Atomic-frequency-comb quantum memory via piecewise adiabatic passage

In this paper, we propose a method to create an atomic frequency comb (AFC) in hot atomic vapors using the piecewise adiabatic passage (PAP) technique. Due to the Doppler effect, the trains of pulses used for PAP give rise to a velocity-dependent transfer of the atomic population from the initial state to the target one, thus forming a velocity comb whose periodicity depends not only on the repetition rate of the applied pulses but also on the specific atomic transitions considered. We highlight the advantages of using this transfer technique with respect to standard methods and discuss, in particular, its application to store a single telecom photon in an AFC quantum memory using a high density Ba atomic vapor.

Figure 1

Scheme of the $\mathrm{\Lambda }$-type system modeling an atom at rest, initially in $\left|1\right.〉$, interacting with the pump and dump trains of pulses with temporal spacing $T_{\text{int}}$. In the frequency domain, the fields correspond to an OFC with a frequency separation of $2\pi /T_{\text{int}}$ around its nominal frequency. See the main text for the definition of the parameters.

Figure 2

Atomic VC via PAP generated using nominal detunings (a) ${\mathrm{\Delta }}^0=0$, (b) ${\mathrm{\Delta }}^0=2\pi ·63.7\mathrm{MHz}$, and (c) ${\mathrm{\Delta }}^0=2\pi ·127.4\mathrm{MHz}$. Here ${\rho }_{33}$ is weighted by the Maxwell–Boltzmann velocity distribution with $\eta =350$ m/s and rescaled to show the single atom probability instead of the atomic density. See text for the rest of parameters.

Figure 3

Schematics of two AFC configurations to store a single photon. The signal photon $\mathcal{E}$ is stored in the $\left|3\right.〉\leftrightarrow \left|4\right.〉$ transition via a (a) one-photon or (b) two-photon process using a control field ${\mathrm{\Omega }}_c$.

Figure 4

Numerical example of the (a) temporal sequence of a piecewise adiabatic passage (PAP) with $N=16$ simultaneous dump (blue lines) and pump (red lines) pulses with temporal interpulse spacing $T_{\text{int}}$, and pulse width $\sigma$, which generates (b) an atomic frequency comb (AFC) with ${\mathrm{N}}_{\mathrm{c}}$ peaks, bandwidth $\mathrm{\Gamma }$, detuning peak separation $\mathrm{\Delta }\delta$, and peak FWHM $\varpi$. Here $\eta =350$ m/s and ${\rho }_{33}\left(\delta \right)$ is rescaled to show the single atom probability instead of atomic density. See text for the parameter values.

Figure 5

Relevant energy-levels for Ba with the Rabi frequencies and detunings involved in the VC creation via PAP (left frame) and the single telecom photon QM (right frame). See the main text for the definition of the parameters.

Figure 6

(a) Comb distribution ${\rho }_{33}/\varrho$ (black line) as a function of the detuning $\delta \left(v\right)$, together with the input photon spectral distribution seen by the atoms (red line). (b) Temporal evolution of the photon intensity at $z=0$ (solid line) and $z=L$ (dashed). The retrieved pulse in the backward direction is found at $\tilde{\mathcal{T}}\simeq 3.6\mu \mathrm{s}$ with respect to the input pulse. (c) Scaled photon intensity as a function of position and time. The simulation is performed with an AFC comb created using $N=40$ pulses, ${\mathrm{\Omega }}_0=2\pi ·51.72$ MHz, and ${\mathrm{\Delta }}^0\simeq 2\pi ·129.35$ MHz (see text for the rest of parameters).

Figure 7

(a), (c), (e) Storage and (b), (d), (f) retrieval efficiency for the signal photon as a function of the nominal detuning used to produce the AFC for pulse number $N=10$ (red lines—crosses), $N=20$ (blue lines—plus signs), $N=30$ (yellow lines—circles), and $N=40$ (green lines—squares), and Rabi frequency (a), (b) ${\mathrm{\Omega }}_0=2\pi ·27.85$ MHz, (c), (d) ${\mathrm{\Omega }}_0=2\pi ·39.78$ MHz, and (e), (f) ${\mathrm{\Omega }}_0=2\pi ·51.72$ MHz. The rest of parameters are as in Fig. 5. The vertical dashed lines correspond to the values given by Eq. (B2) (a), (c), (e) and Eq. (16) (b), (d), (f).

Figure 8

Density plot of ${\rho }_{33}$ via STIRAP as a function of the atomic velocity $v$ and the ratio ${\mathrm{\Delta }}^0/{\mathrm{\Omega }}_0$. Note that the region in which the population is transfered to $\left|3\right.〉$, named optimal zone, is bounded by the curves ${\mathrm{V}}_{\mathrm{s},\mathrm{p}}^{\pm }$. The values for the frequencies, couplings, and decays are the same as in Fig. 4.

Figure 9

Modeling of the ${\rho }_{33}\left(\delta \right)$ profile for (a) STIRAP and (b) PAP with rectangles of the same area. We can reconstruct the rectangle of (a) by combining conveniently the ${\mathrm{N}}_{\mathrm{c}}$ peaks of the comb (b) as shown in (c). This allows us to relate the widths of the STIRAP and PAP peaks (see text).