Manipulating quantum wave packets via time-dependent absorption

A pulse of matter waves may dramatically change its shape when traversing an absorbing barrier with time-dependent transparency. Here we show that this effect can be utilized for controlled manipulation of spatially localized quantum states. In particular, in the context of atom-optics experiments, we explicitly demonstrate how the proposed approach can be used to generate spatially shifted, split, squeezed, and cooled atomic wave packets. We expect our work to be useful in devising new interference experiments with atoms and molecules and, more generally, to enable new ways of coherent control of matter waves.

Figure 1

Illustration of matter pulse carving.

Figure 2

Aperture function given by (a) Eq. (22) with $\gamma =100{\text{s}}^{-1}$ (solid blue curve) and $\gamma =-100{\text{s}}^{-1}$ (dashed red curve), (b) Eq. (23) with $\gamma =100{\text{s}}^{-1}$, and (c) Eq. (24) with $\gamma =100{\text{s}}^{-1}$.

Figure 3

Husimi distributions for a ${}^{87}\mathrm{Rb}$ atom in (a)–(c) a pure and (d)–(f) a mixed finite-temperature state, i.e., $H_{{\alpha }_0,x_0,v_0}^{\left(t\right)}(\tilde{x},\tilde{v})$ and ${\mathcal{H}}_{{\alpha }_0,x_0,v_0,\Delta v}^{\left(t\right)}(\tilde{x},\tilde{v})$, respectively. The system parameters are $m=86.909$ u, $\sigma =30\mu \text{m}, x_0=-0.15$ mm, $v_0=3$ mm/s, $\Delta v=0.1$ mm/s, and $t=100$ ms. The aperture function is defined by Eq. (22). The rate of change of the barrier transparency (a) and (d) $\gamma =0$, (b) and (e) $\gamma =100{\text{s}}^{-1}$, and (c) and (f) $\gamma =-100{\text{s}}^{-1}$.

Figure 4

Husimi distribution ${\mathcal{H}}_{{\alpha }_0,x_0,v_0,\Delta v}^{\left(t\right)}(\tilde{x},\tilde{v})$ for a mixed state, characterized by the same set of parameters as in Figs. 3–3, in the presence of an absorbing barrier specified by Eq. (23) with (a) $\gamma =125{\text{s}}^{-1}$, (b) $\gamma =150{\text{s}}^{-1}$, (c) $\gamma =175{\text{s}}^{-1}$, and (d) $\gamma =225{\text{s}}^{-1}$.

Figure 5

Relative spatial (solid red curve), velocity (solid blue curve), and phase-space (dashed green curve) uncertainties and total transmission probability (dash-dotted purple curve) as functions of the rate $\gamma$ for the aperture function defined in Eq. (24). All system parameters are the same as in Figs. 3–3 and 4.