Propagation of coupled dark-state polaritons and storage of light in a tripod medium

We consider slow-light propagation in an atomic medium with a tripod level scheme. We show that the coexistence of two types of dark-state polaritons leads to the propagation dynamics, which is qualitatively different from that in a $\mathrm{\Lambda }$ medium, and allows therefore for very efficient conversion of signal photons into spin excitations. This efficiency is shown to be very close to 1 even for very long signal light pulses, which could not be entirely compressed into a $\mathrm{\Lambda }$ medium at a comparable strength of the control field.

Figure 1

Tripod scheme of atomic levels.

Figure 2

Efficiency $\eta$ of the conversion of the signal photons into spin excitations of the $\mathrm{{\rm Y}}$ type as a function of the retarded time $\tau$ for the boundary condition ${\mathrm{\Psi }}_0\left(\tau \right)={\mathrm{\Psi }}_{0\mathrm{A}}\{exp[-{(\tau -3{\tau }_{\mathrm{p}})}^2/{\tau }_{\mathrm{p}}^2]-exp[-{(\tau +3{\tau }_{\mathrm{p}})}^2/{\tau }_{\mathrm{p}}^2]\}$ for $\tau \ge 0$ ($|{\mathrm{\Psi }}_{0\mathrm{A}}{|}^2$ determines the pulse energy). Units on the axes are dimensionless, and the time $\tau$ is scaled to the characteristic time ${\tau }_{\mathrm{p}}$ of the pulse duration. $\beta =\pi /4$ for all plots. The detuning ${\nu }_0$ is (a) ${\nu }_0=1/{\tau }_p$, (b) $5/{\tau }_p$, and (c) $10/{\tau }_p$. On each panel the length $L$ of the medium is $1.0v_{\mathrm{g}}{\tau }_{\mathrm{p}}$ (solid line), $0.5v_{\mathrm{g}}{\tau }_{\mathrm{p}}$ (long-dashed line), $0.25v_{\mathrm{g}}{\tau }_{\mathrm{p}}$ (short-dashed line), and $0.1v_{\mathrm{g}}{\tau }_{\mathrm{p}}$ (dot-dashed line). The decrease of the dot-dashed line in (b) and (c) is very slow and can bee seen on a time scale $\tau /{\tau }_{\mathrm{p}}\sim {10}^2$.

Figure 3

The same as in Fig. 2, but for ${\mathrm{\Psi }}_0\left(\tau \right)={\mathrm{\Psi }}_{0\mathrm{A}}\{exp[-{(\tau -3{\tau }_{\mathrm{p}})}^2/{\tau }_{\mathrm{p}}^2]-exp[-{(\tau +3{\tau }_{\mathrm{p}})}^2/{\tau }_{\mathrm{p}}^2]\}exp\left(i{\nu }_0{cos}^2\beta \tau \right)$ for $\tau \ge 0$. The values of ${\nu }_0$ assigned to (a)–(c) and of $L$ assigned to the lines of different type as well as $\beta$ are the same as in the previous plot. Note that for a properly detuned signal pulse $\eta \approx 1$ can be attained.