Coherent Transfer between Low-Angular-Momentum and Circular Rydberg States

We realize a coherent transfer between a laser-accessible low-angular-momentum Rydberg state and the circular Rydberg level with maximal angular momentum. It is induced by a radio frequency field with a high-purity ${\sigma }^{+}$ polarization resonant on Stark transitions inside the hydrogenic Rydberg manifold. We observe over a few microseconds more than 20 coherent Rabi oscillations between the initial Rydberg state and the circular level. We characterize these many-Rydberg-level oscillations and find them in perfect agreement with a simple model. This coherent transfer opens the way to hybrid quantum gates bridging the gap between optical communication and quantum information manipulations with microwave cavity and circuit quantum electrodynamics.

Figure 1

(a) Scheme of the hydrogen Rydberg levels in the $n$th manifold in a static electric field (only states with $m\ge 0$ are shown). A ${\sigma }^{+}$ drive couples the $n_1=0$ levels (in red) from $m=0$ to the CRL. (b) Scheme of Rb Rydberg levels. $\mathrm{A}\sim 2\mathrm{V}/\mathrm{cm}$ electric field lifts the degeneracy of the $n$th Stark manifold. States with $m\ge 3$ are hydrogenoid, while lower $m$ levels are affected by quantum defects. The ground state atoms are excited to the lower $m=2$ state. A ${\sigma }^{+}$ polarized rf field couples $|n,i⟩$ to an angular-momentum-like subspace $\mathcal{D}$ (red levels) via $\mathrm{\Delta }m=+1$ transitions, leading to a transfer toward the CRL $|n,c⟩$ (blue arrow). The population of each Stark level can be probed by selective mw transitions towards the corresponding level in the $n-2$ manifold (dotted arrow). (c) Simplified experimental setup. Atoms from a thermal beam are optically excited at the center of the structure by lasers (red, 780 and 776 nm lasers; green, 1258 nm laser). A set of electrodes is used to apply static and rf electric fields. After a $\sim 230\mu \mathrm{s}$ time of flight, the atoms are detected out of the structure by field ionization.

Figure 2

(a) Rabi oscillation induced by the ${\sigma }^{-}$ polarization component of the rf field on the $|52,i⟩\to |52,i^{\prime }⟩$ transition (electric field along the $+\mathit{z}$ direction). Population $P_{i^{\prime }}$ of $|52,i^{\prime }⟩$ versus the rf pulse duration $t$ (dots). The fit (red line) provides ${\mathrm{\Omega }}_{i{i}^{\prime }}^{-}/2\pi =107\pm 25\mathrm{kHz}$. (b) Autler-Townes doublet of the $|52,i⟩\to |52,i^{\prime }⟩$ transition (electric field along $-\mathit{z}$) dressed by the ${\sigma }^{+}$ rf field. Points are experimental; red lines are Gaussian fits leading to ${\mathrm{\Omega }}_{i{i}^{\prime }}^{+}/2\pi =30.0\mathrm{MHz}$.

Figure 3

Adiabatic passage in the $n=51$ manifold. (a) Field ionization spectra (signal versus the ionization detector field) of the initial state $|51,i⟩$ (dashed cyan line) and after the adiabatic passage (solid black line). (b) Populations $P_p$ for $p=i,c,d,e,f,g$ of the states $|51,p⟩$ (color code for level identification in the inset) as a function of the Rabi frequency ${\mathrm{\Omega }}_{\mathrm{rf}}/2\pi$. Dots are experimental with statistical error bars. Solid lines are the result of a numerical simulation of the full Hamiltonian evolution.

Figure 4

Dynamics of the atomic state for a rf pulse duration $\mathrm{\Delta }{t}_{\mathrm{rf}}$. (a) Long time scale evolution of the CRL population $P_c$ (dots). The solid line is the result of a numerical simulation, with ${\mathrm{\Omega }}_{\mathrm{rf}}/2\pi =3.52\mathrm{MHz}$ and a rf pulse shortened by 68 ns to model the rise and fall times of the driving electronics. (b) Populations $P_p$ for $p=c$, $d$, $e$, $f$, $g$ around the second maximum of $P_c$ (same color conventions as in Fig. 2). Dots are experimental, and solid lines are the results of the simulation. (c) Calculated (bars) and measured (open circles) populations $P_p$ at the top of the second CRL population maximum. (d) Enlargement of (a) around three late CRL population maxima. (e) Calculated (bars) and measured (open circles) populations $P_p$ at the top of the first CRL population maximum in (d). For all panels, the experimental error bars correspond to the statistical fluctuations.