Spontaneous emission in quantum walks of a kicked Bose-Einstein condensate

We analytically investigate the recently proposed and implemented discrete-time quantum walk based on a kicked Bose-Einstein condensate. We extend previous work on the effective dynamics by taking into account spontaneous emission due to the kicking light. Spontaneous emission affects both the internal and external degrees of freedom, arising from the entanglement between them during the walk dynamics. The result is a measurable degrading of the experimental walk signal that we characterise.