnnesKamerlingh Onnes
LondonLondon
Superfluid Density Superfluid Density ss(T)(T)
Superfluid Density ρS (T) = 0 at T = Tλ
Bulk Liquid 4He
Phase Diagram of Bulk HeliumPhase Diagram of Bulk Helium
BOSE-EINSTEIN CONDENSATIONBOSE-EINSTEIN CONDENSATION
Atoms in TrapsAtoms in Traps
Bose-Einstein Condensation: Bose-Einstein Condensation: Atoms in TrapsAtoms in Traps
Bose-Einstein CondensationBose-Einstein Condensation
Glyde, Azuah, and StirlingPhys. Rev. B62, 14337 (2000)
Bose-Einstein CondensationBose-Einstein Condensation
Expt: Glyde et al. PRB (2000)
Condensate fraction bulk Condensate fraction bulk 44HeHe
L. Vranjes and J. Boronat et al. L. Vranjes and J. Boronat et al. PRL (2005)PRL (2005)
Condensate fraction bulk Condensate fraction bulk 44HeHe
Moroni and Boninsegni JLTP (2004)Moroni and Boninsegni JLTP (2004)
50 bars
Bose-Einstein CondensationBose-Einstein CondensationSolid Helium p = 41 barsSolid Helium p = 41 bars
Diallo et al. PRL 98, 205301 (2007)
PHONONS AND ROTONSPHONONS AND ROTONS
Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)
Roton Energy versus PressureRoton Energy versus Pressure
Roton energy at Q ~ 2.1 Å-1 as a function of pressure.
Vranjes et al. PRL (2005)
Liquid Liquid 44He at Negative PressureHe at Negative Pressure
Liquid Liquid 44He at Negative Pressure He at Negative Pressure
Dispersion curve at SVP and - 5 bar
Liquid Liquid 44He at Negative Pressure He at Negative Pressure MCM-41 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 versus Pressure
Maxon energy at Q = 1.1 Å-1 as a function of pressure.
Phonon-roton mode of Phonon-roton mode of 44He He under pressure, 24.7 barsunder pressure, 24.7 bars
Phonon-roton mode of Phonon-roton mode of 44He He under pressure, 31.2 barsunder pressure, 31.2 bars
Temperature dependence of mode Temperature dependence of mode intensity: Maxon, bulk liquid intensity: Maxon, bulk liquid 44He He
Talbot et al., PRB, 38, 11229 (1988)
Roton in Bulk Liquid Roton in Bulk Liquid 44HeHe
Talbot et al., PRB, 38, 11229 (1988)
Beyond the Roton in Bulk Beyond the Roton in Bulk 44HeHe
Data: Pearce et al. J Phys Conds Matter (2001)
Phonons and Rotons (sharply Phonons and Rotons (sharply defined modes) arise From Bose-defined modes) arise From Bose-Einstein CondensationEinstein Condensation
Bogoliubov (1947) showed: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.
cQQ
Phonons and Rotons Arise From Phonons and Rotons Arise From Bose-Einstein CondensationBose-Einstein Condensation
Gavoret and NoziGavoret and Nozièreères (1964) showed:s (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).
cQQ
Ma and Woo (1967), Griffin and Ma and Woo (1967), Griffin and Cheung (1973), and others showed:Cheung (1973), and others showed:
Only a single mode at all Q with BEC -- the phonon-roton mode.
Excitations in a Bose FluidExcitations in a Bose Fluid
ρ+
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Bulk Liquid Bulk Liquid 44HeHe
BEC, well-defined phonon-roton modes at Q > 0.8 Å-1 and superfluidity coincide.
