Dark stationary matter waves via parity-selective filtering in a Tonks-Girardeau gas

We propose a scheme for observing dark stationary waves in a Tonks-Girardeau (TG) gas. The scheme is based on parity-selective dynamical filtering of the gas via a time-dependent potential, which excites the gas from its ground state towards a desired specially-tailored many-body state. These excitations of the TG gas are analogous to linear partially coherent nondiffracting beams in optics, as evident from the mapping between the quantum dynamics of the TG gas and the propagation of incoherent light in one-dimensional linear photonic structures.