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.

Figure 1

(Color online) The dark and anti-dark many-body eigenstates: structure and excitation. (a) The container potential $V_c\left(\xi \right)$ (black dot-dashed line), the even ${\rho }^{+}$ (blue dashed line), odd ${\rho }^{-}$ (red dotted line), and total SP density $\rho ={\rho }^{+}+{\rho }^{-}$ (black solid line) of the ground state with $20$ bosons; the first $20$ eigenvalues are shown as blue squares (even SP eigenstates) and red circles (odd SP eigenstates). (b) The spectrum $P_i$ of the excitation at $\tau =0$ (black squares) and $\tau =19.8$ (red circles), and (c) the dynamics of the SP density following the time-dependent perturbation. (d) The SP density $\rho \left(\xi \right)$ of an anti-dark (black dotted line) and dark (red solid line) many-body eigenstate in the periodic potential (see text for details).