Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

Figure 1

Nonlinear stimulated Raman exact passage with resonance locking, for $\epsilon =0.2$ and $\eta =0.96$. Top: Evolution of the populations. Middle: Stokes (blue) and pump (red) Rabi frequencies, determined by the inverse engineering. For the corresponding linear system, the pump frequency is shown as a dashed line (the Stokes frequency remains unchanged). Bottom: Stokes (blue) and pump (red) detunings determined to compensate the Kerr nonlinearities of a gas of ${}^{87}\mathrm{Rb}$ atoms (using $T=3.1\times {10}^{-5}\mathrm{s}$).

Figure 2

Robustness of the nonlinear Raman exact passage with respect to the delay between the pulses and to the pump (normalized) peak, with (right) and without (left) Kerr nonlinearities compensation (see text) for a fixed Stokes (normalized) peak $S_{\max }T=3$ and for various ratios $S_{\max }/\mathrm{\Lambda }$. The white star points to the exact solution of the inverse engineering, depicted in Fig. 1.