Einsteins Legacy in Low Temperature Physics Superfluids and Supersolids

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Einsteins Legacy in Low Temperature
Physics Superfluids and Supersolids

• Moses Chan
• The Pennsylvania State University
• Supported by National Science Foundation

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Where is Penn State University?
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Outline

• Quantum mechanics at low temperatures de-Broglie
  wave-packets, Bose-Einstein Condensation in vapor
  and liquid.
• Experimental principle for the of observation of
  Superfluidity Torsional Pendulum
• Observation of superflow in solid helium

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Temperature Scale (K)
1Kpot (1.2K)
Still(0.7K)
Mixing Chamber(10mK)
The lowest possible temperature 0
K-273.15oC-459.7oF
1061,000,000 10-60.000001
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Superfluidity in liquid 4He was discovered in
1938.

• Superfluid
• helium film
• can flow up
• a wall
• Superfluid
• Fountain

T?2.176K
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Persistent current in superfluid

• Vanishing viscosity The viscosity of He II is
  at least 1500 times smaller than that of normal
  helium (He I)
• P. Kapitza, Nature 141, 74 (1938)
• Allen Misener Nature 141,75 (1938)

Liquid helium
Persistent current can be created by stirring the
liquid helium while cooling through T?.
Superfluid will continue to rotate after the
stirring is stopped. Our understanding of
superfluidity can be traced to Einstein
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• Many prominent physicists have made contributions
  towards the understanding of superfluidity,
• F. London, O. Penrose, L. Onsager, L. Tisza,
  C. N. Yang, L. Landau, R. Feynman, I. M.
  Khalatnikov, P. W. Anderson, A. J. Leggett, P.
  Kapitza, V. P. Peshkov, W. M. Fairbank, E. L.
  Andronikashivili, W. F. Vinen, H. E. Hall, J. D.
  Reppy, D. M. Lee, R. C. Richardson, D. D.
  Osheroff, J. Wheatley,
• too numerous to name all.

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Superconductivity
B
I
The phenomenon of superconductivity is
analogous to superfluidity. In superconductivity,
electric current can flow with no resistance. A
similar persistent current of electron pairs can
be set up.

• MRI uses magnet powered by superconducting
  current in the persistent mode. In this mode the
  current and therefore the magnetic field is
  extremely stable.

• Superfluidity and superconductivity are
• macroscopic
  quantum phenomenon

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Miraculous year in Physics

• In 1905, Einstein published 4 monumental papers.
• March 1905
• Light Quanta Light wave can behave like
• a stream of particles with discrete energy
• May 1905
• Theory of Brownian Motion Heat or thermal
  energy is responsible for the random motions of
  small particles suspended in a liquid.
• June 1905
• Theory of Special Relativity
• September 1905
• Energy equivalent theory, Emc2

A storm broke loose in my mind
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Quantum Theory simplifiedThermal de Broglie
Wavelength ?dB (1924)

• Light wave behaves like a particle, conversely a
  particle, e.g., an atom, electron, elementary
  particles, and indeed all objects can behave like
  a wave.
• kBT is a measure of energy of motion

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Classical and Quantum pictures of an object (e.g.
atom, electron, etc.)
Quantum
Classical
?dB de Broglie wave
length

• kB 1.3810-23 Joules-K Boltzmann constant
• T absolute temperature
• h 6.62610-34 Joules-s Planck constant
• m mass of the object of interest

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Some ?dB
?? in 1D

• 1) m70kg (human) at T300K
• ?dB 810-23cm
• 0.00000000000000000000008cm
• 2) m9.110-31kg (electron) at T300K
• ?dB 410-7cm 4nm
• 3) m 6.6910-27kg(4He) at T300K
• ?dB 510-9cm0.05nm
• at T 2K ?dB 610-8cm 0.6nm
• at T0.2K ?dB 210-7cm 2nm
• 4) m1.4210-25kg (Rubidium atom) at 1nK
• ?dB 110-3cm 10µm

?dB
?? in 3D
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Collection of identical particles
l
?dB
If the distance between the particles, l, is
much larger than ?dB then the particles retain
their individual identity and their behavior is
governed by classical thermodynamics
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Bose-Einstein Condensation

• What if the temperature is reduced so that ?dB
  grows to be on the order or even larger than l,
  the inter-particle spacing?
• Einstein, built on the idea of Bose, proposed in
  1924 that these identical particles lose their
  individual identity and begin to behave as one
  single giant atom.
• This is known as Bose-Einstein condensation
  (BEC).
• Now we know that this prediction is correct only
  for bosons ( with integer spins)

