Temporally multiplexed quantum repeaters with atomic gases

We propose a temporally multiplexed version of the Duan-Lukin-Cirac-Zoller (DLCZ) quantum-repeater protocol using controlled inhomogeneous spin broadening in atomic gases. A first analysis suggests that the advantage of multiplexing is negated by noise due to spin-wave excitations corresponding to unobserved directions of Stokes photon emission. However, this problem can be overcome with the help of a moderate-finesse cavity which is in resonance with Stokes photons, but invisible to the anti-Stokes photons. Our proposal promises greatly enhanced quantum repeater performance with atomic gases.

Figure 1

Temporally multiplexed creation and recall of spin waves. (Left) The atomic ensemble is excited by a sequence of write pulses. Each write pulse can lead to the emission of a Stokes photon. The cavity is in resonance with the Stokes photons, such that emission into the cavity mode is enhanced by a factor $F$, the cavity finesse. The cavity is asymmetric, such that the Stokes photons leave the cavity in one direction. Emission into the cavity occurs for a fraction ${\beta }_S$ of all Stokes emissions (e.g., here at time $t_2$). Every Stokes emission is associated with the creation of a spin wave, which dephases due to the applied magnetic field gradient. This dephasing can be reversed by flipping the sign of the field (e.g., at time $T$). The spin wave created by the Stokes emission at $t_2$ will be in phase at $2T-t_2$. Applying a read pulse at this time (right) creates an anti-Stokes photon, whose emission direction is correlated with that of the Stokes photon due to collective interference. A Stokes photon emitted into the cavity creates a standing spin wave; the associated anti-Stokes photon is therefore emitted into a superposition of two counter-propagating modes. The anti-Stokes photons have a polarization orthogonal to that of the Stokes photons and are ejected from the cavity on their first pass through the polarizing beam splitter (PBS). (The mirrors are highly reflective for the anti-Stokes photons.) Out-of-phase spin waves (e.g., those created at $t_1$ and $t_3$), lead to the emission of anti-Stokes photons without any preferred direction at $t_2$. Since there is no cavity-induced enhancement for them, only a small fraction ${\beta }_{\mathit{AS}}\ll {\beta }_S$ go in the same direction as the “good” anti-Stokes photon which is correlated to the Stokes photon from $t_2$.