Electric Rydberg-Atom Interferometry

An electric analogue of the longitudinal Stern-Gerlach matter-wave interferometer has been realized for atoms in Rydberg states with high principal quantum number $n$. The experiments were performed with He atoms prepared in coherent superpositions of the $n=55$ and $n=56$ circular Rydberg states in a zero electric field by a $\pi /2$ pulse of resonant microwave radiation. These atoms were subjected to a pulsed inhomogeneous electric field to generate a superposition of momentum states before a $\pi$ pulse was applied to invert the internal states. The same pulsed inhomogeneous electric field was then reapplied for a second time to transform the motional states to have equal momenta before a further $\pi /2$ pulse was employed to interrogate the final Rydberg state populations. This Hahn-echo microwave pulse sequence, interspersed with a pair of equivalent inhomogeneous electric field pulses, yielded two spatially separated matter waves. Interferences between these matter waves were observed as oscillations in the final Rydberg state populations as the amplitude of the pulsed electric field gradients was adjusted.

Figure 1

Schematic diagram of the experimental apparatus (not to scale).

Figure 2

(a) Sequence of electric field and microwave pulses. (b) Difference between the induced electric dipole moments, $\mathrm{d}{E}_{nc}/\mathrm{d}F$, of the $|55c⟩$ and $|56c⟩$ states in He in an electric field applied perpendicular to a magnetic field $\overrightarrow{B}=(0,0,15.915)\mathrm{G}$. The difference between the static electric dipole moments of the outermost LFS Stark states in a pure electric field is indicated by the dashed red line.

Figure 3

(a) Measured, and (b) calculated Rydberg-atom interference patterns for $T_{\mathrm{grad}}=225$, 325, 425, and 525 ns (as indicated). Individual datasets are vertically offset for clarity.

Figure 4

Effects of modifications to the microwave and electric field pulse sequence on the interference patterns observed when $T=525\mathrm{ns}$. (a) The complete $\pi /2–\nabla {\overrightarrow{F}}_{\mathrm{grad}}–\pi –\nabla {\overrightarrow{F}}_{\mathrm{grad}}–\pi /2$ sequence as in Fig. 3; (b) and (c) incomplete pulse sequences in which the first $\pi /2$ pulse was omitted, and only the pulsed electric field gradients were applied, respectively. (d) Parallel electrodes (see text for details). The data in (a) and (c) are vertically offset for clarity.