e.g., all have some “critical” temperature,
Tλ = 2.17 K SVP
Tλ = 1.76 K 25 bar
Phase Diagram of Bulk HeliumPhase Diagram of Bulk Helium
SuperfluiditySuperfluidity
Landau TheoryLandau 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, BEC and Phase Coherence, Ø (r)Ø (r)
Superfluidity follows directly from BEC, phase conherence .)(r
s
LandauLandau
POROUS MEDIAPOROUS MEDIA
AEROGEL 95% porousOpen 87% porous A
87% porous B-- grown with
deuterated materials or flushed
with D2
VYCOR 30% porous70 Å pore Diameter -- grown with B11 isotope
GELSIL (GELTECH) 50% porous44 Å pore Diameter34 Å pore Diameter25 Å pore Diameter
MCM-41 30% porous
47 Å pores
Superfluid Properties in Superfluid Properties in Confinement/DisorderConfinement/Disorder
Confinement 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)
2.17KTλ
)(Ts
)(Ts
TTcc in Porous Media in Porous Media
Geltech (25 Å pores)
Superfluid Density in Porous MediaSuperfluid Density in Porous Media
Chan et al. (1988)
Miyamoto and Takeno (1996)
- - Yamamoto et al. Yamamoto et al. Phys. Rev. Lett. 93, 075302 (2004) Phys. Rev. Lett. 93, 075302 (2004)
Superfluid Density in gelsil Superfluid Density in gelsil (Geltech) – 25 A diameter(Geltech) – 25 A diameter
Schematic Phase Diagram of Schematic Phase Diagram of Helium Confined to NanoscalesHelium Confined to Nanoscales
e.g. 2 - 4 nme.g. 2 - 4 nm
- - Yamamoto et al,Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phys. Rev. Lett. 93, 075302 (2004)
Phase Diagram of gelsil: Phase Diagram of gelsil: 25 25 ÅÅ pore diameter pore diameter
Bose-Einstein CondensationBose-Einstein CondensationLiquid Liquid 44He in VycorHe in Vycor
Azuah et al., JLTP (2003)
Tc (Superfluidity) = 2.05 K
Bose-Einstein Condensation Bose-Einstein Condensation VycorVycor
Azuah et al., JLTP (2003)
Phonons, Rotons, and Layer Modes Phonons, Rotons, and Layer Modes in Vycor and Aerogelin Vycor and Aerogel
Temperature DependenceTemperature Dependenceof Roton Energyof Roton Energy
Fåk et al., PRL, 85 (2000)
• Liquid helium in porous media supports well defined phonon-roton excitations – up to wave vectors Q ≈ 2.8 Å.
• 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:Conclusions:
Excitations of Liquid Excitations of Liquid 44He in He in ConfinementConfinement
Intensity in P-R Mode vs. Intensity in P-R Mode vs. TT
Glyde et al., PRL, 84 (2000)
Mode Intensity in Vycor:Mode Intensity in Vycor:T = 1.95 KT = 1.95 K
Mode Intensity in VycorMode Intensity in Vycor T = 2.05 K T = 2.05 K
Mode Intensity in Vycor:Mode Intensity in Vycor:T = 2.15 KT = 2.15 K
Mode Intensity in Vycor:Mode Intensity in Vycor:T = 2.25 KT = 2.25 K
Fraction, Fraction, ffss(T)(T), of Total Intensity , of Total Intensity
in Phonon-Roton Modein Phonon-Roton Mode
Vycor TVycor Tcc = 2.05 K = 2.05 K
Albergamo et al. Phys. Rev. B69, 014514 (2004)
Mode Intensity in 44A Gelsil:Mode Intensity in 44A Gelsil:versus T. Tversus T. Tcc = 1.92 K = 1.92 K
Albergamo et al. PRB (2007)
Fraction, Fraction, ffss(T)(T), of total scattering , of total scattering
intensity in Phonon-Roton Modeintensity in Phonon-Roton Mode- gelsil 44 A pore diameter - gelsil 44 A pore diameter
Liquid Liquid 44He in 25 A gelsil (Geltech)He in 25 A gelsil (Geltech)
Tc (Superfluidity) ~ 1.3 K
Conclusions:Conclusions:
Localization of Bose-Einstein Localization of Bose-Einstein Condensation in disorderCondensation in disorder
• 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.
Vycor Tc = 2.05 K
gelsil (44 Å) Tc = 1.92 K
gelsil (25 Å) Tc = 1.3 K
• At temperatures Tc < T < Tλ - BEC is localized by disorder- No extended phase coherence across the sample- No superflow
Conclusions:Conclusions:
Liquid 4He in Disorder and Boson Liquid 4He in Disorder and Boson LocalizationLocalization
• Extended BEC at temperature below Tc in superfluid phase.
• Superfluid - Normal liquid transition associated with an extended to localized BEC cross over at SVP.
Schematic Phase DiagramSchematic Phase Diagram of BEC in Nanoporous media of BEC in Nanoporous media
PRESSURE DEPENDENCE PRESSURE DEPENDENCE Phonon-Roton modes, Low TPhonon-Roton modes, Low T
• gelsil 44 Å mean pore diameter,– Pearce et al. PRL (2004)
• gelsil 34 Å mean pore diameter - Pearce et al. Preprint (2006)
• gelsil 25 Å mean pore diameter - being analysed (2006)
- Compare with Yamamoto et al. PRL (2004) , superfluid density in 25 Å gelsil.
