Optical absorption in a degenerate Bose gas

We here develop a theory on optical absorption in a dilute Bose gas at low temperatures. This theory is motivated by the Bogoliubov theory of elementary excitations for this system, and takes into account explicitly the modification of the nature and dispersion of elementary excitations due to Bose-Einstein condensation. Our results show important differences from existing theories. PACS numbers: 03.75.Fi, 32.70.Jz, 32.80.-t A remarkable property of a degenerate Bose gas is the modification of the nature of excitations in the system. This has been elucidated by the work of Feymann and Bogoliubov [1]. For a classical or non-degenerate Bose gas, elementary excitations are basically quasiparticles. For a degenerate Bose gas however, the long wavelength elementary excitations are the same as density waves of the system, propagating at the sound velocity. They correspond to neither addition nor removal of a quasiparticle, but a linear combination of both. At short wavelengths these excitations resemble more closely quasiparticles, with the dispersion the same as free particles apart from a shift. Recently there is much interest in optical excitations in dilute degenerate Bose gas. The frequency of absorption has been used as an indication of the formation of Bose-Einstein condensation in the system [2]. An optical excitation is a non-trivial process, as one of the original atoms (referred to as a-atoms below), all identical before the excitation occurs, is converted to another one which is distinguishable from all the others. Moreover a-atoms which are not excited internally interact differently with this ‘foreign’ atom (referred to as c-atom below) than among themselves, and must respond by rearrangement of their relative motion. The frequencies at which optical absorption occur are therefore different from ω0, the value for a single isolated atom. Optical absorption in a Bose gas has been considered by Oktel and Levitov [3], and also by Pethick and Stoof [4]. Johnsen and Kavoulakis [5] considered the case of excitons in semiconductors where the initial and final bosons have different effective masses, using an approximation equivalent to that used by Oktel and Levitov [3]. Let us briefly summarize the main results of Ref. [3] most relevant to the discussions below. These authors concentrate on intermediate to high temperatures and ignore the modifications of the nature of quasiparticles below the transition temperature. They make the dramatic prediction that, for T < Tc and in the limit of no momentum transfer, there is actually not one but two absorption lines. These lines are located at the frequencies ω = ω0 + gacn− gaa(n0 + 2nT ) + y (1)