Control of Four-Level Quantum Coherence via Discrete Spectral Shaping of an Optical Frequency Comb

We present experiments demonstrating high-resolution and wide-bandwidth coherent control of a four-level atomic system in a diamond configuration. A femtosecond frequency comb is used to excite a specific pair of two-photon transitions in cold ${}^{87}\mathrm{Rb}$. The optical-phase-sensitive response of the closed-loop diamond system is studied by controlling the phase of the comb modes with a pulse shaper. Finally, the pulse shape is optimized resulting in a 256% increase in the two-photon transition rate by forcing constructive interference between the mode pairs detuned from an intermediate resonance.

Figure 1

(a) Energy level diagram of the diamond configuration in ${}^{87}\mathrm{Rb}$, the arrows indicate the resonant comb modes. (b) Pulse spectrum and phase mask used for the first experiment. The hatched region in the spectrum and the inset energy level diagram indicates the portion of the spectrum to which the phase mask is applied. The arrows indicate resonant wavelengths in relation to the phase mask.

Figure 2

(a) Measured interference fringes with fits under four different excitation conditions. All the results are obtained by scanning the phase $\Phi$ of the phase mask shown in Fig. 1b. The top panels correspond to illuminating the atoms from only one direction (traveling waves). The bottom panels are under counter-propagating pulse excitation. The left panels (a) and (c) use the $f_r$ for excitation from the $5S_{1/2}F=2$ ground state; the right panels (b) and (d) use the $f_r$ for excitation from the $5S_{1/2}F=1$ ground state.

Figure 3

(a) Measured signal enhancement. The ratio of signals with and without the phase mask in (b), versus position of the SLM in the spectrum. The zero of the offset frequency is chosen to be the position of the maximum signal increase. (b) The applied phase mask is indicated by the hatched region. Exactly $\pi$ radians of phase is applied just below 762 and 776 nm to add an extra phase shift to those mode pairs that join in the hatched region.