Improvement of the stabilization loops performances of a DF-VECSEL dedicated to cesium CPT clocks application by fully-correlated multi-mode pumping

It was shown that cesium double transitions could be used to obtain very high contrast Ramsey fringes [1]. Such a scheme needs to uses lin-lin configuration, where two linear and orthogonal laser beams couple the atomic transitions, with a frequency detuning equal to the level splitting. The frequency difference should be very stable, and one solution is to use a dual-frequency vertical external cavity surface emitting lasers (DF-VECSEL) such as the one shown in Fig.1. A birefringent crystal in the cavity allows to emit slightly detuned orthogonal polarisations with a very stable frequency difference, which is targeted to be limited by the Dick effect [2]. However, in this reference, the laser noise contribution to the Allan standard deviation is dominant : the relative intensity noise (RIN) level of -115 dB/Hz technically limits the clock stability to σ_y (τ) = 1.6 × 10^-12 · τ^-1/2 while state-of-the-art atomic clocks based on CPT give σ_y (τ) = 3.2 × 10^-13 · τ^-1/2 [3]. The beatnote noise depends on the coupling and the noise correlations between the two pump spots used for both polarisations (see Fig.1). However, a reduction of both the phase noise of the RF beatnote and the pump-to-laser RIN transfer was recently demonstrated [4]. It requires both a strong in-phase correlation of the pump noises and a low coupling strength, which can be obtained with a fully-correlated multi-mode pumping architecture [5]. In the present work, we investigate the consequences of such a scheme on the laser stabilization loops performances both experimentally and theoretically.