Carrier-Envelope Phase Effect on Atomic Excitation by Few-Cycle rf Pulses

We present an experimental and theoretical study of the carrier-envelope phase effects on population transfer between two bound atomic states interacting with intense ultrashort pulses. Radio frequency pulses are used to transfer population among the ground state hyperfine levels in rubidium atoms. These pulses are only a few cycles in duration and have Rabi frequencies of the order of the carrier frequency. The phase difference between the carrier and the envelope of the pulses has a significant effect on the excitation of atomic coherence and population transfer. We provide a theoretical description of this phenomenon using density matrix equations. We discuss the implications and possible applications of our results.

Figure 1

A few-cycle rf pulse with different carrier-envelope phases: (a) $\phi =0$; (b) $\phi =\pi /2$. Panel (c) shows a two-level system. Panel (d) shows the population of $|c⟩$ excited by cosine ($\phi =0$) and sine ($\phi =\pi /2$) pulses.

Figure 2

The upper block shows a diagram of the relevant energy levels and the geometry of the Rb cell and the applied fields. The lower block shows the time sequence of the laser pulses and the rf pulses.

Figure 3

The population of the upper Zeeman sublevels excited by cosine (a) and sine (b) rf pulses with different pulse durations ranging from 28 to $20\mu \mathrm{s}$. Corresponding theoretical simulations are shown in (c) and (d).

Figure 4

Excited state population versus CEP: Experiment (left), simulation (right).