Information hiding and retrieval in Rydberg wave packets using half-cycle pulses

We demonstrate an information hiding and retrieval scheme with the relative phases between states in a Rydberg wave packet acting as the bits of a data register. We use a terahertz half-cycle pulse (HCP) to transfer phase-encoded information from an optically accessible angular momentum manifold to another manifold which is not directly accessed by our laser pulses, effectively hiding the information from our optical interferometric measurement techniques. A subsequent HCP acting on these wave packets reintroduces the information back into the optically accessible data register manifold which can then be read out.

Figure 1

Correlations vanish. The choice of ${\mathrm{HCP}}_1$ delay $T_1=5\mathrm{ps}$ moves population from the $31p$ state into neighboring angular momentum states such that the phase information that was contained in $31p$ cannot be measured. All correlations involving $31p$ vanish.

Figure 2

Correlations recovered. Applying a second HCP at $T_2=6.3\mathrm{ps}$ coherently transfers population from neighboring angular momentum states into the data register state $n=31p$. The correlations with $31p$ are seen to return; phase information is recovered.

Figure 3

Two-state wave packet correlations. (a) In the absence of a HCP, the $27p\text{−}32p$ correlation is strong; the phase relationship is well defined and easily read. (b) $T_1=7\mathrm{ps}$. The operation of the HCP moves phase information into the $31d$ and $32s$ states, and that phase information becomes unreadable. (c) $T_2=14.2\mathrm{ps}$. Application of a second HCP at a later delay recovers phase information in the $32p$ state.

Figure 4

Information recovered following second HCP. In the absence of any HCP, the information recovered is at the level indicated by the dotted line. An HCP arrives at a fixed delay $T_1=4.1\mathrm{ps}$ after wave packet excitation, and the total phase information retrieved following this HCP kick is indicated by the dashed horizontal line. Following the first HCP, a second HCP kicks the wave packet at various delays $T_2$. The information recovered following the second HCP (solid line) is shown as a function of the time difference between the first and second kicks.