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We develop a light-matter interface enabling strong and uniform couplingbetween a chain of cold atoms and photons of an optical cavity. This interfaceis a fiber Fabry-Perot cavity, doubly resonant for both the wavelength of theatomic transition and for a geometrically commensurate red-detuned intracavitytrapping lattice. Fulfilling the condition of a strong and uniform atom-photoncoupling requires optimization of the spatial overlap between the two standingwaves in the cavity. In a strong-coupling cavity, where the mode waists andRayleigh range are small, we derive the expression of the optimal trappingwavelength taking into account the Gouy phase. The main parameter controllingthe overlap of the standing waves is the relative phase shift at the reflectionon the cavity mirrors between the two wavelengths, for which we derive theoptimal value. We have built a microcavity optimized according to theseresults, employing custom-made mirrors with engineered reflection phase forboth wavelengths. We present a method to measure with high precision therelative phase shift at reflection, which allows us to determine the spatialoverlap of the two modes in this cavity.

Overlapping two standing-waves in a microcavity for a multi-atom photon interface