Nondestructive Rydberg Atom Counting with Mesoscopic Fields in a Cavity

We present an efficient, state-selective, nondemolition atom-counting procedure based on the dispersive interaction of a sample of circular Rydberg atoms with a mesoscopic field contained in a high-quality superconducting cavity. The state-dependent atomic index of refraction, proportional to the atom number, shifts the classical field phase. A homodyne procedure translates the information from the phase to the intensity. The final field intensity is readout by a mesoscopic atomic sample. This method opens promising routes for quantum information processing and nonclassical state generation with Rydberg atoms.

Figure 1

(a) Scheme of the experimental apparatus. (b) Pictorial representation of the cavity field evolution when a single atom in $|e⟩$ or $|g⟩$ crosses the cavity. The displacement ${\mathcal{D}}_1$ is represented by the solid straight arrow, the atom-induced phase shift by the curly arrows, and ${\mathcal{D}}_2$ by dashed arrows. Coherent states are depicted as circles, symbolizing the quantum fluctuations around the classical amplitude. The open circles represent the fields after the atom-cavity interaction, the gray circles the fields after ${\mathcal{D}}_2$.

Figure 2

Cavity field phase distributions (dephasing sample prepared in level $|e⟩$). Probability $P_g(\phi )$ for finding the probe atom in $|g⟩$ versus the displacement phase $\phi$. Open circles, reference field; solid squares, phase distribution after interaction with the dephasing atom sample. The error bars reflect statistical fluctuations. The peaks corresponding to zero, one, and two atoms are clearly separated. The lines are Gaussian fits.

Figure 3

Nondemolition detection of an atomic sample. (a) Conditional probability distribution $P_e(N|N_a)$ for detecting $N$ atoms in $|e⟩$ in the readout samples, provided the field-ionization counter has detected $N_a$ atoms in the dephasing sample (atoms prepared in $|g⟩$), for $N_a=0$ (open circles), $N_a=1$ (solid circles), and $N_a=2$ (solid diamonds). The detection thresholds $N_1$ and $N_2$ are indicated by vertical bars. (b) Histograms of $P_e(N|e)$ (solid squares), $P_e(N|0)$ (open circles) and $P_e(N|g)$ (solid circles). Vertical bars indicate the thresholds $N_e$ and $N_g$. The insets in (a) and (b) show the cavity fields in phase space before (open circles) and after (gray circles) the displacement ${\mathcal{D}}_2$ with the same conventions as in Fig. 1b.