SUPERFLUIDIT Y

T E R E S A K U L K AU N I V E R S I T Y O F W A R S A W

1 8 . 1 1 . 2 0 1 9

OUTLINE

• History

• Superfluid properties

• Quantum fluid

• 4𝐻𝑒

• 3𝐻𝑒

• Other superfluids

• Some applications

HISTORY

• 1908 – 4𝐻𝑒 was cooled below 4.2 K and liquefied

• 1927 – 4𝐻𝑒 was cooled below 2.17 K and phase transition to

superfluid took place

• 1938 – superfluid properties of liquid 4𝐻𝑒 were estabilished

• 1972 – two of the superfluid transitions in 3𝐻𝑒 were observed

SUPERFLUID PROPERTIES

• Remains in the liquid state even down to absolute zero temperature

• Flows with zero viscosity (superflow)

• Has infinite thermal conductivity

• Has zero entropy

SUPERFLUID EXPERIMENTS

Source: [2]

LEAKING FLUID

Source: [2]

WETTING LAYER

Source: [2]

• concave meniscus

Source: [3]

TWO-FLUID MODEL

Source: [4]

FOUNTAIN EFFECT

Source: [2]Source: [4]

WHY ONLY SOME CHEMICAL ELEMENTSCAN BECOME SUPERFLUIDS?

• Classical fluid – its roperties are purely determined by the laws of classical

mechanics

• Quantum fluid – remains fluid at such low temperatures that the effects of

quantum mechanics play a dominant role

• For quantum fluid we would search the element which atoms weakly interact

between each other

RARE GASES

Source: [3]

HELIUM VERSUS NEON

• The interatomic potential contains a

short ranged repulsion and a weak

but long ranged van der Waals

attraction

• The potential near the attractive

minimum can be represented by

Lennard-Jones type potential:

𝑉 𝑟 = 𝜖0(𝑑12

𝑟12− 2

𝑑6

𝑟6)

Source: [4]

HELIUM VERSUS NEON

Helium Neon

Atomic mass of 4 u Atomic mass of 20 u

Weak interatomic potential well(1.03 meV)

Strong interatomic potential well(3.94 meV)

Interatomic separation of 0.265 nm Interatomic separation of 0.296 nm

De Broglie wavelengthequal to 0.4 nm

De Broglie wavelengthequal to 0.07 nm

Quantum fluid Classical fluid

• Other rare gases become even further into the classical regime

HELIUM VERSUS NEONPHASE DIAGRAM

Source: [4]

WHY LIQUID HELIUM DOES NOTCRYSTALLIZE, EVEN AT ABSOLUTE ZERO?

• Quantum fluids have zero point motion

• Einstein oscillator phonon model states that each atom in the crystal

vibrates around its equilibrium position as an independent quantum

harmonic oscillator

• The zero point energy per atom is: 𝐸0 =3

2ℏ𝜔0

• The zero point energy of helium is about 7 meV

• This would be equivalent to a thermal motion corresponding to about 70 K

SUPERFLUID 4𝐻𝑒 SPECIFIC HEAT

Source: [4]

SUPERFLUID 4𝐻𝑒 DISPERSION

• A superfluid acts as a single coherent object with its own

excitations called quasiparticles

• An object moving in a superfluid below critical velocity is

unable to create quasiparticles and is in a state of virtual

free fall

• A superfluid can also flow unimpeded down a capillary if

its velocity is not too high

SUPERFLUID 4𝐻𝑒 DISPERSION

• Conservation of energy and momentum gives:

1

2𝑀𝑉2 =

1

2𝑀𝑉′2 + 𝜀𝑘

𝑀𝑉 = 𝑀𝑉′ + ℏ𝑘

• We obtain a relation:

ℏ𝑉 ∙ 𝑘 −ℏ2𝑘2

2𝑀= 𝜀𝑘

• The magnitude of the velocity required to create an excitation is:

𝑉 =𝜀𝑘 +

ℏ2𝑘2

2𝑀ℏ𝑘

≈𝜀𝑘ℏ𝑘

SUPERFLUID 4𝐻𝑒 DISPERSION

• The circles represent

measurements at 1.2 K made

with neutron scattering

• In the He II phase the minumum

velocity to create an excitation is:

50𝑚

𝑠

• In the He I phase for any velocity

exist quasiparticles that can be

excited

Source: [5]

3𝐻𝑒 SUPERFLUIDITY

• 3𝐻𝑒 is a spin ½ fermion

• At temepratures around mK 3𝐻𝑒

atoms form so-called Cooper pairs

which behave as spin 1 bosons

• It is similar to the electron pairing

in superconductivity

• There are two distinct superfluid

phases 3𝐻𝑒 A and 3𝐻𝑒 B which

have different types of pairing

states between atomsSource: [6]

OTHER SUPERFLUIDS

• Para hydrogen • Neutron stars

Source: [3]

Source: [3]

SOME APPLICATIONS

• As a coolant for high-field magnets

Source: [8]

SOME APPLICATIONS

• As a quantum solvent in spectroscopic techniques

Source: [9]

SOME APPLICATIONS

• To trap and dramatically reduce the speed of light

Source: [3]

SOME APPLICATIONS

• In the development of theory and understanding high-temperature

superconductivity

• In high-precision devices such as gyroscopes for the measurement

of some theoretically predicted gravitational effects

1978 NOBEL PRIZE

• Piotr Leonidovich

Kapitsa

• Prize motivation: ”for

his basic inventions and

discoveries in the area

of low-temperature

physics”

• Prize share: ½Source: [1]

1996 NOBEL PRIZE

• Prize motivation: ”for their discovery of superfluidity in helium-3”

• Douglas D. Osheroff

• Prize share: 1/3

• David M. Lee

• Prize share: 1/3

• Robert C. Richardson

• Prize share: 1/3

Source: [1] Source: [1] Source: [1]

2003 NOBEL PRIZE

• Prize motivation: ”for pioneering contributions to the theory of

superconductors and superfluids”

• Anthony J. Leggett

• Prize share: 1/3• Alexei A. Abrikosov

• Prize share: 1/3

• Vitaly L. Ginzburg

• Prize share: 1/3

Source: [1] Source: [1] Source: [1]

T H A N K Y O UF O R AT T E N T I O N

BIBLIOGRAPHY

[1] The Nobel Prize webpage: https://www.nobelprize.org/prizes/physics

[2] https://www.youtube.com/watch?v=2Z6UJbwxBZI

[3] https://en.wikipedia.org/wiki

[4] James F. Annett, ”Superconductivity, Superfluids, and Condensates”, Oxford

University Press, 2004

[5] Statistical Mechanics lectures at University of British Columbia, 2019

[6] Helsinki University of Technology webpage:

http://ltl.tkk.fi/research/theory/he3.html

[7] Andreas Schmitt, ”Introduction to Superfluidity”, Springer International Publishing,

2015

[8] CERN webpage: https://home.cern/

[9] https://phys.org/