Named after Satyendra N. Bose of India
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Collection of identical particles
l
?dB
Decreasing temperature increases ?dB
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?dB gtgt l
Particles behave coherently like a
single giant atom
One for all and all for one
In the Bose-condensed state particles or atoms do
not run into each other. Because they act as a
single coherent entity they cannot easily lose or
gain energy from the surroundings. Hence
superfluidity is possible.
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Bose-Einstein Condensation
in the vapor phase
1) Introduce Rb vapor into a vacuum space 2) Cool
the Rb atoms by colliding them with appropriate
laser beam and other clever techniques so that
their ?dB is larger than the separation of the
atoms. 3) First accomplished by Carl Wieman and
Eric Cornell in 1995 on Rb atoms
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Bose-Einstein Condensation in the vapor phase
1) Introduce Rb vapor into a vacuum space 2) Cool
the Rb atoms by colliding them with appropriate
laser beam and other clever techniques so that
their ?dB is larger than the separation of the
atoms. 3) First accomplished by Carl Wieman and
Eric Cornell in 1995 on Rb atoms
Wieman Cornell
Nobel Prize in 2001
Ketterle
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BEC of Rubidium gases
JILA BEC group(1995)
400nK 200nK 50nK
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Fritz London is the first person to recognize
that superfluidity in liquid 4He is a BEC
phenomenon.
Liquid helium
Persistent current is possible in the superfluid
phase.
At 2K, ?dB of 4He 0.6nm , separation of 4He
atoms l 0.3nm
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Principle for the observation of liquid helium
behaving as a Macroscopic Atom torsional
pendulum
rigid support point
Period of Oscillation
I Rotational Inertia (proportional to mass) K
Spring constant of torsion rod (Stiffness)
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Torsional Pendulum
rigid support point
Period of Oscillation
I Rotational Inertia (proportional to mass) K
Spring constant of torsion rod (Stiffness)
What if we have a set of infinitely smooth ball
bearings?
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Torsional Pendulum
rigid support point
Period of Oscillation
The ring on the top remains stationary and
decouples from the oscillation, I decreases and
period decreases.
I Rotational Inertia (proportional to mass) K
Spring constant of torsion rod (Stiffness)
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Torsional oscillator ideal for detection of
superfluidity
Resolution Resonant period (?o) 1
ms stability in ? is 0.1ns ??/?o 510-7
Mass sensitivity 10-7g
Be-Cu Torsion Rod
Torsion Bob containing helium
?f
Drive
Amp
Detection
f0
Qf0/?f 2106
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Measurement of superfluidity
Above 2.176K, liquid helium behaves as a normal
fluid. It will oscillate with the disk if d is
smaller than the viscous penetration depth (?).
liquid helium
d
(? 3µm, if the oscillating frequency is
2?1000 rad/s )
d lt ? of normal fluid
In the normal fluid phase, I total I cylinder
Ihelium
? viscosity
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Superfluid fraction stays still when the
container is being oscillated we can measure the
fraction of superfluid.
As temperature is cooled below T?
d
I total I cylinder I ?n(T) I total I
cylinder at T0, ?n0 Non-Classical Rotational
Inertia
d lt ? of normal fluid
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Empty torsional cell
I total I torsion cell
?1,723,000ns
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Helium is introduced into the cell
I total I torsion cell I normal helium
Period shifted by 2155ns due to mass loading
of normal liquid helium
?1,723,000ns
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Expected background if there is no superfluid
transition
?1,723,000ns
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A certain fraction of the liquid, known as
superfluid fraction decouples from the
oscillation of the torsional cell and does not
contribute to the rotational inertia
Superfluid Decoupling ??
?1,723,000ns
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Superfluid fraction
??s?n two fluid model of Tisza and Landau
At T0K 100 superfluid
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Does Bose-Einstein Condensation also occur in a
solid?

• 1) In principle it is possible, however
  conventional wisdom said it is unlikely to
  happen or immeasurably small.
• 2) If it is going to occur, the likely
  candidate is solid 4He, the most quantum
  mechanical solid.

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Search for the supersolid phase
in solid 4He.
Eunseong Kim
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Torsional Oscillator
Torsion rod
Torsion cell
3.5 cm
Detection
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Solid 4He at 51 bars
Amplitude of oscillation is 0.7Å
A decrease in the resonant period, similar to
that found in superfluid liquid helium, appears
below 0.25K
?0 1,096,465ns at 0 bar 1,099,477ns
at 51 bars
(total mass loading3012ns due to filling with
helium)
The supersolid fraction is on the order of 1.3
Nature, 425, 227 (2004) Solid helium in porous
glass Science 305, 1941 (2004) Bulk solid
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Different Speed of Oscillation
4µm/s is equivalent to oscillation amplitude of
0.7Å
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Supersolid fraction
The supersolid fraction at T0K is on the order
of 1.3
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Control experiment I Solid 3He?
Nature 427,225(2004)
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Control experiment II

• With a barrier in the annulus, there should be NO
  simple superflow and the measured superfluid
  decoupling should be vastly reduced

Torsion cell with blocked annulus
Mg barrier
Al shell
Solid helium
Channel OD15mm Width1.5mm
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Phase Diagram
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Pressure dependence

• As a function of pressure the supersolid fraction
  shows a maximum near 55bars. The supersolid
  fraction extrapolates to zero near 170 bars.

