Quantum-state storage and processing for polarization qubits in an inhomogeneously broadened $\Lambda$-type three-level medium

We address the propagation of a single-photon pulse with two polarization components, i.e., a polarization qubit, in an inhomogeneously broadened “phaseonium” $\Lambda$-type three-level medium. We combine some of the nontrivial propagation effects characteristic for this kind of coherently prepared systems and the controlled reversible inhomogeneous broadening technique to propose several quantum information-processing applications, such as a protocol for polarization qubit filtering and sieving as well as a tunable polarization beam splitter. Moreover, we show that by imposing a spatial variation of the atomic coherence phase, an efficient quantum memory for the incident polarization qubit can be also implemented in $\Lambda$-type three-level systems.

Figure 1

(a) Physical system under investigation: a single pulse with central frequency ${\omega }_0$ and two circular polarization components enters a medium with transverse inhomogeneous broadening. (b) Scheme of the $\Lambda$-type interaction between the single-pulse polarization components and the three-level atoms of the phaseonium medium. ${\Omega }_{13}$ and ${\Omega }_{23}$ are the Rabi frequencies of the corresponding interaction and $\Delta$ is the two-photon detuning.

Figure 2

Normalized intensities of the single-pulse polarization components (see text for definition) coupled with the $|1\rangle -|3\rangle$ (black lines) and $|2\rangle -|3\rangle$ (gray lines) optical transitions as a function of the optical distance $\alpha z$. The solid lines correspond to the propagation of the incident field, while the dashed lines correspond to the backward-retrieved components. The initial prepared state of the phaseonium medium is ${\sigma }_{11}=0.6$, ${\sigma }_{22}=0.4$, ${\phi }_{12}=\pi /3$, whereas the field components are initially weighed as $I_{13}^{\mathrm{in}}(0,t_c)=0.9$ and $I_{23}^{\mathrm{in}}(0,t_c)=0.1$, with the relative phase between them being ${\phi }_{13}\left(0\right)-{\phi }_{23}\left(0\right)=0$.

Figure 3

Normalized intensities of the single-pulse polarization components (see text for definition) $|{\Omega }_{13}{|}^2$ (black line) and $|{\Omega }_{23}{|}^2$ (gray line) as a function of the optical distance $\alpha z$. The solid lines correspond to the incident field while the dashed lines correspond to the backward-retrieved components. Initially $\Lambda$-type three-level atoms of phaseonium are prepared in state ${\sigma }_{11}={\sigma }_{22}=0.5$ with a phase gradient given by $\theta =3\pi$. The field components are initially weighed as $I_{13}^{\mathrm{in}}(0,t_c)=0.9$, $I_{23}^{\mathrm{in}}(0,t_c)=0.1$ and the relative phase between them is ${\phi }_{13}\left(0\right)-{\phi }_{23}\left(0\right)=0$, both for the forward input and the backward output.

Figure 4

Normalized intensities of the single-pulse polarization components coupled with the $|1\rangle -|3\rangle$ (black symbols) and $|2\rangle -|3\rangle$ (gray symbols) optical transitions as a function of the optical distance $\alpha z$ after numerical integration of the full optical Bloch equations (1) and (5). The crosses correspond to the propagation of the incident field, while the circles correspond to the backward-retrieved components. The parameters are the same as in Fig. 3.