Coherent control and storage of a microwave pulse in a one-dimensional array of artificial atoms using the Autler-Townes effect and electromagnetically induced transparency

In this paper we propose a scheme for coherent control and storage of a microwave pulse in superconducting circuits exploiting the idea of electromagnetically induced transparency (EIT) and the Aulter-Townes (AT) effect. We show that superconducting artificial atoms in a four-level tripod configuration act as EIT based coherent microwave $\left(\mu \mathrm{w}\right)$ memories with gain features, when they are attached to a one-dimensional transmission line. These atoms are allowed to interact with three microwave fields, such that there are two control fields and one probe field. Our proposed system works in such a way that one control field with large Rabi frequency when interacting with atoms, produces the AT effect. While the second control field with relatively small Rabi frequency produces EIT in one of the absorption windows produced due to the AT splitting for the weak probe field. The group velocity of the probe pulse reduces significantly through this EIT window. Interestingly, the output intensity of the probe pulse increases as we increase the number of artificial atoms. Our results show that the probe microwave pulse can be stored and retrieved with high fidelity.

Figure 1

Schematics for the system. (a) Here $n$ superconducting artificial atoms equally spaced with separation $L$ are attached to a one-dimensional transmission line. Total length of the linear array of atoms is $d$. Each atom has a tripod type configuration coupled to three microwave fields with Rabi frequencies ${\mathrm{\Omega }}_c$, ${\mathrm{\Omega }}_s$, and ${\mathrm{\Omega }}_p$. (b) Input and output field at the interface of a single atom.

Figure 2

Real and imaginary parts of ${\rho }_{03}$ as a function of ${\delta }_p$. $\text{Im}\left({\rho }_{03}\right)$ is shown for (i) ${\mathrm{\Omega }}_s=0$ (dashed curve) and (ii) ${\mathrm{\Omega }}_s=0.25{\mathrm{\Omega }}_c$ (solid curve). $\text{Re}\left({\rho }_{03}\right)$ is shown by the dotted curve, with ${\mathrm{\Omega }}_s=0.25{\mathrm{\Omega }}_c$. Other parameters are ${\gamma }_3=2\pi \times 55$ MHz, ${\mathrm{\Omega }}_c=1.5{\gamma }_3$, ${\mathrm{\Omega }}_p=0.01{\mathrm{\Omega }}_c$, ${\delta }_s=-0.5{\mathrm{\Omega }}_c$, ${\delta }_c=0$, ${\gamma }_0=0$, ${\gamma }_1=2\pi \times 1.7$ MHz, ${\gamma }_2=2\pi \times 6.9$ MHz, ${\rho }_{00}=0.4$, ${\rho }_{22}=0.6$, and ${\rho }_{33}=0$.

Figure 3

Transmission $T$ versus $\delta p$ for (i) $n=150$ (dashed curve) and (ii) $n=100$ (solid curve). For (i) and (ii) ${\mathrm{\Omega }}_c=1.5{\gamma }_3$, while for (iii) (dot-dashed curve) ${\mathrm{\Omega }}_c={\gamma }_3$ and $n=150$. All the other parameters are the same as in Fig. 2, with $L=1$ mm and ${\omega }_{30}=2\pi \times 10.5$ GHz.

Figure 4

Group velocity $v$ versus $n$ with (i) $L=1.5$ mm (solid curve). (ii) $L=1$ mm (dotted curve). (iii) $L=0.5$ mm (dashed curve). Other parameters are the same as in Fig. 2, with ${\omega }_{30}=2\pi \times 10.5$ GHz.

Figure 5

Window width $w$ versus $n$ with $L=1$ mm. Other parameters are the same as in Fig. 4.

Figure 6

Optical depth $\alpha$ versus $n$ for (i) $L=1.5$ mm (solid curve). (ii) $L=1$ mm (dot-dashed curve). (iii) $L=0.5$ mm (dashed curve). With ${\mathrm{\Omega }}_c=0$, ${\mathrm{\Omega }}_s=0$, ${\mathrm{\Omega }}_p=0.015{\gamma }_3$, ${\delta }_s=0$, ${\delta }_p=0$. Other parameters are the same as in Fig. 4.

Figure 7

Output intensity as function of ${\delta }_p$ and number of SAAs $n$ with $\sigma =15$ MHz and $\mu =-259$ MHz. Other parameters are the same as in Fig. 4.

Figure 8

Fidelity $F$ as a function of number of SAAs $n$. All other parameters are the same as in Fig. 7.