Single-Photon Transistor Using a Förster Resonance

An all-optical transistor is a device in which a gate light pulse switches the transmission of a target light pulse with a gain above unity. The gain quantifies the change of the transmitted target photon number per incoming gate photon. We study the quantum limit of one incoming gate photon and observe a gain of 20. The gate pulse is stored as a Rydberg excitation in an ultracold gas. The transmission of the subsequent target pulse is suppressed by Rydberg blockade, which is enhanced by a Förster resonance. The detected target photons reveal in a single shot with a fidelity above 0.86 whether a Rydberg excitation was created during the gate pulse. The gain offers the possibility to distribute the transistor output to the inputs of many transistors, thus making complex computational tasks possible.

Figure 1

(a) Level scheme. Gate and target pulse each consist of signal light and control light for EIT. Both pulses use the same signal transition, but the control light operates at different frequencies, thus reaching different Rydberg states $|r_g⟩$ and $|r_t⟩$. The hyperfine quantum numbers are $F=1$, $m_F=-1$ and $F=2$, $m_F=-2$ for states $|g⟩$ and $|e⟩$, respectively, whereas both Rydberg states have $m_J=1/2$ and $m_I=-3/2$. The fact that the principal quantum numbers $n_g$ and $n_t=n_g-2$ differ suppresses undesired retrieval of stored gate excitations by target control light much more efficiently than the polarization scheme of Ref. [16]. In addition, both signal light pulses profit from a large electric-dipole matrix element. We typically operate at $n_g=69$. (b) Input power timing scheme, not to scale (see text). (c),(d) EIT spectra (see text).

Figure 2

Single-photon transistor. The number of transmitted signal photons is shown for $N_g=1.0$ incoming signal gate photons (red circles). For reference, the same number is shown in the absence of target signal light $N_g=0$ (green triangles). The lines show exponential fits multiplied by a step function. The ratio of the areas under the two data sets yields an extinction of $\epsilon =0.89(1)$. The gain is $G=20(1)$. This is far above unity, thus demonstrating a single-photon transistor.

Figure 3

Effect of the Förster resonance on the single-photon transistor. (a) Theoretical estimates of the energy mismatch $\mathrm{\Delta }E$ in Rb at infinite interatomic distance. Some states from the fine-structure manifold of the state $|(n-1)P,(n-2)P⟩$ lie close to the state $|n{S}_{1/2},(n-2)S_{1/2}⟩$. Two energy mismatches cross zero near $n=70$, thus creating the Förster resonance used in our experiment. The measured values of the extinction (b) and the gain (c) clearly profit from the Förster resonance. The target pulse is operated at $n_t=n_g-2$. The lines show Lorentzian fits to guide the eye.

Figure 4

Bimodal distribution. The histogram for the number of detector clicks $N_c$ during the target pulse is shown. The reference pulse with $N_g=0$ (green triangles) has mean value $⟨N_c{⟩}_{\text{ref}}=8.62(4)$ and variance 9.87. It is well approximated by the Poisson distribution with this mean value (green dashed line). The distribution for $N_g=1.0$ (red circles) is bimodal. Its peak near $N_c=8$ is caused by events in which zero gate excitations were stored. This peak is identical to the green line except for an overall factor $p_0$, expressing the probability for storing zero excitations. A fit (red dotted line) to the data with $N_c>9.5$ yields the best-fit value $p_0=0.60$. The black solid line shows the difference between the red data and the red fit curve. It represents the histogram if a Rydberg excitation was stored. From the value of $N_c$ measured in a single shot, one can infer whether a Rydberg excitation was stored. Setting the discrimination threshold to $N_{\text{thr}}=5.5$ (dash-dotted vertical line) yields a fidelity for this inference of $F=0.86$ (see text).