Special Section: the Legacy of Albert Einstein

Classically identical particles become quantum mechanically indistinguishable. Satyendra Nath Bose taught us, in 1924, how to correctly count the distinct microstates for the indistinguishables, and for a gas of light quanta (later photons), whose number is not conserved, e.g., can vary with temperature, he gave a proper derivation of Planck’s law of black body radiation. Einstein, in 1925, generalized the Bose statistics to a quantum gas of material particles whose number is now fixed, or conserved, e.g., He, and thus opened a new direction in condensed matter physics: He showed that for low enough temperatures (~1 Kelvin and below), a macroscopic number of the particles must accumulate in the lowest one-particle state. This degenerate gas with an extensively occupied single one-particle state is the Bose–Einstein condensate, now called BEC. (Fragmented BEC involving a multiplicity of internal states of non-scalar Bose atoms is, however, also realizable now). Initially thought to be a pathology of an ideal non-interacting Bose system, the BEC turned out to be robust against interactions. Thus, the Bose–Einstein condensation is a quantum phase transition, but one with a difference – it is a purely quantum statistical effect, and requires no inter-particle interaction for its occurrence. Indeed, it happens in spite of it. The condensate fraction, however, diminishes with increasing interaction strength – to less than ten per cent for He. The BEC turned out to underlie superfluidity, namely that the superfluid may flow through finest atomic capillaries without any viscosity. Interaction, however, seems essential to superfluidity. But, the precise connection between BEC and the superfluidity remains elusive. Thus, for example, we may have superfluidity in two-dimensions where there is no condensate! Seventy years later now, the BEC has come alive with the breakthrough in 1995 when near-ideal BEC was created in dilute alkali gases of Rb and Na atoms cooled in the gaseous state down to nanokelvins and localized in a trap. There are reasons why we ought to be mindful of the BEC – if only because here even the interaction between the particles is tunable at will – the sign as well as the strength of it. BEC has now become an ideal laboratory for basic and condensed matter experiments, and for high resolution applications. Properly viewed, it is indeed a new state of matter. This article is about the saga of BEC that really began with Einstein in 1925.