Photonic quantum memory in two-level ensembles based on modulating the refractive index in time: Equivalence to gradient echo memory

We present a quantum memory protocol that allows us to store light in ensembles of two-level atoms, e.g., rare-earth-metal ions doped into a crystal, by modulating the refractive index of the host medium of the atoms linearly in time. We show that under certain conditions the resulting dynamics is equivalent to that underlying the gradient echo memory protocol, which relies on a spatial gradient of the atomic resonance frequencies. We discuss the prospects for an experimental implementation.

Figure 1

(a) In the GEM protocol, a longitudinal energy shift in the atoms (solid dots) allows one to cover all of the frequency components of the incoming light. (b) In the protocol proposed here, due to the linear change of the refractive index in time, the light experiences an effective position-dependent frequency shift $\dot{k}z$. This allows different frequency components of the light to interact on resonance with a spectrally narrow line of atoms.

Figure 2

The efficiency of the proposed memory protocol based on refractive index modulation in terms of the initial optical depth $d_{\mathrm{in}}$. The efficiency is given by $e^{-2\gamma \tau }{[1-\exp (-d_{\mathrm{in}}\gamma /\dot{k}L)]}^2$. The figure shows the efficiency for different pulse durations, $\tau$, relative to the excited-state linewidth, $\gamma$. We assume $\dot{k}L\tau =2$. Depending on the available optical depth, one can optimize the achievable efficiency by choosing an appropriate pulse duration.