Spin-wave storage using chirped control fields in atomic frequency comb-based quantum memory

It has been shown that an inhomogeneously broadened optical transition shaped into an atomic frequency comb can store a large number of temporal modes of the electromagnetic field at the single-photon level without the need to increase the optical depth of the storage material. The readout of light modes is made efficient thanks to the rephasing of the optical-wavelength coherence similar to photon-echo-type techniques, and the reemission time is given by the comb structure. For on-demand readout and long storage times, two control fields are used to transfer the optical coherence back and forth into a spin wave. Here, we present a detailed analysis of the spin-wave storage based on chirped adiabatic control fields. In particular, we verify that chirped fields require significantly weaker intensities than $\pi$ pulses. The price to pay is a reduction of the multimode storage capacity that we quantify for realistic material parameters associated with solids doped with rare-earth-metal ions.

Figure 1

Principle of quantum memory for light based on the AFC. The inhomogeneously broadened optical transition $|g\rangle \text{−}|e\rangle$ is shaped into an AFC made of narrow peaks separated by $\Delta$ and spanning a large frequency range $\Gamma$. When a resonant signal field (corresponding classically to the Rabi frequency ${\Omega }_s$) is absorbed, the comb modes are excited. They dephase, then rephase at time $2\pi /\Delta$ when the signal field is reemitted through a photon-echo-type process. A pair of control pulses ${\Omega }_c$ on the $|e\rangle \text{−}|s\rangle$ transition allows for both on-demand readout and long storage times.

Figure 2

Transfer efficiency with $\pi$ (dotted blue line) and with chirped (red lines) pulses. The dashed line corresponds to chirped pulses of minimal temporal durations (satisfying the adiabatic criteria) for which the multimode capacity decreases by one mode. The full line is associated with chirped pulses of maximal temporal durations such that only one mode can be stored. The gain, in terms of the required intensity, depends both on the desired efficiency and on the number of modes that can be sacrificed. The circles and crosses are the values obtained using the relation (12c). One can see very good agreement with the numerical simulations.

Figure 3

Overlap between the input signal and the retrieved field for $\pi$ (dotted blue line) and for chirped (red lines) pulses for different values of the Rabi frequency. As in Fig. 2, the dashed line corresponds to chirped pulses of minimal temporal durations (satisfying the adiabatic criteria) for which the multimode capacity decreases by one mode. The full line is associated with chirped pulses of maximal temporal durations such that only one mode can be stored.