Quantum Condensates: BEC vs Fermionic Condensates

Both are exotic states of matter occurring at near-absolute zero temperatures (nanokelvins) where quantum effects dominate macroscopic behavior.

Bose-Einstein Condensate (BEC)

What it is

A state where bosons collapse into the lowest quantum state when cooled below critical temperature (Tc). Particles lose individual identities and behave as a single quantum wave.

Key Particles

Bosons (integer spin: 0, 1, 2...): Photons, helium-4, rubidium-87, sodium-23

Quantum Principle

Not restricted by Pauli Exclusion Principle → Multiple bosons can occupy identical quantum states

Formation

Cooling below Tc causes overlapping de Broglie wavelengths → Wavefunction synchronization

Key Properties

• Macroscopic wavefunction (giant matter wave)
• Perfect atomic coherence
• Superfluidity (frictionless flow)

Discovery

• Predicted by Bose & Einstein (1924-25)
• First created in 1995 (Cornell, Wieman, Ketterle)
• Nobel Prize 2001

Examples

Ultracold alkali gases (Rb, Na, Li), Superfluid helium-4

Fermionic Condensate

What it is

Fermions form Cooper pairs that behave as composite bosons, which then undergo condensation.

Key Particles

Fermions (half-integer spin: 1/2, 3/2...): Electrons, protons, helium-3, lithium-6, potassium-40

Quantum Principle

Restricted by Pauli Exclusion Principle → Requires pairing before condensation

Formation Process

1. Pairing: Fermions form Cooper pairs via attractive interactions
2. Composite bosons: Pairs acquire integer spin
3. Condensation: Pairs undergo BEC-like process

Key Properties

• Superfluidity/Superconductivity
• Long-range coherence of Cooper pairs

Discovery Timeline

• BCS Theory (1957) - Nobel 1972
• Superfluid helium-3 (1972) - Nobel 1996
• First atomic gas condensate (Deborah Jin, 2003)

Examples

Superconductors, Superfluid helium-3, Ultracold fermionic gases (Li-6, K-40)

Key Differences

Feature	Bose-Einstein Condensate (BEC)	Fermionic Condensate
Particle Type	Bosons (integer spin)	Fermions (half-integer spin)
Pauli Exclusion	Not restricted	Fundamentally restricted
Formation Mechanism	Direct condensation	Pairing → Condensation
Core Theory	Bose-Einstein statistics	BCS Theory + BEC
Temperature	Ultra-low (nK)	Even lower (nK)
First Ultracold Gas	1995 (Rb-87, Na-23)	2003 (K-40)

In Essence:

• BEC = Bosons marching in perfect unison as one giant wave

• Fermionic Condensate = Fermions first form dance pairs, then those pairs march in unison