Coherent Logic Gate for Light Pulses Based on Storage in a Bose-Einstein Condensate

A classical logic gate connecting input and output light pulses is demonstrated. The gate operation is based on three steps: First, two incoming light pulses are stored in a Bose-Einstein condensate; second, atomic four-wave mixing generates a new matter wave; and third, the light pulses are retrieved. In the presence of the new matter wave, the retrieval generates a new optical wave. The latter will only be generated if both input light pulses are applied, thus realizing an AND gate. Finally, we show that the gate operation is phase coherent, an essential prerequisite for a quantum logic gate.

Figure 1

Scheme of the experimental procedure. Two Raman pulses are applied, preparing three BECs with momenta $\mathbf{0}$, $\mathit{k}$, and $\mathit{k}+\mathit{q}$. During a subsequent dark time, atomic FWM creates a BEC with momentum $\mathit{q}$. Arrows show the propagation directions of the light beams. Circles represent atomic momentum components. The internal state is color coded: white denotes $|1⟩$, gray (red) denotes $|2⟩$. A third light pulse with only control light applied retrieves the signal light. The retrieved light will have a component propagating downward only if signal light is applied during both Raman pulses, thus realizing an AND gate. A modified state preparation can additionally populate the momentum component $-\mathit{q}$ so that atomic FWM also populates $\mathit{k}-\mathit{q}$. This extended scheme, in which the dashed circles are populated, generates a time-dependent interference pattern in the retrieved light.

Figure 2

Atomic four-wave mixing. The atom number $N_q$ in the atomic momentum component $\mathit{q}$ is extracted from time-of-flight absorption images. $N_q$ depends on the four-wave mixing time. At short times, this dependence is quadratic. Inset: An image oriented as Fig. 1, taken for $t_{\mathrm{FWM}}=1.8\mathrm{ms}$ without applying depletion light.

Figure 3

Logic gate. The retrieved photon number propagating downward is shown for four different experimental settings, in which the signal beams during Raman pulses 1 and 2 are turned on or off independently. Downward propagating light will only be retrieved if both signal beams are on. This demonstrates an AND gate for classical light pulses based on storage in a BEC and FWM of matter waves.

Figure 4

Phase coherence. The retrieved photon number propagating downward exhibits a sinusoidal oscillation as a function of the FWM time. The best-fit value for the oscillation frequency is 15.4 kHz. The oscillation occurs because two pathways contribute to this signal in the extended scheme with six momentum components.