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Is the supersolid phase unique with 4He?

• Apparently not!

Preliminary torsional oscillator data of Tony
Clark and Xi Lin indicate similar supersolid-like
decoupling in solid H2.
de Boer parameter

• 3He ? 3.09
• 4He ? 2.68
• H2 ? 1.73
• HD ? 1.41
• D2 ? 1.22

More quantum mechanical
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Study of Isotopically Pure para-H2 (lt10ppm HD)
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Study of Isotopically Pure para-H2 (lt10ppm HD)
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Study of Isotopically Pure para-H2 (lt10ppm HD)
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Study of Isotopically Pure para-H2 (lt10ppm HD)
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Study of Isotopically Pure para-H2 (lt10ppm HD)
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What is the precise mechanism for the supersolid
phase and why the supersolid fraction is so
small? We do not know yet.
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• At high temperature the de Broglie
  matter waves of the helium atoms in the solid are
  disconnected, then it is not possible for
  superflow.

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• At sufficiently low temperature, Tlt0.2K,
  the de Broglie waves of the atoms overlap each
  other slightly allowing the appearance of
  superflow

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Bose-Einstein Condensation and Superfluidity were
seen in vapor and liquid, and now also in solid
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• Thanks to
• Philip W. Anderson,
• Jayanth R. Banavar,
• John Beamish,
• John M. Goodkind,
• T. L. Ho,
• Jainendra K. Jain,
• Anthony J. Leggett,
• John D. Reppy ,
• Wayne Saslow ,
• David S. Weiss,

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• Thanks to
• Phillip W. Anderson,
• Jayanth R. Banavar,
• Milton W. Cole,
• John M. Goodkind,
• T. L. Ho,
• Jainendra K. Jain,
• Anthony J. Leggett,
• Jay D. Maynard,
• John D. Reppy ,
• Wayne Saslow ,
• David S. Weiss,

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Period increased by 2900ns when the torsional
cell is filled with H2
Torsional oscillator Q 600,000 ?o
980,486ns ?? 0.1ns ?H2 - ?o 2900ns
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Supersolid fraction in hydrogen is 1ns/2900ns
0.035
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No decoupling seen in solid HD within 0.05ns
Torsional Oscillator Q 1.3 million ?o
560,395ns ?? 0.05ns ?HD - ?o 4014ns
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Supersolid fraction 4He at 51 bars 1.3 4He at
136 bar 0.5 H2 0.035
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Control experiment II Solid 3He?
Nature 427,225(2004)
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Solid 4He at 51 bars
4µm/s corresponds to amplitude of oscillation of
0.7Å
NCRI appears below 0.25K Strong vmax
dependence (above 14µm/s) Amplitude minimum,
Tp
?0 1,096,465ns at 0 bar 1,099,477ns
at 51 bars
(total mass loading3012ns due to filling with
helium)
Science 305, 1941(2004)
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Non-Classical Rotational Inertia Fraction
vmax
?S/?
NCRIF
Total mass loading 3012ns at 51 bars
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Velocity dependence of NCRIF
at low temperature
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With a block in the annulus, irrotational flow of
the supersolid fraction contributes about 1
(Erich Mueller) of the barrier-free
decoupling. ??1.5ns
?-?ns
Irrotational flow pattern in a blocked annular
channel (viewed in the rotating frame)
A. L. Fetter, JLTP(1974)
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With a block in the annulus, irrotational flow of
the supersolid fraction contributes about 1
(Erich Mueller) of the barrier-free
decoupling. ??1.5ns
?-?ns
Irrotational flow pattern in a blocked annular
channel (viewed in the rotating frame)
A. L. Fetter, JLTP(1974)
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Similar reduction in superfluid response is seen
in liquid helium at 19 bars in the blocked cell
measured superfluid decoupling in the blocked
cell ??(T0) 93ns. While the expected
decoupling in unblocked cell is 5270ns. Hence the
ratio is 1.7 similar to that for solid.
??ns
Conclusion superflow in solid as in superfluid
is irrotational.
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Pressure dependence of supersolid fraction
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?s near T?
Greywall and Ahlers, Lipa and Chui
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Temperature Scale(K)