Quantum control of population transfer between vibrational states in an optical lattice

We study quantum control techniques, specifically Adiabatic Rapid Passage (ARP) and Gradient Ascent Pulse Engineering (GRAPE), for transferring atoms trapped in an optical lattice between different vibrational states. We compare them with each other and with previously studied coupling schemes in terms of performance. In our study of ARP, we realize control of the vibrational states by tuning the frequency of a spatial modulation through the inhomogeneously broadened vibrational absorption spectrum. We show that due to the presence of multiple crossings, the population transfer depends on the direction of the frequency sweep, in contrast to traditional ARP. In a second study, we control these states by applying a pulse sequence involving both the displacement of the optical lattice and modulation of the lattice depth. This pulse is engineered via the GRAPE algorithm to maximize the number of atoms transferred from the initial (ground) state to the first excited state. We find that the ARP and the GRAPE techniques are superior to the previously tested techniques at transferring population into the first excited state from the ground state: $38.9\pm0.2\%$ and $39\pm2\%$ respectively. GRAPE outperforms ARP in leaving the higher excited states unpopulated (less than $3.3\%$ of the ground state population, at $84\%$ confidence level), while $18.7\pm0.3\%$ of the ground state population is transferred into higher excited states by using ARP. On the other hand, ARP creates a normalized population inversion of $0.21\pm0.02$, which is the highest obtained by any of the control techniques we have investigated.