Diffusion effects in gradient echo memory

We study the effects of diffusion on a $\Lambda$-gradient echo memory, which is a coherent optical quantum memory, using thermal gases. The efficiency of this memory is high for short storage time, but decreases exponentially due to decoherence as the storage time is increased. We study the effects of both longitudinal and transverse diffusion in this memory system, and give both analytical and numerical results that are in good agreement. Our results show that diffusion has a significant effect on the efficiency. Further, we suggest ways to reduce these effects to improve storage efficiency. We also report on a mechanism by which the rate of expansion of the transverse width of the beam is reduced compared to the naive expectation of diffusive effects, as observed in recent experiments.

Figure 1

Level structure of $\Lambda$-type three-level atom.

Figure 2

The efficiency decay with respect to the dimensionless parameter ${\tau }_W$ for longitude diffusion during the write-in time; the points are numerical results, and the curve is Eq. (14).

Figure 3

The efficiency decay with respect to the dimensionless parameter ${\tau }_H$ for longitude diffusion during hold time; the points are numerical results, and the curve is Eq. (17).

Figure 4

Efficiency decay with respect to ${\tau }_{\perp }$ for transverse diffusion; the points are numerical results, and the curve is Eq. (21).

Figure 5

(a) The gradient is turned off during hold time and flipped for read-out. (b) An illustration of the spatial frequency for ${\sigma }_{12}(z,t)$, $k$ decreases or increases depending on the sign of the gradient.

Figure 6

Numerical results of $|{\sigma }_{12}(k,t)|$ with write-in gradient ${\eta }^{\prime }<0$.

Figure 7

The extra phase $\theta$ for control field with Gaussian profile. Points are numerical results using typical parameters given in the main text, and the curve is the approximate expression in Eq. (32).

Figure 8

The intensity distribution for the read-out signal with $t_H=16$ $\mu$s. To see the expansion clearly, we have renormalized the maximum of $I\left(r_{\perp }\right)$ to 1, and $I_0$ is the renormalized intensity distribution. The black solid curve is the input signal, the dotted one (blue online) is the read-out signal for the homogeneous control field, and the dashed one (red online) is the read-out signal for the control field with Gaussian profile.

Figure 9

Expansion of the read-out signal. Circles are numerical results for the homogeneous control field. Squares are numerical results for the control field with a Gaussian profile, and the solid line is Eq. (31) for the homogeneous control field.