Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas

The pioneering paper by Bogoliubov in 1947 was the starting point for a microscopic theory of superfluidity [1]. Bogoliubov found the non-perturbative solution for a weakly interacting gas of bosons. The main step in the diagonalization of the Hamiltonian is the famous Bogoliubov transformation, which expresses the elementary excitations (or quasiparticles) with momentum q in terms of the free particle states with momentum +q and – q. For small momenta, the quasiparticles are a superposition of +q and -q momentum states of free particles. Following the theoretical suggestion in ref. [2] we observed such superposition states by first optically imprinting phonons with wavevector q into a Bose-Einstein condensate and probing their momentum distribution using Bragg spectroscopy with a high momentum transfer. By combining both momentum and frequency selectivity, we were able to “directly photograph” the Bogoliubov transformation [3].