Coherent Population Oscillation-Based Light Storage

We theoretically study the propagation and storage of a classical field in a $\mathrm{\Lambda }$-type atomic medium using coherent population oscillations (CPOs). We show that the propagation eigenmodes strongly relate to the different CPO modes of the system. Light storage in such modes is discussed by introducing a “populariton” quantity, a mixture of populations and field, by analogy to the dark state polariton used in the context of electromagnetically induced transparency light storage protocol. As experimentally shown, this memory relies on populations and is then—by contrast with usual Raman coherence optical storage protocols—robust to dephasing effects.

Figure 1

(a) The $\mathrm{\Lambda }$ system of interest. The two circularly polarized transitions are characterized by the same population (optical coherence) decay rate ${\mathrm{\Gamma }}_0/2$ ($\mathrm{\Gamma }$). Atomic thermal motion of results in a transit-population loss of rate ${\gamma }_t(\ll {\mathrm{\Gamma }}_0,\mathrm{\Gamma })$ for the three states, while the two ground states are fed with the same rate ${\gamma }_t/2$. The system is coupled to the coherent superposition of two linearly polarized fields, respectively, along $\{{\mathbf{e}}_{\parallel },\mathbf{u}\}$. A magnetic field $\mathbf{B}$ Zeeman shifts the two ground states by $2{\mathrm{\Delta }}_z$. (b) The incident fields propagate along $z$ in the medium. Atoms in the cell interact with the fields within a volume represented in light color, symbolizing the spatial extension of the beams. (c) Spectrum of the resonant driving field (${\omega }_0$) and an example of detuned signal field at (${\omega }_0+\delta$). The spectrum of the signal is assumed to be contained within the saturation-broadened linewidth of the CPO resonance, limited by dashed vertical lines. In that case, an idler field at (${\omega }_0-\delta$) is generated along propagation.

Figure 2

Group velocities (a) and transmission coefficients (b) of the eigenquadratures as functions of the saturation parameter $s$, for He* parameters taken from [9]. The inset shows the ${\beta }_{\mathrm{\Delta },\mathrm{\Sigma }}$ parameters as functions of $s$. The quadratures $P^{\perp }$ and $Q^{\parallel }$—which do not explicitly couple to the CPO modes—always experience absorption and propagate at a supraluminal group velocity. By contrast, the quadrature $Q^{\perp }$ ($P^{\parallel }$) which couples to the antisymmetric (symmetric) CPO mode experiences a strongly reduced group velocity and amplification in the regime $3{\gamma }_t/{\mathrm{\Gamma }}_0\sim 0.01<s<100$ ($1<s<100$). Above, the signal cannot interact with the over-saturated atomic system. Below, the states’ decay (${\beta }_{\mathrm{\Sigma },\mathrm{\Delta }}\simeq 0$) does not allow for CPO.

Figure 3

Storage sequence. The input signal field—here at frequency ${\omega }_0$—couples to the population difference via $Q^{\perp }$. Renormalized amplitudes of the signal and driving fields at the entrance (a) and the exit (b) of the cell, and population difference (c) at the exit of the cell, as functions of time. During the writing step, the driving field is on, while the signal slowly increases with a rising exponential shape. The shape of the signal is imprinted on the population difference. Although the group velocity is strongly reduced, one observes a leakage of the signal, which was amplified in the cell. Suddenly, the fields are switched off and the storage starts. During this period, the generated population difference decays at rate ${\gamma }_t$. After a $2\mu \mathrm{s}$ storage time, the driving field is switched on again and a retrieval pulse of signal exits the cell.