Entanglement of a Mesoscopic Field with an Atom Induced by Photon Graininess in a Cavity

We observe that a mesoscopic field made of several tens of microwave photons exhibits quantum features when interacting with a single Rydberg atom in a high-$Q$ cavity. The field is split into two components whose phases differ by an angle inversely proportional to the square root of the average photon number. The field and the atomic dipole are phase entangled. These manifestations of photon graininess vanish at the classical limit. This experiment opens the way to studies of large quantum state superpositions at the quantum-classical boundary.

Figure 1

(a) Experimental apparatus. (b) Timing of the experiment. (c) Field phase distribution $S_g(\varphi )$ obtained for a coherent field in $C$ with $\overline{n}=29$ photons on the average.

Figure 2

(a) Field phase distribution $S_g(\varphi )$ for three $\overline{n}$ values (18, 29, and 36) and $t_i=t_a=32\mu \mathrm{s}$. The points are experimental and the curves are fits on a sum of Gaussians. The thick vertical line indicates phase reference. (b) Field phase distribution for $\overline{n}=15$, 22, and 29 and $t_i=t_b=53\mu \mathrm{s}$. (c) Phases of the two field components versus ${\Phi }^{+}=\Omega t/4\sqrt{\overline{n}}$. Dotted and solid lines are theoretical (see text). Inset: computed cavity field Wigner function $W({\beta }_x+i{\beta }_y)$ for $\overline{n}=36$ and $t_i=t_a$.

Figure 3

Field phase distributions $S_g(\varphi )$ following preparation of atomic states $|{\varphi }_a^{\pm }(0)⟩$ by combination of Rabi and Stark pulses ($\overline{n}=27$ and $t_i=t_a$). Open circles: preparation of $|{\varphi }_a^{+}(0)⟩$. Solid squares: preparation of $|{\varphi }_a^{-}(0)⟩$. Solid lines are Gaussian fits.