Anomalous Rabi Oscillations in Multilevel Quantum Systems

We show that the excitation probability of a state within a manifold of levels undergoes Rabi oscillations with the frequency determined by the energy difference between the states and not by the pulse area, for sufficiently strong pulses. The population and coherence remains in the two-level subsystem formed by the initial and target state even at Rabi frequencies exceeding the energy difference. The observed dynamics can be useful in nonlinear spectroscopy and quantum state preparation.

Figure 1

Tripod system in symmetric (a) and asymmetric (c) configurations and their respective dressed states (b) and (d); $t_c=5{\tau }_0$, $\delta {\tau }_0=5$, ${\mathrm{\Omega }}_0{\tau }_0=18$. The thicker blue and red lines correspond to the populated dressed states.

Figure 2

Coherent population transfer to the target state in the symmetric (a) and asymmetric (c) tripod schemes, as a function of the pulse area, for $\delta {\tau }_0=5$. The red dotted line represents the analytical results (neglecting nonadiabatic couplings) and the black solid line represents the numerical solution of the TDSE. (b), (d) The target population at final time $T$ as a function of both pulse area $S_0$ and splitting $\delta$.

Figure 3

Target population at final time as a function of the pulse area (left column) and the corresponding dressed states for ${\mathrm{\Omega }}_0{\tau }_0=10$ (right column) in a system of two coupled five-level ladders with $\delta {\tau }_0=5$. (a), (b) We start and end in the middle of the ladder ($M=M^{\prime }=0$). (c), (d) We start in the middle and end at the lowest level of the ladder ($M^{\prime }=-2$). (e), (f) The target ladder has a different energy splitting (${\delta }^{\prime }=4$). The populated dressed states are always shown with thicker blue lines.

Figure 4

(a) Electronic excited state populations $P_e$ (dashed lines) for two different target vibrational states $v^{\prime }=1$ and $v^{\prime }=4$ of the excited electronic state of ${\mathrm{Na}}_2$, as a function of the pulse amplitude; population of vibrational state $v^{\prime }=1$ of the excited electronic state (solid line). (b) Population dynamics for the electronic transition $v=0$ to $v^{\prime }=1$ using $E_0=0.0045$ a.u. The solid lines are the populations in the initial and target vibrational states, while the dashed lines are the electronic populations $P_g$ and $P_e$.