Excitations, Bose-Einstein Condensation and Superfluidity in by HC111118002528

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									Excitations, Bose-Einstein
    Condensation and
Superfluidity in Liquid 4He

         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 4He and 4He 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 4He in Aerogel, Vycor, Geltech

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

Localization of Bose-Einstein Condensation by Disorder
Superfluid Properties in
Confinement/Disorder
Confinement reduces Tc below T  217 K .


Confinement modifies  s (T ) (T dependence).


Confinement reduces  s (T ) (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)
Graduate Students


Jonathan DuBois

      Bose-Einstein Condensation of Bosons in Traps,
      Variational Monte Carlo, Diffusion MC

Asaad Sakhel

      Models of excitations in liquid 4He
      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-9972011




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:
Atoms in Traps
Bose-Einstein Condensation




       Glyde, Azuah, and Sterling
       Phys. Rev., 62, 14337 (2001)
Bose-Einstein Condensation

           (r )  n (r )1 / 2 ei ( r )
                      o




Condensate Fraction n (t )  0 at T  2.17 K
                          o                
Tc in Porous Media
Superfluid Density s(T)

               Bulk Liquid 4He




Superfluid Density          (t )  0 at T  2.17 K
                         s              
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   (r ).
                     s
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,   cQ
                                 Q
  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 4He




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




     Talbot et al., PRB, 38, 11229 (1988)
Beyond the Roton in Bulk Liquid 4He
BEC, Excitations, and Superfluidity
Excitations, BEC, and Superfluidity

Bulk Liquid 4He
BEC, well-defined excitations and
superfluidity coincide

     e.g., all have some critical
           temperature, T
                           


          T = 2.17 K           SVP
           


          T = 1.92 K           20 bar
           
Porous Media

AEROGEL          95% porous
                 87% porous      A
                 87% porous      B

                 -- grown with deuterated
                    materials or flushed with D2



VYCOR            30% porous
                    
                 70 A diameter pores

                 -- grown with B11 isotope



GELTECH SILICA   50% porous
                    
                 25 A diameter pores

                 -- flushed with D2
Tc in Porous Media
Superfluid Density in Porous Media

           Chan et al. (1988)




       Miyamoto and Takeno (1996)



                      Geltech
                      (25 Å pores)
Bose-Einstein Condensation
Liquid 4He in Vycor

      Tc (Superfluidity) = 1.95-2.05 K




         Azuah et al., JLTP (2003)
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 4He in Geltech Silica

        Tc (Superfluidity) = 0.725 K
Fraction, fs(T), of Total Scattering
Intensity in Phonon-Roton Mode
BEC, Excitations, and Superfluidity
Excitations, BEC, and Superfluidity

Liquid 4He in disorder
BEC, well-defined excitations and
separated from superfluidity in disorder

 e.g., Tc     - superfluidity

      Tc (BEC) - Bose-Einstein condensation

      Tc (BEC) > Tc

Disorder localizes the condensate.


New Here
Measurements of phonon-roton
excitations and BEC in disorder
BEC in Disorder

Both no and  s reduced by static disorder
(homogeneous).

        Huang & Meng, PR 1992
               dilute gas limit, analytic

        Astraljparehik, et al., preprint (2002)
                fluid densities, Monte Carlo

        s reduced more than no


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 4He.

The well defined phonon-roton excitations in superfluid
4He (the sharp dispersion curve) is a consequence of

BEC. Well defined phonon-roton excitations do not exist
above        the
          in T normal phase where no = 0 (no phase
coherence).

Landau theory and BEC theories of superfluidity have
common dependence on BEC.

In liquid 4He in disorder, observe phonons and rotons as
in bulk liquid 4He. In addition, observe 2D layer modes.
Also observe excitations above Tc – in the normal phase.

Disorder can localize BEC and superfluidity. In
disorder, have phase coherence over short length scales
above Tc for macroscopic superfluidity. Can ―see‖ this
localized BEC in excitations but not in Torsional
Oscillator measurements.

Future: Use confinement/disorder to ―tune‖ Tc ,  s (T )
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 4He (and
3He) 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 (1941-1947) - phonons-rotons
         (no BEC)

        London (1938) - BEC
        (no phonons-rotons)
Bose-Einstein Condensation
Liquid 4He in Vycor

      Tc (Superfluidity) = 1.95-2.05 K




         Azuah et al., JLTP (2003)
Phonons and Rotons Arise From
Bose-Einstein Condensation

Bogoliubov (1947) showed:

  Bose gas with BEC -- quasiparticles
  have energy:
          cQ - phonon (sound) form
         Q

  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 Q,  Q  C Q.



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:               (r )    (r ) (r )
   Second quantization:

      (r )    (r ) (r )
     ˆ         ˆ       ˆ              -- density operator


                          (r )     -- creates a particle at r


   (r )k a  e  ik  r
               k
                                    -- creates particle with
                             ak         momentum k



 (Q)  k a   Q a k
             k                       -- density operator



    Density operator is a two particle operator.
Density and Quasiparticle Excitations (BEC)

A macroscopic number of particles No in k = 0 state.

          a ak  N k
           k                 -- number in state k


          ao ao  No
           
                             -- large (1022)


          a o  No           -- a number



Density Operator
                  
       (Q)   a k  Q a k
                k


              a Q No  'k a k  Q a k
                             



              a Q No   (Q)
                 


Density operator includes quasiparticle excitation.
Excitations and Bose-Einstein Condensation in Quantum
                  Liquids in Disorder
   Henry R. Glyde, University of Delaware, DMR-9972011




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.
     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-0115663


Our neutron scattering
studies of liquid 4He 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 4He is

								
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