Coupling between cw lasers and a frequency comb in dense atomic samples

We report on a detailed investigation of the coupling between a femtosecond-laser frequency comb and a cw diode laser interacting with an atomic medium of variable density. The comb is printed on a Doppler-broadened atomic transition and the frequency-dependent transmission of the cw laser is monitored as it is scanned over the inhomogenously broadened absorption profile. The printing process and its probing are analysed, experimentally and theoretically, as a function of both laser intensities and the atomic density. The results reveal the importance of optical pumping and power broadening by both lasers, allowing us to determine various regimes of competition between them.

1. Introduction
2. Experiment

1. Introduction

In the last decade, femtosecond (fs) lasers have been established as an essential tool for coherent control, highresolution spectroscopy and frequency measurements in general, with applications in the fields of biology, chemistry and physics [1–4]. In particular, the new sets of techniques built around the use of the recently developed frequency combs are remarkable for their simplicity [4], all of which may be classified into one of the following categories, according to the use of the fs frequency comb: (i) as a ruler to measure the frequency of a cw laser which interacts with an atomic transition; (ii) as a single direct probe of an atomic transition; and (iii) combined with a cw laser, both interacting with the atomic system. In the present paper we will be interested in the last two techniques, when the frequency comb directly excites the atomic samples. In this case, it is possible to combine the temporal, ultrafast aspect of femtosecond lasers with the spectral resolution of its frequency comb [5], pointing to the future merging of coherent control and high-resolution spectroscopic techniques [6, 7].

Direct excitation of samples by a frequency comb, however, requires a deeper understanding of the various processes responsible for the medium response to the pulseto- pulse phase change of the femtosecond laser. The study of dilute atomic samples is then essential to this approach, because it allows for a comparison between theory and experiment. Recent examples of such studies include the detailed treatment of the temporal-coherent-control technique in cascade atomic transitions [6, 8], the printing of femtosecond frequency combs in Doppler-broadened atomic vapours [9–13] and high-resolution optical frequency measurements in cold atomic samples [5, 7, 14]. Most of these works consider only the frequency comb exciting the atoms. More recently the idea of printing a population grating in the frequency domain has also been used to obtain high visibilities in the inhomogeneously broadened profile of rare earth ions in solid-state samples with the goal of obtaining multimode solid-state quantum memories [15].

On the other hand, [10–13] introduce a second, cw laser in the experiments in order to probe the action of the femtosecond laser over the various velocity groups of a room-temperature atomic vapour. These studies have revealed situations in which the cw laser has a role beyond that of a simple probe, as in the case where it induces the blurring of the frequency-comb impression in the Doppler profile [13]. Here, we report on a new study on the coupling between cw lasers and a frequency comb. We experimentally investigate this coupling process as a function of atomic density and both laser intensities. The theoretical analysis to model the experimental results reveals the existence of various regimes of competition between the two lasers, depending on their relative intensities and on the nature of the atomic transition (open or closed) excited by the cw laser.

For a better understanding of the physical situation exploited here we recall some of the basic characteristics of the interaction of a mode-locked femtosecond laser with an atomic system. This laser delivers a pulse train which has a repetition rate of the order of 100 MHz, corresponding to a pulse-to-pulse temporal separation of tens of ns. The relaxation rate of the atomic medium occurs on a longer time scale. Therefore, the first pulse creates a polarization in the atomic medium which lasts enough to interact with the next pulse. Depending on the relative phase between the medium polarization and the following pulses, interference between them will determine how the atoms are excited. This process leads to an excited state population distributed over the different frequencies within the Doppler profile, and is what we denote as coherent accumulation [6, 9]. We can also understand this process as a kind of Ramsey fringe formation process, with the difference that multiple pulses are responsible for imprinting the frequency comb on the Doppler profile. A classic review on this topic is found in [16], which also dealswith two-photon absorption processes. To the lowest order in the diode-laser intensity, this second laser will simply probe the frequency comb imprinted on the atomic medium. As the diode-laser intensity is increased, however, its role in the atomic excitation process becomes important.

In the following, we introduce our experimental setup in section 2 together with the central experimental results. In section 3 we present our model for the experiments of section 2. The goal is to explain the results with the simplest possible model: one that considers the interaction of the two lasers with an ensemble of four-level atoms. We use this model to interpret the blurring of the printed comb as a result of power broadening of the atomic transition by the cw laser. We show that the various velocity groups of atoms are still sensitive to the femtosecond-laser frequency comb, even for high cw-laser powers, but the Stark shift of the atomic transitions by the cw laser displaces the position of the comb teeth in the Doppler profile, around the cw-laser frequency. We also showthat open or closed transitions have considerably different behaviours as the cw power is increased, which explains the distortions observed in the comb impressed in the Doppler profile as the atomic density is altered. Finally, in section 4 we present our conclusions.