Liquid 4He up 57 bars in gelsil
- - Yamamoto et al,Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phys. Rev. Lett. 93, 075302 (2004)
Quantum Phase Transition in Quantum Phase Transition in 25 A pore diameter gelsil ?25 A pore diameter gelsil ?
Phonon-roton mode of Phonon-roton mode of 44He He under pressure, 31.2 barsunder pressure, 31.2 bars
Pressure dependence: 44 Å gelsil
phonon (Q = 0.7 Ǻ-1) roton (Q=2.1Å-1)
Pressure dependence of S(Q,ω) at the roton (Q=2.1Å-1)
34 A gelsil
Pressure dependence of S(Q,ω) at the roton (Q=2.1Å-1)
25 A gelsil
Roton energy and intensity Roton energy and intensity in roton peak vs pressurein roton peak vs pressure
gelsil 34 gelsil 34 ÅÅ
Pearce et al. (2006)
Phase diagram of modes of Phase diagram of modes of liquid liquid 44He in 34 He in 34 ÅÅ pore diameter pore diameter gelsilgelsil
44He remains liquid in 34 A gelsil He remains liquid in 34 A gelsil up to what pressure?up to what pressure?
Δp = pL – pS = 2α / Rc
pS = 25.3 bars Rc = 14 Å
(a) α = 0.17 erg/cm2 -- constant
pL = 50 bars
(b) α = -increases with pressure (Maris and Caupin, JLTP 131, 145 (2003))
pL = 70 bars
Vycor, pL = 45 bars Rc = 35 Å
- - Yamamoto et al,Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phys. Rev. Lett. 93, 075302 (2004)
Quantum Phase Transition in Quantum Phase Transition in 25 A pore diameter gelsil ?25 A pore diameter gelsil ?
Schematic Phase DiagramSchematic Phase Diagram QPT in Nanoporous media QPT in Nanoporous media
Net Scattering intensity Net Scattering intensity gelsil 34 gelsil 34 ÅÅ
Pearce et al. PRL ( rejected 2006-7) Compare with L. Vranjes, J. Boronat et al. PRL,95, 145302 (2005)
Net Scattering intensity, Net Scattering intensity, gelsil 34 gelsil 34 Å Å
and bulk liquid simulation compared.and bulk liquid simulation compared.
Pearce et al. (in progress)
← 60 bars
Bulk liquid
Scattering intensity, Scattering intensity, gelsil 70 gelsil 70 ÅÅ
and p = 70 barsand p = 70 bars
Wallacher et al. JLTP 138, 1013 (2005)
Schematic Phase DiagramSchematic Phase Diagram QPT in Nanoporous media QPT in Nanoporous media
Conclusions:Conclusions:
Liquid 4He in Disorder and Boson Liquid 4He in Disorder and Boson LocalizationLocalization
• 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 Quantum Phase Transition at p ~ 35 bars Only localized BEC at p > 35 bars.Only localized BEC at p > 35 bars.
Conclusions (QPT):Conclusions (QPT):
Liquid 4He in Disorder and Boson Liquid 4He in Disorder and Boson LocalizationLocalization
• At T ~ 0 K and higher pressure, ( p > 25 At T ~ 0 K and higher pressure, ( p > 25 bars) BEC condensate fraction is small.bars) BEC condensate fraction is small.
(n(n00 ~ 1 % at p = 70 bars, bulk ~ 1 % at p = 70 bars, bulk 44He)He)
. 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 bars
- Have liquid up to 38 bars and liquid-solid co-existence above 38 bars, probably up to 45-50 bars.
Excitations of superfluid Excitations of superfluid 44He at He at pressures up to 40 barspressures up to 40 bars
Phase diagran and excitations of Phase diagran and excitations of superfluid superfluid 44He in 44 He in 44 ÅÅ gelsil gelsil
Pearce et al., PRL (2004)
Bose-Einstein CondensationBose-Einstein Condensation
PHONONS AND ROTONSPHONONS AND ROTONS
Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)
Superfluid Properties in Superfluid Properties in Confinement/DisorderConfinement/Disorder
Confinement 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)
2.17KTλ
)(Ts
)(Ts
Excitations of liquid Excitations of liquid 44He in 34 He in 34 ÅÅ pore diameter gelsilpore diameter gelsil
Pearce et al.,(2006) (in progress)
BEC, Excitations, and SuperfluidityBEC, Excitations, and Superfluidity
BEC in 2DBEC in 2D
Boninsegni et al. PRL 96, 070601 (2006)
Condensate fraction bulk Condensate fraction bulk 44HeHe
L. Vranjes and J. Boronat et al. L. Vranjes and J. Boronat et al. PRL (2005)PRL (2005)
Condensate fraction bulk Condensate fraction bulk 44HeHe
Moroni and Boninsegni JLTP (2004)Moroni and Boninsegni JLTP (2004)
50 bars
Sum rule for condensate component Sum rule for condensate component of S(Q, of S(Q,ωω))
HRG, PRL (1995)
Topic of Talk:Topic of Talk:
cT
• Well defined p-r excitations (Q > 0.8 Å) exist because there is Bose-Einstein condensation (BEC).
