Observing the onset of effective mass of a Bose-Einstein condensate in an optical lattice

The concept of the effective mass is ubiquitous in the study of electronic conduction in solid state physics, allowing for a semi-classical treatment of a particle's response to an external force. However, in 1954 Pfirsch and Spenke [1] predicted that this description breaks down on very short timescales, and that the initial response to a force is in fact described by the bare mass. This is because the external force F unavoidably leads to interaction energies associated with both intraband and interband dynamics, and while the intraband portion of the interaction alone would lead to a response described by the effective mass m, the interband contribution ensures an initial response given by the bare mass m_o. Over time, the interband coupling results in rapid oscillations in the complex amplitudes of the initial and neighbouring bands, and an acceleration {a) which itself oscillates around F/m. For typical solid state systems, the fast timescales of these dynamics have thus far prohibited observation of this phenomenon. Duque-Gomez and Sipe [2] have recently revisited this idea specifically in the context of ultracold atoms in optical lattices, where the narrow momentum widths and inherent length and time scales involved make observation of long-range quantum coherent phenomena experimentally accessible.