Physic Labs

Condensed matter physics

Bose–Einstein statistics

Explore the Bose–Einstein distribution of an ideal boson gas as temperature drops. Observe the build-up of particles in the ground state (Bose–Einstein condensation) and compare with nˉi=1/(e(ϵi−μ)/kBT−1)\bar n_i = 1/(e^{(\epsilon_i-\mu)/k_BT}-1).

Advanced

Equipment

  • Bose–Einstein distribution plot versus energy
  • Virtual 3D box of bosons
  • Sliders for temperature, density/frequency, and state count

Procedure

  1. Observe the distribution vs temperature

    Drag the "Temperature" slider from high to low and follow the distribution curve in figure 1 and the particle cloud in figure 2. Record the readout values. At high temperature the distribution spreads across many levels; as TT falls, particles pile into low-energy levels per nˉi=1/(e(ϵi−μ)/kBT−1)\bar n_i = 1/(e^{(\epsilon_i-\mu)/k_BT}-1).

  2. Vary density and state count

    Keeping temperature low, raise the "Density / frequency" slider and then "Number of states" to see how the distribution responds. High density pushes the chemical potential μ\mu toward the ground-state level; compare with the quantum-concentration criteria in the readout. Use "Pause motion" for a stable reading.

  3. Predict and verify

    Predict how the onset of condensation shifts when density rises at fixed temperature, then test it in the simulation. Compare with the high-temperature, low-density limit where the distribution approaches Maxwell–Boltzmann: e−(ϵ−μ)/kBT≪1e^{-(\epsilon-\mu)/k_BT} \ll 1.

Simulation

Experiment history

In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper deriving Planck's spectrum by counting photon states in a new way — treating identical particles as indistinguishable. Einstein recognized its importance, translated the paper into German for publication, and applied the same counting to an atomic gas. He predicted that below a critical temperature a macroscopic fraction of particles would occupy the lowest energy state: what we now call Bose–Einstein condensation. Seventy years later, in 1995, the group of Eric Cornell and Carl Wieman at JILA produced the first condensate in rubidium-87 gas cooled to about 170 nanokelvin; Wolfgang Ketterle achieved a similar result with sodium. The three shared the 2001 Nobel Prize in Physics. Today BECs underpin research on superfluidity, superconductivity analogues, and quantum simulation.

Related physicists

Albert EinsteinLouis de BroglieCarl Edwin Wieman

Related library topics

Bose–Einstein statistics