Figure 1

(a) Scheme of the experimental apparatus. The rubidium atomic beam effuses from oven $O$. Circular atoms are prepared one at a time in box $B$. They cross the cavity $C$ before being counted in the field-ionization detector $D$. The source $S$ is used for the cavity field displacement. The source $S^{\prime }$ is used for the Ramsey interferometer. (b) Experimental timing for the one-photon Wigner function measurement. The time origin corresponds to the atom crossing the cavity axis (central vertical dotted line). The two other dotted lines indicate the cavity mode waist limits. The lower curve presents, versus time, the detuning $\Delta$ between the atomic transition and mode $M_a$. The horizontal dotted line corresponds to the atom-$M_a$ resonance condition. The resonant period between $t=-74\mu \mathrm{s}$ and $t=-27\mu \mathrm{s}$ corresponds to the $\pi$-Rabi pulse preparing a single photon in $M_a$. The narrow feature around $95\mu \mathrm{s}$ is the field pulse used to tune the phase $\phi$ of the Ramsey interferometer. The two upper curves present the “on” periods for sources $S$ and $S^{\prime }$.Reuse & Permissions

Figure 2

Determination of the “vacuum state” Wigner function. (a) Ramsey fringes for an injected amplitude $\alpha =0$. Probability $p_e$ for detecting the atom in state $e$ as a function of the Ramsey interferometer phase $\phi /\pi$. Dots are experimental with error bars reflecting the variance of the binomial detection statistics. The solid curve is a sine fit. (b) and (c) Ramsey fringes for $\alpha =0.57$ and $\alpha =1.25$, respectively. (d) Dots: vacuum state Wigner function versus $\alpha$ with error bars reflecting the uncertainty on the Ramsey fringes fit. The solid line is a theoretical fit (see text). (e) Corresponding photon number distribution $p_n$.Reuse & Permissions

Figure 3

Determination of the “one-photon” Wigner function. (a) Ramsey fringes for an injected amplitude $\alpha =0$. (b) Ramsey fringes for $\alpha =0.81$ (c) Dots: experimental Wigner function. The solid line is a theoretical fit. (d) Inferred photon number distribution.Reuse & Permissions