17.3 Bose-Einstein condensation

Bose-Einstein condensation is a mind-bending state of matter where particles act as one big quantum wave. It happens when bosons get super cold, crowding into the lowest energy state and behaving collectively.

This weird quantum soup has some wild properties. It can flow without friction, create interference patterns like light waves, and even be used for ultra-precise measurements and quantum computing.

Bose-Einstein Condensation

Properties of Bose-Einstein condensation

Top images from around the web for Properties of Bose-Einstein condensation

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

• 

  Bose–Einstein condensate - wikidoc View original

  Is this image relevant?

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

1 of 3

Top images from around the web for Properties of Bose-Einstein condensation

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

• 

  Bose–Einstein condensate - wikidoc View original

  Is this image relevant?

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

• 

  Bose Einstein Condensation | Introduction to the physics of atoms, molecules and photons View original

  Is this image relevant?

1 of 3

• Macroscopic quantum state where quantum effects are observable on a large scale (superconductivity, superfluidity)
• Coherence means all particles in the condensate have the same quantum phase leading to collective behavior
• Superfluidity allows the condensate to flow without friction similar to liquid helium below the lambda point
• Interference between condensates demonstrates their wave-like properties analogous to light interference patterns

Critical temperature for condensation

• Temperature below which a significant fraction of bosons occupy the ground state determined by the Bose-Einstein distribution
• $f(E) = \frac{1}{e^{(E - \mu) / k_B T} - 1}$ gives the average number of particles in a state with energy $E$, chemical potential $\mu$, Boltzmann constant $k_B$, and temperature $T$
• Critical temperature $T_c = \frac{2\pi\hbar^2}{mk_B} \left(\frac{n}{\zeta(3/2)}\right)^{2/3}$ depends on reduced Planck constant $\hbar$, particle mass $m$, particle density $n$, and Riemann zeta function $\zeta(3/2) \approx 2.612$
• Higher particle density leads to a higher critical temperature allowing condensation to occur at relatively higher temperatures

Experimental realization of condensates

• First achieved in 1995 by Eric Cornell and Carl Wieman (NIST/JILA) using laser cooling and magnetic trapping of rubidium-87 atoms
• Condensates have been realized in various atomic species including alkali metals (rubidium, sodium, lithium), hydrogen, and metastable helium
• Precision measurements applications include atomic clocks and gravitational wave detection due to the condensate's sensitivity
• Quantum simulation allows studying complex quantum systems and phase transitions by manipulating the condensate
• Quantum information processing applications include quantum computing and cryptography using the condensate's coherence properties

Condensates vs classical states

• Bose-Einstein condensates are quantum degenerate with a large fraction of particles in the lowest quantum state, unlike classical gases and liquids
• Condensates exhibit macroscopic quantum coherence where all particles have the same phase, while classical states do not have coherence
• Superfluidity allows condensates to flow without friction, but classical gases and liquids experience friction and viscosity
• Condensates have limited compressibility due to repulsive interactions between particles, similar to classical liquids but unlike highly compressible gases