• Measure superfluid density ρs (T) and determine the normal to superfluid transition temperature Tc in Vycor (same sample). Find:
Tc = 2.05 K < Tλ = 2.17 K
(Vycor) (Bulk)
- disorder suppresses Tc below Tλ
• Find well defined phonon–roton excitations in Vycor at temperatures T > Tc, up to T = Tλ = 2.17 K
• Thus BEC in Vycor above Tc , at temperatures
Tc < T < Tλ . - localized BEC.
Momentum distribution solid Momentum distribution solid 44HeHe
Layer Mode in Porous MediaLayer Mode in Porous Media
Layer Mode in Vycor and AerogelLayer Mode in Vycor and Aerogel
Conclusions:Conclusions:
Liquid 4He in Disorder and Boson Liquid 4He in Disorder and Boson LocalizationLocalization
• 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.
Vycor Tc = 2.05 K
Geltech (44 Å) Tc = 1.92 K
Geltech (25 Å) Tc = 1.0 K
• At temperatures Tc < Tc < Tλ - BEC is localized by disorder- No extended phase coherence across the sample- No superflow
Quantum Liquids in ConfinementQuantum Liquids in Confinement
Lopatin and Vinokur (2002):Lopatin 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.
]6
)/(1[(BEC) 02
320
Rn
mkTTT cocc
])(27
321[ 2
00 RTTcc
Quantum Liquids in ConfinementQuantum Liquids in Confinement
Giorgini Giorgini et al.et al. (1994): (1994):
Same model as Huang & Meng -- disorder arising from random impurities
Sound velocity
Half width of phonons
]3
51[2
02
N
Ncc R
0222
4
)/(24)( R
cm
Quantum Liquids in ConfinementQuantum Liquids in Confinement
Huang and Meng (1992):Huang 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.
0)( xu
)()()( yxRyuxu o
)(xu
N
Nna
nN
N Ro 2/13
3)(
81
N
N Rs
3
41
02/1
02/3
22
)(8
)/(Ran
n
m
n
n
N
N RR
Beyond the Roton in Bulk Liquid Beyond the Roton in Bulk Liquid 44HeHe
- - Yamamoto et al,Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phys. Rev. Lett. 93, 075302 (2004)
Phase Diagram of gelsil: Phase Diagram of gelsil: 25 A pore diameter25 A pore diameter
Bose-Einstein CondensationBose-Einstein CondensationLiquid Liquid 44He in VycorHe in Vycor
Azuah et al., JLTP (2003)
Tc (Superfluidity) = 1.95-2.05 K
Phonon in Bulk Liquid Phonon in Bulk Liquid 44HeHe
Q= 0.4 Q= 0.4 ÅÅ-1-1
Stirling and Glyde, PRB, 41, 4224 (1990)
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Liquid Liquid 44He in confinement, disorderHe 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 < Tλ .Localized BEC at p > pc
New HereNew Here
Measurements of phonon-roton excitations and BEC in disorder
- - Yamamoto et al,Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004) Phys. Rev. Lett. 93, 075302 (2004)
Quantum Phase Transition in Quantum Phase Transition in 25 A pore diameter gelsil ?25 A pore diameter gelsil ?
Superfluid and Normal 4He
J(Q,s) = 1(s) R(Q,s)
J(Q,s) - Fourier transform of J(Q,y)
Shows difference arising from the condensate
Physics &
Astronomy
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Neutron 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 Phonon-roton mode of liquid 44He He in 34 in 34 Å pore diameter gelsilÅ pore diameter gelsil
Pearce et al. (2006)
Pressure dependence of S(Q,ω) at the roton (Q=2.1Å-1)
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Conclusions -- porous mediaConclusions -- porous media
At SVP and lower p, have localized BEC in “normal” liquid phase, i.e. for temperatures Tc < T < Tλ . Have order in the normal phase up to Tλ
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 < Tλ .No phonon - roton mode at p > pc
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Future program:Future program:
* Observe BEC in solid helium.
* Observe P-R modes in 25 Å gelsil (same sample as used by Yamamoto et al). Compare directly with ρS (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 CornellCarl Weyman and Eric Cornell