Two-Photon Gateway in One-Atom Cavity Quantum Electrodynamics

Single atoms absorb and emit light from a resonant laser beam photon by photon. We show that a single atom strongly coupled to an optical cavity can absorb and emit resonant photons in pairs. The effect is observed in a photon correlation experiment on the light transmitted through the cavity. We find that the atom-cavity system transforms a random stream of input photons into a correlated stream of output photons, thereby acting as a two-photon gateway. The phenomenon has its origin in the quantum anharmonicity of the energy structure of the atom-cavity system. Future applications could include the controlled interaction of two photons by means of one atom.

Figure 1

The energy level structure of one atom strongly coupled to a quantized field (a) governs the statistics of photons which leak out of the cavity (b). Photons arrive randomly at the input mirror and exit in pairs as soon as two laser photons are on resonance with the two-photon dressed state $|2,\pm ⟩$.

Figure 2

Photon number squared (dotted line) and two-photon correlation functions versus the cavity detuning with an input field corresponding to 0.01 photon in an empty cavity. The normalized $g^{(2)}(0)-1$ function (dashed line) presents a maximum at zero cavity detuning ${\Delta }_c=0$, so that the two-photon dressed states $|2,\mp ⟩$ appear as shoulders. In contrast, the differential correlation function $C^{(2)}(0)$ (solid line) has clear maxima on the second dressed states. Notice that $C^{(2)}(0)$ is the product of the dotted and dashed lines. The negative values for $C^{(2)}(0)$ and $g^{(2)}(0)-1$ on the dressed states $|1,\mp ⟩$ indicate sub-Poissonian emission of single photons [though hardly visible in this plot for $g^{(2)}(0)-1$].

Figure 3

Time-dependent correlation function for different cavity detunings. The error bars are standard deviations. The detunings are for (a)–(d) ${\Delta }_c/2\pi =(0,-3,-10,-18)\mathrm{MHz}$. (a) shows large bunching with long-tail oscillations, yielding information on the micromotion of the atom in the trap. From (b)–(d), the correlations are produced by the atom-cavity system, notably showing a bunching in [(c) and inset] at the two-photon resonance.

Figure 4

Correlation spectrum for zero time delay as a function of the cavity detuning. The spectrum shows that the rate of coincidences (left scale) is maximum when two laser photons become resonant with the two-photon dressed state $|2,-⟩$. The solid curve is from quantum theory which describes the interaction of one atom and two resonant photons (see text for details). Also shown is the measured photon count rate which is maximum on the single-photon dressed state $|1,-⟩$ (dotted, right scale); the standard deviations (0.2–1 kHz) are not shown for clarity.